Alternating minimization algorithms for transmission tomography

Estimation of Proton Stopping Power Ratio and Mean Excitation Energy Using Electron Density and Its Applications via Machine Learning Approach

Purpose

The purpose of this study was to develop a simple flexible method for accurate estimation of stopping power ratio (SPR) and mean excitation energy (I) using relative electron density (ρ e).

Materials and Methods

The model was formulated using empirical relationships between SPR, mean excitation energy I, and relative electron density. Some examples were implemented, and a comparison was carried out using other existing methods. The needed coefficients in the model were estimated using optimization tools. Basis vector method (BVM) and Hunemohr and Saito (H-S) method were applied to estimate the ρ e used in the application section. 80 kVp and 150 kVpSn were used as low and high energy, respectively, for the implementation of dual-energy methods.

Results

All the examples of the proposed method considered have modeling error that is ≤0.32% and testing root mean square error (RMSE) ≤0.92% for SPR with a mean error close to 0.00%. The method was able to achieve modeling RMSE of 2.12% for mean excitation energy with room for improvement. Similar or better results were achieved in application to BVM.

Conclusion

The method showed robustness in application by achieving lower testing error than other presented methods in most cases. It achieved accurate estimation which can be improved using the machine learning algorithm since it is flexible to implement in terms of the function (model) degree and tissue classification.

Report on the AAPM deep-learning spectral CT Grand Challenge

BACKGROUND

This Special Report summarizes the 2022 AAPM Grand Challenge on Deep-Learning spectral Computed Tomography (DL-spectral CT) image reconstruction.

PURPOSE

The purpose of the challenge is to develop the most accurate image reconstruction algorithm possible for solving the inverse problem associated with a fast kilovolt switching dual-energy CT scan using a three tissue-map decomposition. Participants could choose to use a deep-learning (DL), iterative, or a hybrid approach.

METHODS

The challenge is based on a 2D breast CT simulation, where the simulated breast phantom consists of three tissue maps: adipose, fibroglandular, and calcification distributions. The phantom specification is stochastic so that multiple realizations can be generated for DL approaches. A dual-energy scan is simulated where the x-ray source potential of successive views alternates between 50 and 80 kilovolts (kV). A total of 512 views are generated, yielding 256 views for each source voltage. We generate 50 and 80 kV images by use of filtered back-projection (FBP) on negative logarithm processed transmission data. For participants who develop a DL approach, 1000 cases are available. Each case consists of the three 512 × 512 tissue maps, 50 and 80-kV transmission data sets and their corresponding FBP images. The goal of the DL network would then be to predict the material maps from either the transmission data, FBP images, or a combination of the two. For participants developing a physics-based approach, all of the required modeling parameters are made available: geometry, spectra, and tissue attenuation curves. The provided information also allows for hybrid approaches where physics is exploited as well as information about the scanned object derived from the 1000 training cases. Final testing is performed by computation of root-mean-square error (RMSE) for predictions on the tissue maps from 100 new cases.

RESULTS

Test phase submission were received from 18 research groups. Of the 18 submissions, 17 were results obtained with algorithms that involved DL. Only the second place finishing team developed a physics-based image reconstruction algorithm. Both the winning and second place teams had highly accurate results where the RMSE was nearly zero to single floating point precision. Results from the top 10 also achieved a high degree of accuracy; and as a result, this special report outlines the methodology developed by each of these groups.

CONCLUSIONS

The DL-spectral CT challenge successfully established a forum for developing image reconstruction algorithms that address an important inverse problem relevant for spectral CT.

Deep Filtered Back Projection for CT Reconstruction

Filtered back projection (FBP) is a classic analytical algorithm for computed tomography (CT) reconstruction, with high computational efficiency. However, images reconstructed by FBP often suffer from excessive noise and artifacts. The original FBP algorithm uses a window function to smooth signals and a linear interpolation to estimate projection values at un-sampled locations. In this study, we propose a novel framework named DeepFBP in which an optimized filter and an optimized nonlinear interpolation operator are learned with neural networks. Specifically, the learned filter can be considered as the product of an optimized window function and the ramp filter, and the learned interpolation can be considered as an optimized way to utilize projection information of nearby locations through nonlinear combination. The proposed method remains the high computational efficiency of the original FBP and achieves much better reconstruction quality at different noise levels. It also outperforms the TV-based statistical iterative algorithm, with computational time being reduced in an order of two, and state-of-the-art post-processing deep learning methods that have deeper and more complicated network structures.

MB-DECTNet: a model-based unrolling network for accurate 3D dual-energy CT reconstruction from clinically acquired helical scans

Objective.Over the past several decades, dual-energy CT (DECT) imaging has seen significant advancements due to its ability to distinguish between materials. DECT statistical iterative reconstruction (SIR) has exhibited potential for noise reduction and enhanced accuracy. However, its slow convergence and substantial computational demands render the elapsed time for 3D DECT SIR often clinically unacceptable. The objective of this study is to accelerate 3D DECT SIR while maintaining subpercentage or near-subpercentage accuracy.Approach.We incorporate DECT SIR into a deep-learning model-based unrolling network for 3D DECT reconstruction (MB-DECTNet), which can be trained end-to-end. This deep learning-based approach is designed to learn shortcuts between initial conditions and the stationary points of iterative algorithms while preserving the unbiased estimation property of model-based algorithms. MB-DECTNet comprises multiple stacked update blocks, each containing a data consistency layer (DC) and a spatial mixer layer, with the DC layer functioning as a one-step update from any traditional iterative algorithm.Main results.The quantitative results indicate that our proposed MB-DECTNet surpasses both the traditional image-domain technique (MB-DECTNet reduces average bias by a factor of 10) and a pure deep learning method (MB-DECTNet reduces average bias by a factor of 8.8), offering the potential for accurate attenuation coefficient estimation, akin to traditional statistical algorithms, but with considerably reduced computational costs. This approach achieves 0.13% bias and 1.92% mean absolute error and reconstructs a full image of a head in less than 12 min. Additionally, we show that the MB-DECTNet output can serve as an initializer for DECT SIR, leading to further improvements in results.Significance.This study presents a model-based deep unrolling network for accurate 3D DECT reconstruction, achieving subpercentage error in estimating virtual monoenergetic images for a full head at 60 and 150 keV in 30 min, representing a 40-fold speedup compared to traditional approaches. These findings have significant implications for accelerating DECT SIR and making it more clinically feasible.

Motion-compensated scheme for sequential scanned statistical iterative dual-energy CT reconstruction

Objective.Dual-energy computed tomography (DECT) has been widely used to reconstruct numerous types of images due its ability to better discriminate tissue properties. Sequential scanning is a popular dual-energy data acquisition method as it requires no specialized hardware. However, patient motion between two sequential scans may lead to severe motion artifacts in DECT statistical iterative reconstructions (SIR) images. The objective is to reduce the motion artifacts in such reconstructions.Approach.We propose a motion-compensation scheme that incorporates a deformation vector field into any DECT SIR. The deformation vector field is estimated via the multi-modality symmetric deformable registration method. The precalculated registration mapping and its inverse or adjoint are then embedded into each iteration of the iterative DECT algorithm.Main results.Results from a simulated and clinical case show that the proposed framework is capable of reducing motion artifacts in DECT SIRs. Percentage mean square errors in regions of interest in the simulated and clinical cases were reduced from 4.6% to 0.5% and 6.8% to 0.8%, respectively. A perturbation analysis was then performed to determine errors in approximating the continuous deformation by using the deformation field and interpolation. Our findings show that errors in our method are mostly propagated through the target image and amplified by the inverse matrix of the combination of the Fisher information and Hessian of the penalty term.Significance.We have proposed a novel motion-compensation scheme to incorporate a 3D registration method into the joint statistical iterative DECT algorithm in order to reduce motion artifacts caused by inter-scan motion, and successfully demonstrate that interscan motion corrections can be integrated into the DECT SIR process, enabling accurate imaging of radiological quantities on conventional SECT scanners, without significant loss of either computational efficiency or accuracy.

