A scheme for multisource interior tomography

Deep-Interior: A new pathway to interior tomographic image reconstruction via a weighted backprojection and deep learning

BACKGROUND

In recent years, deep learning strategies have been combined with either the filtered backprojection or iterative methods or the direct projection-to-image by deep learning only to reconstruct images. Some of these methods can be applied to address the interior reconstruction problems for centered regions of interest (ROIs) with fixed sizes. Developing a method to enable interior tomography with arbitrarily located ROIs with nearly arbitrary ROI sizes inside a scanning field of view (FOV) remains an open question.

PURPOSE

To develop a new pathway to enable interior tomographic reconstruction for arbitrarily located ROIs with arbitrary sizes using a single trained deep neural network model.

METHODS

The method consists of two steps. First, an analytical weighted backprojection reconstruction algorithm was developed to perform domain transform from divergent fan-beam projection data to an intermediate image feature space,B ( x ⃗ ) $B(\vec{x})$ , for an arbitrary size ROI at an arbitrary location inside the FOV. Second, a supervised learning technique was developed to train a deep neural network architecture to perform deconvolution to obtain the true imagef ( x ⃗ ) $f(\vec{x})$ from the new feature spaceB ( x ⃗ ) $B(\vec{x})$ . This two-step method is referred to as Deep-Interior for convenience. Both numerical simulations and experimental studies were performed to validate the proposed Deep-Interior method.

RESULTS

The results showed that ROIs as small as a diameter of 5 cm could be accurately reconstructed (similarity index 0.985 ± 0.018 on internal testing data and 0.940 ± 0.025 on external testing data) at arbitrary locations within an imaging object covering a wide variety of anatomical structures of different body parts. Besides, ROIs of arbitrary size can be reconstructed by stitching small ROIs without additional training.

CONCLUSION

The developed Deep-Interior framework can enable interior tomographic reconstruction from divergent fan-beam projections for short-scan and super-short-scan acquisitions for small ROIs (with a diameter larger than 5 cm) at an arbitrary location inside the scanning FOV with high quantitative reconstruction accuracy.

A modified algebraic reconstruction algorithm for sparse projection

Background

Computed tomography (CT) is an advanced medical imaging technology. The images obtained by CT are helpful for improving diagnostic accuracy. Currently, CT is widely used in clinical settings for diagnosis and health examinations. However, full angle CT scanning has the disadvantage of causing radiation damage to the human body. Sparse angle projection CT scanning is the most effective way to minimize this damage, but the quality of the reconstructed image is reduced. Therefore, it is important to improve the reconstructed image quality produced by sparse angle projection.

Methods

In this paper, we focused on the algebraic reconstruction algorithm. To reduce the accumulation of random noise, we formulated a modified algebraic reconstruction algorithm. Firstly, the algebraic reconstruction algorithm was used to compute two consecutive results, and then the weighted sum of these two results was used to correct the reconstructed image, and an iterative result was obtained. Using this method, we aimed to reduce the noise accumulation caused by iteration.

Results

In this study, 20 angle projections were used for the reconstruction. The experimental object was the Shepp-Logan phantom test image. The experiments were implemented under two conditions: without noise and with noise. The peak signal to noise ratio (PSNR) and the mean squared error (MSE) of the reconstructed image from projections without noise were 76.0896 and 0.0016, respectively. The PSNR and MSE of the reconstructed image from projections with noise were 75.8263 and 0.0017, respectively. The reconstructed performance was superior to the previous algebraic reconstruction algorithm.

Conclusions

The performance of the proposed method was superior to other algorithms, which confirms that noise accumulation caused by iteration can be effectively reduced by the weighted summation of two consecutive reconstruction results. Moreover, the reconstruction performance under noisy projection is superior to other algorithms, which demonstrates that the proposed method improves anti-noise performance.