Deep learning method for reducing metal artifacts in dental cone-beam CT using supplementary information from intra-oral scan

Objective. Recently, dental cone-beam computed tomography (CBCT) methods have been improved to significantly reduce radiation dose while maintaining image resolution with minimal equipment cost. In low-dose CBCT environments, metallic inserts such as implants, crowns, and dental fillings cause severe artifacts, which result in a significant loss of morphological structures of teeth in reconstructed images. Such metal artifacts prevent accurate 3D bone-teeth-jaw modeling for diagnosis and treatment planning. However, the performance of existing metal artifact reduction (MAR) methods in handling the loss of the morphological structures of teeth in reconstructed CT images remains relatively limited. In this study, we developed an innovative MAR method to achieve optimal restoration of anatomical details. Approach. The proposed MAR approach is based on a two-stage deep learning-based method. In the first stage, we employ a deep learning network that utilizes intra-oral scan data as side-inputs and performs multi-task learning of auxiliary tooth segmentation. The network is designed to improve the learning ability of capturing teeth-related features effectively while mitigating metal artifacts. In the second stage, a 3D bone-teeth-jaw model is constructed with weighted thresholding, where the weighting region is determined depending on the geometry of the intra-oral scan data. Main results. The results of numerical simulations and clinical experiments are presented to demonstrate the feasibility of the proposed approach. Significance. We propose for the first time a MAR method using radiation-free intra-oral scan data as supplemental information on the tooth morphological structures of teeth, which is designed to perform accurate 3D bone-teeth-jaw modeling in low-dose CBCT environments.

A fidelity-embedded learning for metal artifact reduction in dental CBCT

PURPOSE

Dental cone-beam computed tomography (CBCT) has been increasingly used for dental and maxillofacial imaging. However, the presence of metallic inserts, such as implants, crowns, and dental braces, violates the CT model assumption, which leads to severe metal artifacts in the reconstructed CBCT image, resulting in the degradation of diagnostic performance. In this study, we used deep learning to reduce metal artifacts.

METHODS

The metal artifacts, appearing as streaks and shadows, are non-local and highly associated with various factors, including the geometry of metallic inserts, energy-dependent attenuation, and energy spectrum of the incident X-ray beam, making it difficult to learn their complicated structures directly. To provide a step-by-step environment in which deep learning can be trained, we propose an iterative learning approach in which the network at each iteration step learns the correction error caused by the previous network, while enforcing the data fidelity in the projection domain. To generate a realistic paired training dataset, metal-free CBCT scans were collected from patients without metallic inserts, and then simulated metal projection data were added to generate the corresponding metal-corrupted projection data.

RESULTS

The feasibility of the proposed method was investigated in clinical metal-affected CBCT scans, as well as simulated metal-affected CBCT scans. The results show that the proposed method significantly reduces metal artifacts while preserving the morphological structures near metallic objects and outperforms direct image domain learning.

CONCLUSION

The proposed fidelity-embedded learning can effectively reduce metal artifacts in dental CBCT compared with direct image domain learning. This article is protected by copyright. All rights reserved.

A Detailed Hydrodynamic Study of the Split-Plate Airlift Reactor by Using Non-Invasive Gamma-Ray Techniques

This study focused on detailed investigations of selected local hydrodynamics in split airlift reactor by using an unconventional measurements facility: computed tomography (CT) and radioactive particle tracking (RPT). The local distribution in a cross-sectional manner with its radial’s profiles for gas holdup, liquid velocity flow field, shear stresses, and turbulent kinetic energy were studied under various gas velocity 1, 2 and 3 cm/s with various six axial level z = 12, 20, 40, 60, 90 and 112 cm. The distribution in gas–liquid phases in the whole split reactor column, the riser and downcomer sides, including their behavior at the top and bottom sections of the split plate was also described. The outcomes of this study displayed an exemplary gas–liquid phases dispersion approximately in all reactor’s zones and had large magnitude over the ring of the sparger as well as upper the split plate. Furthermore, the outcomes pointed out that the distribution of this flow may significantly impacts the performance of the split reactor, which may have essential influence on its performance particularly for microorganisms culturing applications. These outcomes are dependable as benchmark information to validate computational fluid dynamics (CFD) simulations and other models.

Towards sub-percentage uncertainty proton stopping-power mapping via dual-energy CT: direct experimental validation and uncertainty analysis of a statistical iterative image reconstruction method

PURPOSE

To assess the potential of a joint dual-energy CT reconstruction process (Statistical Image Reconstruction method built on a Basis Vector Model (JSIR-BVM)) implemented on a 16-slice commercial CT scanner to measure high spatial-resolution stopping-power ratio (SPR) maps with uncertainties of less than 1%.

METHODS

JSIR-BVM was used to reconstruct images of effective electron density and mean excitation energy from dual-energy CT (DECT) sinograms for ten high-purity samples of known density and atomic composition inserted into head and body phantoms. The measured DECT data consisted of 90 kVp and 140 kVp axial sinograms serially acquired on a Philips Brilliance Big Bore CT scanner without beam-hardening corrections. The corresponding SPRs were subsequently measured directly via ion chamber measurements on a MEVION S250 superconducting synchrocyclotron and evaluated theoretically from the known sample compositions and densities. Deviations of JSIR-BVM SPR values from their theoretically calculated and directly measured ground-truth values were evaluated for our JSIR-BVM method and for our implementation of the Hünemohr-Saito (H-S) DECT image-domain decomposition technique for SPR imaging. A thorough uncertainty analysis was then performed for 5 different scenarios (comparison of JSIR-BVM SPR/SP to International Commission on Radiation Measurements and Units (ICRU) benchmarks; comparison of JSIR-BVM SPR to measured benchmarks; and uncertainties in JSIR-BVM SPR/SP maps for patients of unknown composition) per the Joint Committee for Guides in Metrology (JCGM) and the Guide to expression of Uncertainty in Measurement (GUM), including the impact of uncertainties in measured photon spectra, sample composition and density, photon cross-section and I-value models, and random measurement uncertainty. Estimated SPR uncertainty for three main tissue groups in patients of unknown composition and the weighted proportion of each tissue type for three proton treatment sites were then used to derive a composite range uncertainty for our method.

RESULTS

Mean JSIR-BVM SPR estimates deviated by less than 1% from their theoretical and directly measured ground-truth values for most inserts and phantom geometries except for high density Delrin and Teflon samples with SPR error relative to proton measurements of 1.1% and -1.0% (Head Phantom) and 1.1% and -1.1% (Body Phantom). The overall RMS deviations over all samples were 0.39% and 0.52% (head phantom) and 0.43% and 0.57% (body phantom) relative to theoretical and directly measured ground-truth SPRs, respectively. The corresponding RMS (maximum) errors for the image-domain decomposition method were 2.68% and 2.73% (4.68% and 4.99%) for the head phantom and 0.71% and 0.87% (1.37% and 1.66%) for the body phantom. Compared to H-S SPR maps, JSIR-BVM yielded 30% sharper and two-fold sharper images for soft tissues and bone-like surrogates, respectively, while reducing noise by factors of 6 and 3, respectively. The uncertainty (coverage factor k = 1) of the DECT-to-benchmark values comparison ranged from 0.5% to 1.5% and is dominated by scanning-beam photon-spectra uncertainties. An analysis of the SPR uncertainty for patients of unknown composition showed a JSIR-BVM uncertainty of 0.65%, 1.21%, and 0.77% for soft-, lung-, and bony-tissue groups which led to a composite range uncertainty of 0.6%-0.9%.

CONCLUSIONS

Observed JSIR-BVM SPR estimation errors were all less than 50% of the estimated k = 1 total uncertainty of our benchmarking experiment, demonstrating that JSIR-BVM high spatial-resolution, low-noise SPR mapping is feasible and is robust to variations in the geometry of the scanned object. In contrast, the much larger H-S SPR estimation errors are dominated by imaging noise and residual beam-hardening artifacts. While the uncertainties characteristic of our current JSIR-BVM implementation can be as large as 1.5%, achieving <1% total uncertainty is feasible by improving the accuracy of scanner-specific scatter-profile and photon-spectrum estimates. With its robustness to beam-hardening artifact, image noise and variations in phantom size and geometry, JSIR-BVM has the potential to achieve high spatial-resolution SPR mapping with sub-percentage accuracy and estimated uncertainty in the clinical setting. This article is protected by copyright. All rights reserved.

Pairing Experimental and Mathematical Modeling Studies on Fluidized Beds for Enhancement of Models Predictive Quality: A Current Status Overview

Modeling of gas-solid fluidized systems has been a prevailing challenge over the last few decades. With different approaches and implementing different sub-models to capture the essential multiphase and multiscale phenomena in these systems, major advances have been achieved, even though most models are only subject to a practical validation of macroscopic parameters. The current description of fluidized beds through mathematical models relies on the inclusion of vast sub-models, leading to an unquantifiable degree of uncertainty on the models’ applicability for extrapolation studies. Furthermore, each closure and fitting parameter in the model represents a possible source of deviation, and their optimization, hence, becomes another major challenge. The recent advances in measurement techniques can enable us to troubleshoot and optimize the implemented models and sub-models based on local scale measurements. Local multiphase hydrodynamic information obtained by advanced measurement techniques can enable the validation of local predictions and optimization of the coupled sub-models, leading to the development of simplified and highly predictive models. Thus, pairing advanced experimental studies on these systems with insightful modeling approaches is required to advance the shortcoming and enhance the predictive quality of the models. In this work, an overview of the status of modeling and experimental measurement techniques for gas-solid fluidized beds is presented; then, an overview on pairing both experimental and modeling studies to improve the models’ local predictions for fluidized beds is presented.

Initial Validation of Proton Dose Calculations on SPR Images from DECT in Treatment Planning System

PURPOSE

To investigate and quantify the potential benefits associated with the use of stopping-power-ratio (SPR) images created from dual-energy computed tomography (DECT) images for proton dose calculation in a clinical proton treatment planning system (TPS).

MATERIALS AND METHODS

The DECT and single-energy computed tomography (SECT) scans obtained for 26 plastic tissue surrogate plugs were placed individually in a tissue-equivalent plastic phantom. Relative-electron density (ρe) and effective atomic number (Z eff) images were reconstructed from the DECT scans and used to create an SPR image set for each plug. Next, the SPR for each plug was measured in a clinical proton beam for comparison of the calculated values in the SPR images. The SPR images and SECTs were then imported into a clinical TPS, and treatment plans were developed consisting of a single field delivering a 10 × 10 × 10-cm3 spread-out Bragg peak to a clinical target volume that contained the plugs. To verify the accuracy of the TPS dose calculated from the SPR images and SECTs, treatment plans were delivered to the phantom containing each plug, and comparisons of point-dose measurements and 2-dimensional γ-analysis were performed.

RESULTS

For all 26 plugs considered in this study, SPR values for each plug from the SPR images were within 2% agreement with measurements. Additionally, treatment plans developed with the SPR images agreed with the measured point dose to within 2%, whereas a 3% agreement was observed for SECT-based plans. γ-Index pass rates were > 90% for all SECT plans and > 97% for all SPR image-based plans.

CONCLUSION

Treatment plans created in a TPS with SPR images obtained from DECT scans are accurate to within guidelines set for validation of clinical treatment plans at our center. The calculated doses from the SPR image-based treatment plans showed better agreement to measured doses than identical plans created with standard SECT scans.

Characterization of tissue-specific pre-log Bayesian CT reconstruction by texture-dose relationship

PURPOSE

Tissue textures have been recognized as biomarkers for various clinical tasks. In computed tomography (CT) image reconstruction, it is important but challenging to preserve the texture when lowering x-ray exposure from full- toward low-/ultra-low dose level. Therefore, this paper aims to explore the texture-dose relationship within one tissue-specific pre-log Bayesian CT reconstruction algorithm.

METHODS

To enhance the texture in ultra-low dose CT (ULdCT) reconstruction, this paper presents a Bayesian type algorithm. A shifted Poisson model is adapted to describe the statistical properties of pre-log data, and a tissue-specific Markov random field prior (MRFt) is used to incorporate tissue texture from previous full-dose CT, thus called SP-MRFt algorithm. Utilizing the SP-MRFt algorithm, we investigated tissue texture degradation as a function of x-ray dose levels from full dose (100 mAs/120 kVp) to ultralow dose (1 mAs/120 kVp) by using quantitative texture-based evaluation metrics.

RESULTS

Experimental results show the SP-MRFt algorithm outperforms conventional filtered back projection (FBP) and post-log domain penalized weighted least square MRFt (PWLS-MRFt) in terms of noise suppression and texture preservation. Comparable results are also obtained with shifted Poisson model with 7 × 7 Huber MRF weights (SP-Huber7). The investigation on texture-dose relationship shows that the quantified texture measures drop monotonically as dose level decreases, and interestingly a turning point is observed on the texture-dose response curve.

CONCLUSIONS

This important observation implies that there exists a minimum dose level, at which a given CT scanner (hardware configuration and image reconstruction software) can achieve without compromising clinical tasks. Moreover, the experiment results show that the variance of electronic noise has higher impact than the mean to the texture-dose relationship.

Feasibility study of a point-of-care positron emission tomography system with interactive imaging capability

PURPOSE

We investigated the feasibility of a novel positron emission tomography (PET) system that provides near real-time feedback to an operator who can interactively scan a patient to optimize image quality. The system should be compact and mobile to support point-of-care (POC) molecular imaging applications. In this study, we present the key technologies required and discuss the potential benefits of such new capability.