Projection-based dynamic tomography

Objective. This paper proposes a 4D dynamic tomography framework that allows a moving sample to be imaged in a tomograph as well as the associated space-time kinematics to be measured with nothing more than a single conventional x-ray scan.Approach. The method exploits the consistency of the projection/reconstruction operations through a multi-scale procedure. The procedure is composed of two main parts solved alternatively: a motion-compensated reconstruction algorithm and a projection-based measurement procedure that estimates the displacement field directly on each projection.Main results. The method is applied to two studies: a numerical simulation of breathing from chest computed tomography (4D-CT) and a clinical cone-beam CT of a breathing patient acquired for image guidance of radiotherapy. The reconstructed volume, initially blurred by the motion, is cleaned from motion artifacts.Significance. Applying the proposed approach results in an improved reconstruction quality showing sharper edges and finer details.

X-ray tomography with multiple ultranarrow cone beams

Hollow glass microcapillaries or x-ray waveguides very efficiently confine x-rays to submicron or nanospots, which can be used for point projection imaging. However, x-ray beams exiting from such devices have ultranarrow cones that are limited by the critical angle for the total external reflection to a few milliradians. Narrow cone beams result in small fields of view, and the application of multiple-reflection optics to cone beam tomography is challenging. In this work, we describe a new nonconventional tomographic geometry realized with multiple confocal ultranarrow cone beams. The geometry enables an increase in the effective radiation cone to over 10^° without resolution reduction. The proposed tomographic scans can be performed without truncations of the field of view or limitations of the angular range and do not require sample translations, which are inherent to other multibeam x-ray techniques. Volumetric imaging is possible with a simultaneous iterative reconstruction technique or with a fast approximate noniterative two-step approach. A proof-of-principle experiment was performed in the multipoint projection geometry with polycapillary optics and a multi-pinhole mask inserted upstream of the optics. The geometry is suited for phase-contrast tomography with polychromatic laboratory and synchrotron sources.

Review of CT image reconstruction open source toolkits

Computed tomography (CT) has been widely applied in medical diagnosis, nondestructive evaluation, homeland security, and other science and engineering applications. Image reconstruction is one of the core CT imaging technologies. In this review paper, we systematically reviewed the currently publicly available CT image reconstruction open source toolkits in the aspects of their environments, object models, imaging geometries, and algorithms. In addition to analytic and iterative algorithms, deep learning reconstruction networks and open codes are also reviewed as the third category of reconstruction algorithms. This systematic summary of the publicly available software platforms will help facilitate CT research and development.

FBP-type CT reconstruction algorithms for triple-source circular trajectory with different scanning radii

Multi-source computed tomography (CT) imaging has unique technical advantages not only for dynamic objects, but also for large-size objects by designing its imaging scan mode. Using the triple-source fan-beam imaging scan mode under three circular trajectories with two different radii, we in this study developed and analyzed theoretically several exact reconstruction algorithms in terms of full-scan and short-scan for three sets of truncated projection data. This triple-source scan configuration in different radii cases is easier to be simulated by a single-source scan configuration in an industrial CT system. The proposed algorithms are based on the idea of filtering-back-projection (FBP) algorithm, and can reconstruct the large-size objects under the same CT devices. The developed algorithms avoid data rebinning and can provide exact and fast image reconstruction. The results of the numerical simulation based data analysis verified that new algorithms were accurate and effective.

LEARN: Learned Experts' Assessment-Based Reconstruction Network for Sparse-Data CT