METHODS

The core of this novel PET technology includes trackable PET detectors and a fully three-dimensional, fast image reconstruction engine implemented on multiple graphics processing units (GPUs) to support dynamically changing geometry by calculating the system matrix on-the-fly using a tube-of-response approach. With near real-time image reconstruction capability, a POC-PET system may comprise a maneuverable front PET detector and a second detector panel which can be stationary or moved synchronously with the front detector such that both panels face the region-of-interest (ROI) with the detector trajectory contoured around a patient's body. We built a proof-of-concept prototype using two planar detectors each consisting of a photomultiplier tube (PMT) optically coupled to an array of 48 × 48 lutetium-yttrium oxyorthosilicate (LYSO) crystals (1.0 × 1.0 × 10.0 mm³ each). Only 38 × 38 crystals in each arrays can be clearly re-solved and used for coincidence detection. One detector was mounted to a robotic arm which can position it at arbitrary locations, and the other detector was mounted on a rotational stage. A cylindrical phantom (102 mm in diameter, 150 mm long) with nine spherical lesions (8:1 tumor-to-background activity concentration ratio) was imaged from 27 sampling angles. List-mode events were reconstructed to form images without or with time-of-flight (TOF) information. We conducted two Monte Carlo simulations using two POC-PET systems. The first one uses the same phantom and detector setup as our experiment, with the detector coincidence re-solving time (CRT) ranging from 100 to 700 ps full-width-at-half-maximum (FWHM). The second study simulates a body-size phantom (316 × 228 × 160 mm³ ) imaged by a larger POC-PET system that has 4 × 6 modules (32 × 32 LYSO crystals/module, four in axial and six in transaxial directions) in the front panel and 3 × 8 modules (16 × 16 LYSO crystals/module, three in axial and eight in transaxial directions) in the back panel. We also evaluated an interactive scanning strategy by progressively increasing the number of data sets used for image reconstruction. The updated images were analyzed based on the number of data sets and the detector CRT.

RESULTS

The proof-of-concept prototype re-solves most of the spherical lesions despite a limited number of coincidence events and incomplete sampling. TOF information reduces artifacts in the reconstructed images. Systems with better timing resolution exhibit improved image quality and reduced artifacts. We observed a reconstruction speed of 0.96 × 10⁶ events/s/iteration for 600 × 600 × 224 voxel rectilinear space using four GPUs. A POC-PET system with significantly higher sensitivity can interactively image a body-size object from four angles in less than 7 min.

CONCLUSIONS

We have developed GPU-based fast image reconstruction capability to support a PET system with arbitrary and dynamically changing geometry. Using TOF PET detectors, we demonstrated the feasibility of a PET system that can provide timely visual feedback to an operator who can scan a patient interactively to support POC imaging applications.

Positron emission tomography image reconstruction using feature extraction

PURPOSE

To reduce the cost of positron emission tomography (PET) scanning systems, image reconstruction algorithms for low-sampled data have been extensively studied. However, the current method based on total variation (TV) minimization regularization nested in the maximum likelihood-expectation maximization (MLEM) algorithm cannot distinguish true structures from noise resulting losing some fine features in the images. Thus, this work aims to recover fine features lost in the MLEM-TV algorithm from low-sampled data.

METHOD

A feature refinement (FR) approach previously developed for statistical interior computed tomography (CT) reconstruction is applied to PET imaging to recover fine features in this study. The proposed method starts with a constant initial image and the FR step is performed after each MLEM-TV iteration to extract the desired structural information lost during TV minimization. A feature descriptor is specifically designed to distinguish structure from noise and artifacts. A modified steepest descent method is adopted to minimize the objective function. After evaluating the impacts of different patch sizes on the outcome of the presented method, an optimal patch size of 7×7 is selected in this study to balance structure-detection ability and computational efficiency.

RESULTS

Applying MLEM-TV-FR algorithm to the simulated brain PET imaging using an emission activity phantom, a standard Shepp-Logan phantom, and mouse results in the increased peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) as comparing to using the conventional MLEM-TV algorithm, as well as the substantial reduction of the used sampling numbers, which improves the computational efficiency.

CONCLUSIONS

The presented algorithm can achieve image quality superior to that of the MLEM and MLEM-TV approaches in terms of the preservation of fine structure and the suppression of undesired artifacts and noise, indicating its useful potential for low-sampled data in PET imaging.

Experimental implementation of a joint statistical image reconstruction method for proton stopping power mapping from dual-energy CT data

PURPOSE

To experimentally commission a dual-energy CT (DECT) joint statistical image reconstruction (JSIR) method, which is built on a linear basis vector model (BVM) of material characterization, for proton stopping power ratio (SPR) estimation.

METHODS

The JSIR-BVM method builds on the relationship between the energy-dependent photon attenuation coefficients and the proton stopping power via a pair of BVM component weights. The two BVM component images are simultaneously reconstructed from the acquired DECT sinograms and then used to predict the electron density and mean excitation energy (I-value), which are required by the Bethe equation for SPR computation. A post-reconstruction image-based DECT method, which utilizes the two separate CT images reconstructed via the scanner's software, was implemented for comparison. The DECT measurement data were acquired on a Philips Brilliance scanner at 90 and 140 kVp for two phantoms of different sizes. Each phantom contains 12 different soft and bony tissue surrogates with known compositions. The SPR estimation results were compared to the reference values computed from the known compositions. The difference of the computed water equivalent path lengths (WEPL) across the phantoms between the two methods was also compared.

RESULTS

The overall root-mean-square (RMS) of SPR estimation error of the JSIR-BVM method are 0.33% and 0.37% for the head- and body-sized phantoms, respectively, and all SPR estimates of the test samples are within 0.7% of the reference ground truth. The image-based method achieves overall RMS errors of 2.35% and 2.50% for the head- and body-sized phantoms, respectively. The JSIR-BVM method also reduces the pixel-wise random variation by 4-fold to 6-fold within homogeneous regions compared to the image-based method. The average differences between the JSIR-BVM method and the image-based method are 0.54% and 1.02% for the head- and body-sized phantoms, respectively.

CONCLUSION

By taking advantage of an accurate polychromatic CT data model and a model-based DECT statistical reconstruction algorithm, the JSIR-BVM method accounts for both systematic bias and random noise in the acquired DECT measurement data. Therefore, the JSIR-BVM method achieves good accuracy and precision on proton SPR estimation for various tissue surrogates and object sizes. In contrast, the experimentally achievable accuracy of the image-based method may be limited by the uncertainties in the image formation process. The result suggests that the JSIR-BVM method has the potential for more accurate SPR prediction compared to post-reconstruction image-based methods in clinical settings.

Impact of joint statistical dual-energy CT reconstruction of proton stopping power images: Comparison to image- and sinogram-domain material decomposition approaches

PURPOSE

The purpose of this study was to assess the performance of a novel dual-energy CT (DECT) approach for proton stopping power ratio (SPR) mapping that integrates image reconstruction and material characterization using a joint statistical image reconstruction (JSIR) method based on a linear basis vector model (BVM). A systematic comparison between the JSIR-BVM method and previously described DECT image- and sinogram-domain decomposition approaches is also carried out on synthetic data.

METHODS

The JSIR-BVM method was implemented to estimate the electron densities and mean excitation energies (I-values) required by the Bethe equation for SPR mapping. In addition, image- and sinogram-domain DECT methods based on three available SPR models including BVM were implemented for comparison. The intrinsic SPR modeling accuracy of the three models was first validated. Synthetic DECT transmission sinograms of two 330 mm diameter phantoms each containing 17 soft and bony tissues (for a total of 34) of known composition were then generated with spectra of 90 and 140 kVp. The estimation accuracy of the reconstructed SPR images were evaluated for the seven investigated methods. The impact of phantom size and insert location on SPR estimation accuracy was also investigated.

RESULTS

All three selected DECT-SPR models predict the SPR of all tissue types with less than 0.2% RMS errors under idealized conditions with no reconstruction uncertainties. When applied to synthetic sinograms, the JSIR-BVM method achieves the best performance with mean and RMS-average errors of less than 0.05% and 0.3%, respectively, for all noise levels, while the image- and sinogram-domain decomposition methods show increasing mean and RMS-average errors with increasing noise level. The JSIR-BVM method also reduces statistical SPR variation by sixfold compared to other methods. A 25% phantom diameter change causes up to 4% SPR differences for the image-domain decomposition approach, while the JSIR-BVM method and sinogram-domain decomposition methods are insensitive to size change.

CONCLUSION

Among all the investigated methods, the JSIR-BVM method achieves the best performance for SPR estimation in our simulation phantom study. This novel method is robust with respect to sinogram noise and residual beam-hardening effects, yielding SPR estimation errors comparable to intrinsic BVM modeling error. In contrast, the achievable SPR estimation accuracy of the image- and sinogram-domain decomposition methods is dominated by the CT image intensity uncertainties introduced by the reconstruction and decomposition processes.

Technical Note: A model-based sinogram correction for beam hardening artifact reduction in CT

PURPOSE

This study aims to propose a physics-based method of reducing beam-hardening artifacts induced by high-attenuation materials such as metal stents or other metallic implants.

METHODS

The proposed approach consists of deriving a sinogram inconsistency formula representing the energy dependence of the attenuation coefficient of high-attenuation materials. This inconsistency formula more accurately represents the inconsistencies of the sinogram than that of a previously reported formula (called the MAC-BC method). This is achieved by considering the properties of the high-attenuation materials, which include the materials' shapes and locations and their effects on the incident X-ray spectrum, including their attenuation coefficients.

RESULTS

Numerical simulation and phantom experiment demonstrate that the modeling error of MAC-BC method are nearly completely removed by means of the proposed method.

CONCLUSION

The proposed method reduces beam-hardening artifacts arising from high-attenuation materials by relaxing the assumptions of the MAC-BC method. In doing so, it outperforms the original MAC-BC method. Further research is required to address other potential sources of metal artifacts, such as photon starvation, scattering, and noise.

Technical Note: On the accuracy of parametric two-parameter photon cross-section models in dual-energy CT applications

PURPOSE

To evaluate and compare the theoretically achievable accuracy of two families of two-parameter photon cross-section models: basis vector model (BVM) and modified parametric fit model (mPFM).

METHOD

The modified PFM assumes that photoelectric absorption and scattering cross-sections can be accurately represented by power functions in effective atomic number and/or energy plus the Klein-Nishina cross-section, along with empirical corrections that enforce exact prediction of elemental cross-sections. Two mPFM variants were investigated: the widely used Torikoshi model (tPFM) and a more complex "VCU" variant (vPFM). For 43 standard soft and bony tissues and phantom materials, all consisting of elements with atomic number less than 20 (except iodine), we evaluated the theoretically achievable accuracy of tPFM and vPFM for predicting linear attenuation, photoelectric absorption, and energy-absorption coefficients, and we compared it to a previously investigated separable, linear two-parameter model, BVM.

RESULTS

For an idealized dual-energy computed tomography (DECT) imaging scenario, the cross-section mapping process demonstrates that BVM more accurately predicts photon cross-sections of biological mixtures than either tPFM or vPFM. Maximum linear attenuation coefficient prediction errors were 15% and 5% for tPFM and BVM, respectively. The root-mean-square (RMS) prediction errors of total linear attenuation over the 20 keV to 1000 keV energy range of tPFM and BVM were 0.93% (tPFM) and 0.1% (BVM) for adipose tissue, 0.8% (tPFM) and 0.2% (BVM) for muscle tissue, and 1.6% (tPFM) and 0.2% (BVM) for cortical bone tissue. With exception of the thyroid and Teflon, the RMS error for photoelectric absorption and scattering coefficient was within 4% for the tPFM and 2% for the BVM. Neither model predicts the photon cross-sections of thyroid tissue accurately, exhibiting relative errors as large as 20%. For the energy-absorption coefficients prediction error, RMS errors for the BVM were less than 1.5%, while for the tPFM, the RMS errors were as large as 16%.

CONCLUSION

Compared to modified PFMs, BVM shows superior potential to support dual-energy CT cross-section mapping. In addition, the linear, separable BVM can be more efficiently deployed by iterative model-based DECT image-reconstruction algorithms.

Comparison Between Pre-Log and Post-Log Statistical Models in Ultra-Low-Dose CT Reconstruction

X-ray detectors in clinical computed tomography (CT) usually operate in current-integrating mode. Their complicated signal statistics often lead to intractable likelihood functions for practical use in model-based image reconstruction (MBIR). It is therefore desirable to design simplified statistical models without losing the essential factors. Depending on whether the CT transmission data are logarithmically transformed, pre-log and post-log models are two major categories of choices in CT MBIR. Both being approximations, it remains an open question whether one model can notably improve image quality over the other on real scanners. In this study, we develop and compare several pre-log and post-log MBIR algorithms under a unified framework. Their reconstruction accuracy based on simulation and clinical datasets are evaluated. The results show that pre-log MBIR can achieve notably better quantitative accuracy than post-log MBIR in ultra-low-dose CT, although in less extreme cases, post-log MBIR with handcrafted pre-processing remains a competitive alternative. Pre-log MBIR could play a growing role in emerging ultra-low-dose CT applications.

Multi-GPU Acceleration of Branchless Distance Driven Projection and Backprojection for Clinical Helical CT

Model-based image reconstruction (MBIR) techniques have the potential to generate high quality images from noisy measurements and a small number of projections which can reduce the x-ray dose in patients. These MBIR techniques rely on projection and backprojection to refine an image estimate. One of the widely used projectors for these modern MBIR based technique is called branchless distance driven (DD) projection and backprojection. While this method produces superior quality images, the computational cost of iterative updates keeps it from being ubiquitous in clinical applications. In this paper, we provide several new parallelization ideas for concurrent execution of the DD projectors in multi-GPU systems using CUDA programming tools. We have introduced some novel schemes for dividing the projection data and image voxels over multiple GPUs to avoid runtime overhead and inter-device synchronization issues. We have also reduced the complexity of overlap calculation of the algorithm by eliminating the common projection plane and directly projecting the detector boundaries onto image voxel boundaries. To reduce the time required for calculating the overlap between the detector edges and image voxel boundaries, we have proposed a pre-accumulation technique to accumulate image intensities in perpendicular 2D image slabs (from a 3D image) before projection and after backprojection to ensure our DD kernels run faster in parallel GPU threads. For the implementation of our iterative MBIR technique we use a parallel multi-GPU version of the alternating minimization (AM) algorithm with penalized likelihood update. The time performance using our proposed reconstruction method with Siemens Sensation 16 patient scan data shows an average of 24 times speedup using a single TITAN X GPU and 74 times speedup using 3 TITAN X GPUs in parallel for combined projection and backprojection.