Compressive sensing (CS) has proved effective for tomographic reconstruction from sparsely collected data or under-sampled measurements, which are practically important for few-view computed tomography (CT), tomosynthesis, interior tomography, and so on. To perform sparse-data CT, the iterative reconstruction commonly uses regularizers in the CS framework. Currently, how to choose the parameters adaptively for regularization is a major open problem. In this paper, inspired by the idea of machine learning especially deep learning, we unfold the state-of-the-art "fields of experts"-based iterative reconstruction scheme up to a number of iterations for data-driven training, construct a learned experts' assessment-based reconstruction network (LEARN) for sparse-data CT, and demonstrate the feasibility and merits of our LEARN network. The experimental results with our proposed LEARN network produces a superior performance with the well-known Mayo Clinic low-dose challenge data set relative to the several state-of-the-art methods, in terms of artifact reduction, feature preservation, and computational speed. This is consistent to our insight that because all the regularization terms and parameters used in the iterative reconstruction are now learned from the training data, our LEARN network utilizes application-oriented knowledge more effectively and recovers underlying images more favorably than competing algorithms. Also, the number of layers in the LEARN network is only 50, reducing the computational complexity of typical iterative algorithms by orders of magnitude.

Physics Model-Based Scatter Correction in Multi-Source Interior Computed Tomography

Multi-source interior computed tomography (CT) has a great potential to provide ultra-fast and organ-oriented imaging at low radiation dose. However, X-ray cross scattering from multiple simultaneously activated X-ray imaging chains compromises imaging quality. Previously, we published two hardware-based scatter correction methods for multi-source interior CT. Here, we propose a software-based scatter correction method, with the benefit of no need for hardware modifications. The new method is based on a physics model and an iterative framework. The physics model was derived analytically, and was used to calculate X-ray scattering signals in both forward direction and cross directions in multi-source interior CT. The physics model was integrated to an iterative scatter correction framework to reduce scatter artifacts. The method was applied to phantom data from both Monte Carlo simulations and physical experimentation that were designed to emulate the image acquisition in a multi-source interior CT architecture recently proposed by our team. The proposed scatter correction method reduced scatter artifacts significantly, even with only one iteration. Within a few iterations, the reconstructed images fast converged toward the "scatter-free" reference images. After applying the scatter correction method, the maximum CT number error at the region-of-interests (ROIs) was reduced to 46 HU in numerical phantom dataset and 48 HU in physical phantom dataset respectively, and the contrast-noise-ratio at those ROIs increased by up to 44.3% and up to 19.7%, respectively. The proposed physics model-based iterative scatter correction method could be useful for scatter correction in dual-source or multi-source CT.

Swinging multi-source industrial CT systems for aperiodic dynamic imaging

The goal of this paper is to develop a new architecture for industrial computed tomography (ICT) aiming at dynamically imaging an aperiodic changing object. We propose a data acquisition approach with multiple x-ray source/detector pairs targeting a continuously changeable object with corresponding timeframes. In this named swinging multi-source CT (SMCT) structure, each source and its associated detector swing forth and back within a certain angle for CT scanning. In the SMCT system design, we utilize a circular journal bearing based setup to replace the normal CT slip ring by weakening the scanning speed requirement. Inspired by the prior image constrained compressed sensing (PICCS) algorithm, we apply a modified PICCS algorithm for the SMCT (SM-PICCS). Our numerical simulation and realistic specimen experiment studies demonstrate the feasibility of the proposed approach.

Image quality in coronary CT angiography: challenges and technical solutions

Multidetector CT angiography (CTA) has become a widely accepted examination for non-invasive evaluation of the heart and coronary arteries. Despite its ongoing success and worldwide clinical implementation, it remains an often-challenging procedure in which image quality, and hence diagnostic value, is determined by both technical and patient-related factors. Thorough knowledge of these factors is important to obtain high-quality examinations. In this review, we discuss several key elements that may adversely affect coronary CTA image quality as well as potential measures that can be taken to mitigate their impact. In addition, several recent vendor-specific advances and future directions to improve image quality are discussed.

X-ray scatter correction for multi-source interior computed tomography

PURPOSE

The schemes of multi-source interior computed tomography (CT) have shown promise for ultra-fast, organ-oriented, and low-dose dynamic imaging. Besides forward scattering, x-ray cross scattering from multiple x-ray sources activated simultaneously can further degrade image quality. Here, we investigate the overall x-ray scattering artifact in a recently proposed multi-source interior CT architecture, and present two methods for scatter correction.