A spectral interior CT by a framelet-based reconstruction algorithm

Reducing radiation dose is an important goal in medical computed tomography (CT), for which interior tomography is an effective approach. There have been interior reconstruction algorithms for monochromatic CT, but in reality, X-ray sources are polychromatic. Using a polychromatic acquisition model and motivated by framelet-based image processing algorithms, in this paper, we propose an interior reconstruction algorithm to obtain an image with spectral information assuming only one scan with a current energy-integrating detector. This algorithm is a new nonlinear iterative method by minimizing a special functional under a polychromatic acquisition model for X-ray CT, where the attenuation coefficients are energy-dependent. Experimental results validate that our algorithm can effectively reduce the beam-hardening artifacts and metal artifacts. It also produces color overlays which are useful in tumor identification and quantification.

Does Noise Weighting Matter in CT Iterative Reconstruction?

This paper uses a computer simulation to investigate whether a more accurate noise model always results in less noisy images in CT iterative reconstruction. We start with a hypothetic non-realistic noise model for the CT measurements, by assuming that the attenuation coefficient is energy independent and there is no scattering. A variance formula for this model is derived and presented. Based on this model, computer simulations are conducted with 12 different ad hoc noise weighting methods, and their results are compared. The simple Poisson noise model performs better than other more accurate models, when the projection data are generated with the hypothetical noise model. A more accurate noise model does not necessarily produce a less-noisy image. In this counter example, modeling the system's electronic noise during reconstruction does not help reducing the image noise. A simpler noise model sometimes can outperform the complicated and more accurate noise model.

Line Integral Alternating Minimization Algorithm for Dual-Energy X-Ray CT Image Reconstruction

We propose a new algorithm, called line integral alternating minimization (LIAM), for dual-energy X-ray CT image reconstruction. Instead of obtaining component images by minimizing the discrepancy between the data and the mean estimates, LIAM allows for a tunable discrepancy between the basis material projections and the basis sinograms. A parameter is introduced that controls the size of this discrepancy, and with this parameter the new algorithm can continuously go from a two-step approach to the joint estimation approach. LIAM alternates between iteratively updating the line integrals of the component images and reconstruction of the component images using an image iterative deblurring algorithm. An edge-preserving penalty function can be incorporated in the iterative deblurring step to decrease the roughness in component images. Images from both simulated and experimentally acquired sinograms from a clinical scanner were reconstructed by LIAM while varying the regularization parameters to identify good choices. The results from the dual-energy alternating minimization algorithm applied to the same data were used for comparison. Using a small fraction of the computation time of dual-energy alternating minimization, LIAM achieves better accuracy of the component images in the presence of Poisson noise for simulated data reconstruction and achieves the same level of accuracy for real data reconstruction.

Metal Artifact Reduction for Polychromatic X-ray CT Based on a Beam-Hardening Corrector

This paper proposes a new method to correct beam hardening artifacts caused by the presence of metal in polychromatic X-ray computed tomography (CT) without degrading the intact anatomical images. Metal artifacts due to beam-hardening, which are a consequence of X-ray beam polychromaticity, are becoming an increasingly important issue affecting CT scanning as medical implants become more common in a generally aging population. The associated higher-order beam-hardening factors can be corrected via analysis of the mismatch between measured sinogram data and the ideal forward projectors in CT reconstruction by considering the known geometry of high-attenuation objects. Without prior knowledge of the spectrum parameters or energy-dependent attenuation coefficients, the proposed correction allows the background CT image (i.e., the image before its corruption by metal artifacts) to be extracted from the uncorrected CT image. Computer simulations and phantom experiments demonstrate the effectiveness of the proposed method to alleviate beam hardening artifacts.

Spectral CT Image Restoration via an Average Image-Induced Nonlocal Means Filter

GOAL

Spectral computed tomography (SCT) images reconstructed by an analytical approach often suffer from a poor signal-to-noise ratio and strong streak artifacts when sufficient photon counts are not available in SCT imaging. In reducing noise-induced artifacts in SCT images, in this study, we propose an average image-induced nonlocal means (aviNLM) filter for each energy-specific image restoration.  Methods:  The present aviNLM algorithm exploits redundant information in the whole energy domain. Specifically, the proposed aviNLM algorithm yields the restored results by performing a nonlocal weighted average operation on the noisy energy-specific images with the nonlocal weight matrix between the target and prior images, in which the prior image is generated from all of the images reconstructed in each energy bin.  Results: Qualitative and quantitative studies are conducted to evaluate the aviNLM filter by using the data of digital phantom, physical phantom, and clinical patient data acquired from the energy-resolved and -integrated detectors, respectively. Experimental results show that the present aviNLM filter can achieve promising results for SCT image restoration in terms of noise-induced artifact suppression, cross profile, and contrast-to-noise ratio and material decomposition assessment. Conclusion and Significance: The present aviNLM algorithm has useful potential for radiation dose reduction by lowering the mAs in SCT imaging, and it may be useful for some other clinical applications, such as in myocardial perfusion imaging and radiotherapy.

Task-based image quality evaluation of iterative reconstruction methods for low dose CT using computer simulations

Iterative reconstruction (IR) methods for x-ray CT is a promising approach to improve image quality or reduce radiation dose to patients. The goal of this work was to use task based image quality measures and the channelized Hotelling observer (CHO) to evaluate both analytic and IR methods for clinical x-ray CT applications. We performed realistic computer simulations at five radiation dose levels, from a clinical reference low dose D0 to 25% D0. A fixed size and contrast lesion was inserted at different locations into the liver of the XCAT phantom to simulate a weak signal. The simulated data were reconstructed on a commercial CT scanner (SOMATOM Definition Flash; Siemens, Forchheim, Germany) using the vendor-provided analytic (WFBP) and IR (SAFIRE) methods. The reconstructed images were analyzed by CHOs with both rotationally symmetric (RS) and rotationally oriented (RO) channels, and with different numbers of lesion locations (5, 10, and 20) in a signal known exactly (SKE), background known exactly but variable (BKEV) detection task. The area under the receiver operating characteristic curve (AUC) was used as a summary measure to compare the IR and analytic methods; the AUC was also used as the equal performance criterion to derive the potential dose reduction factor of IR. In general, there was a good agreement in the relative AUC values of different reconstruction methods using CHOs with RS and RO channels, although the CHO with RO channels achieved higher AUCs than RS channels. The improvement of IR over analytic methods depends on the dose level. The reference dose level D0 was based on a clinical low dose protocol, lower than the standard dose due to the use of IR methods. At 75% D0, the performance improvement was statistically significant (p < 0.05). The potential dose reduction factor also depended on the detection task. For the SKE/BKEV task involving 10 lesion locations, a dose reduction of at least 25% from D0 was achieved.

A full-spectral Bayesian reconstruction approach based on the material decomposition model applied in dual-energy computed tomography

PURPOSE

Dual-energy computed tomography (DECT) makes it possible to get two fractions of basis materials without segmentation. One is the soft-tissue equivalent water fraction and the other is the hard-matter equivalent bone fraction. Practical DECT measurements are usually obtained with polychromatic x-ray beams. Existing reconstruction approaches based on linear forward models without counting the beam polychromaticity fail to estimate the correct decomposition fractions and result in beam-hardening artifacts (BHA). The existing BHA correction approaches either need to refer to calibration measurements or suffer from the noise amplification caused by the negative-log preprocessing and the ill-conditioned water and bone separation problem. To overcome these problems, statistical DECT reconstruction approaches based on nonlinear forward models counting the beam polychromaticity show great potential for giving accurate fraction images.