METHODS

Compared to single-source global CT, scattering in multi-source interior CT architecture is affected by two new factors: cross scattering from simultaneously activated multiple x-ray sources and region-of-interest (ROI) oriented interior CT mode. The scatter artifact in the multi-source interior CT architecture was evaluated through both numerical simulation and physical experimentation, and compared to that from conventional single-source global CT. Monte Carlo simulation was conducted with a modified numerical CATphan^® 600 phantom. Physical experiments were performed in an in-house developed CT imaging platform with a custom-built phantom. The simulation and experiments were carried out on the single-source CT architecture and the multi-source CT architecture, respectively in the global CT mode and the interior CT mode for comparison. To correct the scattering artifact, two new methods were presented. The first is a beam-stopper-array (BSA)-based method, which enables an online correction of forward scattering and cross scattering simultaneously. The second is a source-trigger-sequence (STS)-based method dedicated to cross-scatter correction. It enables on-the-fly measurements of the cross scattering signals at a few pre-selected views. The CT image quality was quantitatively evaluated in terms of contrast-to-noise ratio (CNR) and CT number deviation before and after the scatter correction.

RESULTS

X-ray cross scattering degraded image quality in both the simulation and experiments. Before the scatter correction, the multi-source interior CT mode yielded a reduction of CNR at the ROIs by up to 68.5% and 50.7% in the simulation and experiments, respectively. The stationary BSA-based method significantly improved CNR and CT number accuracy in the images from multi-source interior CT mode, by reducing the negative effects from both forward scattering and cross scattering. The STS-based method enabled multi-source interior CT mode to provide comparable image quality to that with the single-source interior CT mode, by correcting the artifact from cross scattering. The remaining forward scattering artifact can be corrected with the fast adaptive scatter kernel superposition (FASKS) technique. With the proposed scatter correction methods, the CT number error at the ROIs was reduced to less than 37 HU in both simulation and experiments, respectively.

CONCLUSIONS

Cross scattering, in addition to forward scattering, can cause significant image quality degradation in the multi-source interior CT architecture. However, image quality can be significantly improved with the proposed scatter correction methods.

Vision 20/20: Single photon counting x-ray detectors in medical imaging

Photon counting detectors (PCDs) with energy discrimination capabilities have been developed for medical x-ray computed tomography (CT) and x-ray (XR) imaging. Using detection mechanisms that are completely different from the current energy integrating detectors and measuring the material information of the object to be imaged, these PCDs have the potential not only to improve the current CT and XR images, such as dose reduction, but also to open revolutionary novel applications such as molecular CT and XR imaging. The performance of PCDs is not flawless, however, and it seems extremely challenging to develop PCDs with close to ideal characteristics. In this paper, the authors offer our vision for the future of PCD-CT and PCD-XR with the review of the current status and the prediction of (1) detector technologies, (2) imaging technologies, (3) system technologies, and (4) potential clinical benefits with PCDs.

The feasibility of an inverse geometry CT system with stationary source arrays

PURPOSE

Inverse geometry computed tomography (IGCT) has been proposed as a new system architecture that combines a small detector with a large, distributed source. This geometry can suppress cone-beam artifacts, reduce scatter, and increase dose efficiency. However, the temporal resolution of IGCT is still limited by the gantry rotation time. Large reductions in rotation time are in turn difficult due to the large source array and associated power electronics. We examine the feasibility of using stationary source arrays for IGCT in order to achieve better temporal resolution. We anticipate that multiple source arrays are necessary, with each source array physically separated from adjacent ones.

METHODS

Key feasibility issues include spatial resolution, artifacts, flux, noise, collimation, and system timing clashes. The separation between the different source arrays leads to missing views, complicating reconstruction. For the special case of three source arrays, a two-stage reconstruction algorithm is used to estimate the missing views. Collimation is achieved using a rotating collimator with a small number of holes. A set of equally spaced source spots are designated on the source arrays, and a source spot is energized when a collimator hole is aligned with it. System timing clashes occur when multiple source spots are scheduled to be energized simultaneously. We examine flux considerations to evaluate whether sufficient flux is available for clinical applications.

RESULTS

The two-stage reconstruction algorithm suppresses cone-beam artifacts while maintaining resolution and noise characteristics comparable to standard third generation systems. The residual artifacts are much smaller in magnitude than the cone-beam artifacts eliminated. A mathematical condition is given relating collimator hole locations and the number of virtual source spots for which system timing clashes are avoided. With optimization, sufficient flux may be achieved for many clinical applications.

CONCLUSIONS

IGCT with stationary source arrays could be an imaging platform potentially capable of imaging a complete 16-cm thick volume within a tenth of a second.

The meaning of interior tomography

The classic imaging geometry for computed tomography is for the collection of un-truncated projections and the reconstruction of a global image, with the Fourier transform as the theoretical foundation that is intrinsically non-local. Recently, interior tomography research has led to theoretically exact relationships between localities in the projection and image spaces and practically promising reconstruction algorithms. Initially, interior tomography was developed for x-ray computed tomography. Then, it was elevated to have the status of a general imaging principle. Finally, a novel framework known as 'omni-tomography' is being developed for a grand fusion of multiple imaging modalities, allowing tomographic synchrony of diversified features.

Tight-frame based iterative image reconstruction for spectral breast CT

PURPOSE

To investigate tight-frame based iterative reconstruction (TFIR) technique for spectral breast computed tomography (CT) using fewer projections while achieving greater image quality.

METHODS

The experimental data were acquired with a fan-beam breast CT system based on a cadmium zinc telluride photon-counting detector. The images were reconstructed with a varying number of projections using the TFIR and filtered backprojection (FBP) techniques. The image quality between these two techniques was evaluated. The image's spatial resolution was evaluated using a high-resolution phantom, and the contrast to noise ratio (CNR) was evaluated using a postmortem breast sample. The postmortem breast samples were decomposed into water, lipid, and protein contents based on images reconstructed from TFIR with 204 projections and FBP with 614 projections. The volumetric fractions of water, lipid, and protein from the image-based measurements in both TFIR and FBP were compared to the chemical analysis.

RESULTS

The spatial resolution and CNR were comparable for the images reconstructed by TFIR with 204 projections and FBP with 614 projections. Both reconstruction techniques provided accurate quantification of water, lipid, and protein composition of the breast tissue when compared with data from the reference standard chemical analysis.

CONCLUSIONS

Accurate breast tissue decomposition can be done with three fold fewer projection images by the TFIR technique without any reduction in image spatial resolution and CNR. This can result in a two-third reduction of the patient dose in a multislit and multislice spiral CT system in addition to the reduced scanning time in this system.

Towards high-resolution synchrotron radiation imaging with statistical iterative reconstruction

Synchrotron radiation (SR) X-ray micro-computed tomography (CT) is an effective imaging modality for high-resolution investigation of small objects, with several applications in medicine, biology and industry. However, the limited size of the detector field of view (FOV) restricts the sample dimensions to only a few millimeters. When the sample size is larger than the FOV, images reconstructed using conventional methods suffer from DC-shift and low-frequency artifacts. This classical problem is known as the local tomography or the interior problem. In this paper, a statistical iterative reconstruction method is introduced to eliminate image artifacts resulting from the local tomography. The proposed method, which can be used in several SR imaging applications, enables high-resolution SR imaging with superior image quality compared with conventional methods. Real data obtained from different SR micro-CT applications are used to evaluate the proposed method. Results indicate a noteworthy quality improvement in the image reconstructed from the local tomography measurements.