METHODS

This work proposes a full-spectral Bayesian reconstruction approach which allows the reconstruction of high quality fraction images from ordinary polychromatic measurements. This approach is based on a Gaussian noise model with unknown variance assigned directly to the projections without taking negative-log. Referring to Bayesian inferences, the decomposition fractions and observation variance are estimated by using the joint maximum a posteriori (MAP) estimation method. Subject to an adaptive prior model assigned to the variance, the joint estimation problem is then simplified into a single estimation problem. It transforms the joint MAP estimation problem into a minimization problem with a nonquadratic cost function. To solve it, the use of a monotone conjugate gradient algorithm with suboptimal descent steps is proposed.

RESULTS

The performance of the proposed approach is analyzed with both simulated and experimental data. The results show that the proposed Bayesian approach is robust to noise and materials. It is also necessary to have the accurate spectrum information about the source-detector system. When dealing with experimental data, the spectrum can be predicted by a Monte Carlo simulator. For the materials between water and bone, less than 5% separation errors are observed on the estimated decomposition fractions.

CONCLUSIONS

The proposed approach is a statistical reconstruction approach based on a nonlinear forward model counting the full beam polychromaticity and applied directly to the projections without taking negative-log. Compared to the approaches based on linear forward models and the BHA correction approaches, it has advantages in noise robustness and reconstruction accuracy.

Prospects for in vivo estimation of photon linear attenuation coefficients using postprocessing dual-energy CT imaging on a commercial scanner: comparison of analytic and polyenergetic statistical reconstruction algorithms

PURPOSE

Accurate patient-specific photon cross-section information is needed to support more accurate model-based dose calculation for low energy photon-emitting modalities in medicine such as brachytherapy and kilovoltage x-ray imaging procedures. A postprocessing dual-energy CT (pDECT) technique for noninvasive in vivo estimation of photon linear attenuation coefficients has been experimentally implemented on a commercial CT scanner and its accuracy assessed in idealized phantom geometries.

METHODS

Eight test materials of known composition and density were used to compare pDECT-estimated linear attenuation coefficients to NIST reference values over an energy range from 10 keV to 1 MeV. As statistical image reconstruction (SIR) has been shown to reconstruct images with less random and systematic error than conventional filtered backprojection (FBP), the pDECT technique was implemented with both an in-house polyenergetic SIR algorithm, alternating minimization (AM), as well as a conventional FBP reconstruction algorithm. Improvement from increased spectral separation was also investigated by filtering the high-energy beam with an additional 0.5 mm of tin. The law of propagated uncertainty was employed to assess the sensitivity of the pDECT process to errors in reconstructed images.

RESULTS

Mean pDECT-estimated linear attenuation coefficients for the eight test materials agreed within 1% of NIST reference values for energies from 1 MeV down to 30 keV, with mean errors rising to between 3% and 6% at 10 keV, indicating that the method is unbiased when measurement and calibration phantom geometries are matched. Reconstruction with FBP and AM algorithms conferred similar mean pDECT accuracy. However, single-voxel pDECT estimates reconstructed on a 1 × 1 × 3 mm(3) grid are shown to be highly sensitive to reconstructed image uncertainty; in some cases pDECT attenuation coefficient estimates exhibited standard deviations on the order of 20% around the mean. Reconstruction with the statistical AM algorithm led to standard deviations roughly 40% to 60% less than FBP reconstruction. Additional tin filtration of the high energy beam exhibits similar pDECT estimation accuracy as the unfiltered beam, even when scanning with only 25% of the dose. Using the law of propagated uncertainty, low Z materials are found to be more sensitive to image reconstruction errors than high Z materials. Furthermore, it is estimated that reconstructed CT image uncertainty must be limited to less than 0.25% to achieve a target linear-attenuation coefficient estimation uncertainty of 3% at 28 keV.

CONCLUSIONS

That pDECT supports mean linear attenuation coefficient measurement accuracies of 1% of reference values for energies greater than 30 keV is encouraging. However, the sensitivity of the pDECT measurements to noise and systematic errors in reconstructed CT images warrants further investigation in more complex phantom geometries. The investigated statistical reconstruction algorithm, AM, reduced random measurement uncertainty relative to FBP owing to improved noise performance. These early results also support efforts to increase DE spectral separation, which can further reduce the pDECT sensitivity to measurement uncertainty.

Compressed sampling strategies for tomography

We investigate new sampling strategies for projection tomography, enabling one to employ fewer measurements than expected from classical sampling theory without significant loss of information. Inspired by compressed sensing, our approach is based on the understanding that many real objects are compressible in some known representation, implying that the number of degrees of freedom defining an object is often much smaller than the number of pixels/voxels. We propose a new approach based on quasi-random detector subsampling, whereas previous approaches only addressed subsampling with respect to source location (view angle). The performance of different sampling strategies is considered using object-independent figures of merit, and also based on reconstructions for specific objects, with synthetic and real data. The proposed approach can be implemented using a structured illumination of the interrogated object or the detector array by placing a coded aperture/mask at the source or detector side, respectively. Advantages of the proposed approach include (i) for structured illumination of the detector array, it leads to fewer detector pixels and allows one to integrate detectors for scattered radiation in the unused space; (ii) for structured illumination of the object, it leads to a reduced radiation dose for patients in medical scans; (iii) in the latter case, the blocking of rays reduces scattered radiation while keeping the same energy in the transmitted rays, resulting in a higher signal-to-noise ratio than that achieved by lowering exposure times or the energy of the source; (iv) compared to view-angle subsampling, it allows one to use fewer measurements for the same image quality, or leads to better image quality for the same number of measurements. The proposed approach can also be combined with view-angle subsampling.

Model-Based Iterative Reconstruction for Dual-Energy X-Ray CT Using a Joint Quadratic Likelihood Model

Dual-energy X-ray CT (DECT) has the potential to improve contrast and reduce artifacts as compared to traditional CT. Moreover, by applying model-based iterative reconstruction (MBIR) to dual-energy data, one might also expect to reduce noise and improve resolution. However, the direct implementation of dual-energy MBIR requires the use of a nonlinear forward model, which increases both complexity and computation. Alternatively, simplified forward models have been used which treat the material-decomposed channels separately, but these approaches do not fully account for the statistical dependencies in the channels. In this paper, we present a method for joint dual-energy MBIR (JDE-MBIR), which simplifies the forward model while still accounting for the complete statistical dependency in the material-decomposed sinogram components. The JDE-MBIR approach works by using a quadratic approximation to the polychromatic log-likelihood and a simple but exact nonnegativity constraint in the image domain. We demonstrate that our method is particularly effective when the DECT system uses fast kVp switching, since in this case the model accounts for the inaccuracy of interpolated sinogram entries. Both phantom and clinical results show that the proposed model produces images that compare favorably in quality to previous decomposition-based methods, including FBP and other statistical iterative approaches.

Information-theoretic discrepancy based iterative reconstructions (IDIR) for polychromatic x-ray tomography

PURPOSE

X-ray photons generated from a typical x-ray source for clinical applications exhibit a broad range of wavelengths, and the interactions between individual particles and biological substances depend on particles' energy levels. Most existing reconstruction methods for transmission tomography, however, neglect this polychromatic nature of measurements and rely on the monochromatic approximation. In this study, we developed a new family of iterative methods that incorporates the exact polychromatic model into tomographic image recovery, which improves the accuracy and quality of reconstruction.

METHODS

The generalized information-theoretic discrepancy (GID) was employed as a new metric for quantifying the distance between the measured and synthetic data. By using special features of the GID, the objective function for polychromatic reconstruction which contains a double integral over the wavelength and the trajectory of incident x-rays was simplified to a paraboloidal form without using the monochromatic approximation. More specifically, the original GID was replaced with a surrogate function with two auxiliary, energy-dependent variables. Subsequently, the alternating minimization technique was applied to solve the double minimization problem. Based on the optimization transfer principle, the objective function was further simplified to the paraboloidal equation, which leads to a closed-form update formula. Numerical experiments on the beam-hardening correction and material-selective reconstruction were conducted to compare and assess the performance of conventional methods and the proposed algorithms.

RESULTS

The authors found that the GID determines the distance between its two arguments in a flexible manner. In this study, three groups of GIDs with distinct data representations were considered. The authors demonstrated that one type of GIDs that comprises "raw" data can be viewed as an extension of existing statistical reconstructions; under a particular condition, the GID is equivalent to the Poisson log-likelihood function. The newly proposed GIDs of the other two categories consist of log-transformed measurements, which have the advantage of imposing linearized penalties over multiple discrepancies. For all proposed variants of the GID, the aforementioned strategy was used to obtain a closed-form update equation. Even though it is based on the exact polychromatic model, the derived algorithm bears a structural resemblance to conventional methods based on the monochromatic approximation. The authors named the proposed approach as information-theoretic discrepancy based iterative reconstructions (IDIR). In numerical experiments, IDIR with raw data converged faster than previously known statistical reconstruction methods. IDIR with log-transformed data exhibited superior reconstruction quality and faster convergence speed compared with conventional methods and their variants.

CONCLUSIONS

The authors' new framework for tomographic reconstruction allows iterative inversion of the polychromatic data model. The primary departure from the traditional iterative reconstruction was the employment of the GID as a new metric for quantifying the inconsistency between the measured and synthetic data. The proposed methods outperformed not only conventional methods based on the monochromatic approximation but also those based on the polychromatic model. The authors have observed that the GID is a very flexible means to design an objective function for iterative reconstructions. Hence, the authors expect that the proposed IDIR framework will also be applicable to other challenging tasks.

Modelling the physics in the iterative reconstruction for transmission computed tomography

There is an increasing interest in iterative reconstruction (IR) as a key tool to improve quality and increase applicability of x-ray CT imaging. IR has the ability to significantly reduce patient dose; it provides the flexibility to reconstruct images from arbitrary x-ray system geometries and allows one to include detailed models of photon transport and detection physics to accurately correct for a wide variety of image degrading effects. This paper reviews discretization issues and modelling of finite spatial resolution, Compton scatter in the scanned object, data noise and the energy spectrum. The widespread implementation of IR with a highly accurate model-based correction, however, still requires significant effort. In addition, new hardware will provide new opportunities and challenges to improve CT with new modelling.

Modelling the physics in the iterative reconstruction for transmission computed tomography

There is an increasing interest in iterative reconstruction (IR) as a key tool to improve quality and increase applicability of x-ray CT imaging. IR has the ability to significantly reduce patient dose; it provides the flexibility to reconstruct images from arbitrary x-ray system geometries and allows one to include detailed models of photon transport and detection physics to accurately correct for a wide variety of image degrading effects. This paper reviews discretization issues and modelling of finite spatial resolution, Compton scatter in the scanned object, data noise and the energy spectrum. The widespread implementation of IR with a highly accurate model-based correction, however, still requires significant effort. In addition, new hardware will provide new opportunities and challenges to improve CT with new modelling.

Experimental implementation of a polyenergetic statistical reconstruction algorithm for a commercial fan-beam CT scanner

PURPOSE

To present a framework for characterizing the data needed to implement a polyenergetic model-based statistical reconstruction algorithm, Alternating Minimization (AM), on a commercial fan-beam CT scanner and a novel method for assessing the accuracy of the commissioned data model.

METHODS

The X-ray spectra for three tube potentials on the Philips Brilliance CT scanner were estimated by fitting a semi-empirical X-ray spectrum model to transmission measurements. Spectral variations due to the bowtie filter were computationally modeled. Eight homogeneous cylinders of PMMA, Teflon and water with varying diameters were scanned at each energy. Central-axis scatter was measured for each cylinder using a beam-stop technique. AM reconstruction with a single-basis object-model matched to the scanned cylinder's composition allows assessment of the accuracy of the AM algorithm's polyenergetic data model. Filtered-backprojection (FBP) was also performed to compare consistency metrics such as uniformity and object-size dependence.

RESULTS

The spectrum model fit measured transmission curves with residual root-mean-square-error of 1.20%-1.34% for the three scanning energies. The estimated spectrum and scatter data supported polyenergetic AM reconstruction of the test cylinders to within 0.5% of expected in the matched object-model reconstruction test. In comparison to FBP, polyenergetic AM exhibited better uniformity and less object-size dependence.

CONCLUSIONS

Reconstruction using a matched object-model illustrate that the polyenergetic AM algorithm's data model was commissioned to within 0.5% of an expected ground truth. These results support ongoing and future research with polyenergetic AM reconstruction of commercial fan-beam CT data for quantitative CT applications.

Dynamic indocyanine green angiography measurements

Dynamic indocyanine green imaging uses a scanning laser ophthalmoscope and a fluorescent dye to produce movies of the dye-filling pattern in the retina and choroid of the eye. It is used for evaluating choroidal neovascularization. Movies are examined to identify the anatomy of the pathology for planning treatment and to evaluate progression or response to treatment. The popularity of this approach is affected by the complexity and difficulty in interpreting the movies. Software algorithms were developed to produce images from the movies that are easy to interpret. A mathematical model is formulated of the flow dynamics, and a fitting algorithm is designed that solves for the flow parameters. The images provide information about flow and perfusion, including regions of change between examinations. Imaged measures include the dye fill-time, temporal dispersion, and magnitude of the dye dilution temporal curves associated with image pixels. Cases show how the software can help to identify clinically relevant anatomy such as feeder vessels, drain vessels, capillary networks, and normal choroidal draining vessels. As a potential tool for research into the character of neovascular conditions and treatments, it reveals the flow dynamics and character of the lesion. Future varieties of this methodology may be used for evaluating the success of engineered tissue transplants, surgical flaps, reconstructive surgery, breast surgery, and many other surgical applications where flow, perfusion, and vascularity of tissue are important.

Image reconstruction and system modeling techniques for virtual-pinhole PET insert systems

Virtual-pinhole PET (VP-PET) imaging is a new technology in which one or more high-resolution detector modules are integrated into a conventional PET scanner with lower resolution detectors. It can locally enhance the spatial resolution and contrast recovery near the add-on detectors, and depending on the configuration, may also increase the sensitivity of the system. This novel scanner geometry makes the reconstruction problem more challenging compared to the reconstruction of data from a stand-alone PET scanner, as new techniques are needed to model and account for the non-standard acquisition. In this paper, we present a general framework for fully 3D modeling of an arbitrary VP-PET insert system. The model components are incorporated into a statistical reconstruction algorithm to estimate an image from the multi-resolution data. For validation, we apply the proposed model and reconstruction approach to one of our custom-built VP-PET systems-a half-ring insert device integrated into a clinical PET/CT scanner. Details regarding the most important implementation issues are provided. We show that the proposed data model is consistent with the measured data, and that our approach can lead to reconstructions with improved spatial resolution and lesion detectability.