Dual-dictionary learning-based iterative image reconstruction for spectral computed tomography application

In this study, we investigated the effectiveness of a novel iterative reconstruction (IR) method coupled with dual-dictionary learning (DDL) for image reconstruction in a dedicated breast computed tomography (CT) system based on a cadmium-zinc-telluride (CZT) photon-counting detector and compared it to the filtered-back-projection (FBP) method with the ultimate goal of reducing the number of projections necessary for reconstruction without sacrificing the image quality. Postmortem breast samples were scanned in a fan-beam CT system and were reconstructed from 100 to 600 projections with both IR and FBP methods. The contrast-to-noise ratio (CNR) between the glandular and adipose tissues of the postmortem breast samples was calculated to compare the quality of images reconstructed from IR and FBP. The spatial resolution of the two reconstruction techniques was evaluated using aluminum (Al) wires with diameters of 643, 813, 1020, 1290 and 1630 µm in a plastic epoxy resin phantom with a diameter of 13 cm. Both the spatial resolution and the CNR were improved with IR compared to FBP for the images reconstructed from the same number of projections. In comparison with FBP reconstruction, the CNR was improved from 3.4 to 7.5 by using the IR method with six-fold fewer projections while maintaining the same spatial resolution. The study demonstrated that the IR method coupled with DDL could significantly reduce the required number of projections for a CT reconstruction compared to the FBP method while achieving a much better CNR and maintaining the same spatial resolution. From this, the radiation dose and scanning time can potentially be reduced by a factor of approximately 6 by using this IR method for image reconstruction in a CZT-based breast CT system.

Interior tomography with continuous singular value decomposition

The long-standing interior problem has important mathematical and practical implications. The recently developed interior tomography methods have produced encouraging results. A particular scenario for theoretically exact interior reconstruction from truncated projections is that there is a known sub-region in the ROI. In this paper, we improve a novel continuous singular value decomposition (SVD) method for interior reconstruction assuming a known sub-region. First, two sets of orthogonal eigen-functions are calculated for the Hilbert and image spaces respectively. Then, after the interior Hilbert data are calculated from projection data through the ROI, they are projected onto the eigen-functions in the Hilbert space, and an interior image is recovered by a linear combination of the eigen-functions with the resulting coefficients. Finally, the interior image is compensated for the ambiguity due to the null space utilizing the prior sub-region knowledge. Experiments with simulated and real data demonstrate the advantages of our approach relative to the POCS type interior reconstructions.

Towards omni-tomography--grand fusion of multiple modalities for simultaneous interior tomography

We recently elevated interior tomography from its origin in computed tomography (CT) to a general tomographic principle, and proved its validity for other tomographic modalities including SPECT, MRI, and others. Here we propose “omni-tomography”, a novel concept for the grand fusion of multiple tomographic modalities for simultaneous data acquisition in a region of interest (ROI). Omni-tomography can be instrumental when physiological processes under investigation are multi-dimensional, multi-scale, multi-temporal and multi-parametric. Both preclinical and clinical studies now depend on in vivo tomography, often requiring separate evaluations by different imaging modalities. Over the past decade, two approaches have been used for multimodality fusion: Software based image registration and hybrid scanners such as PET-CT, PET-MRI, and SPECT-CT among others. While there are intrinsic limitations with both approaches, the main obstacle to the seamless fusion of multiple imaging modalities has been the bulkiness of each individual imager and the conflict of their physical (especially spatial) requirements. To address this challenge, omni-tomography is now unveiled as an emerging direction for biomedical imaging and systems biomedicine.

Completeness map evaluation demonstrated with candidate next-generation cardiac CT architectures

PURPOSE

In this report, the authors introduce the general concept of the completeness map, as a means to evaluate the completeness of data acquired by a given CT system design (architecture and scan mode). They illustrate the utility of completeness map by applying the completeness map concept to a number of candidate CT system designs, as part of a study to advance the state-of-the-art in cardiac CT.

METHODS

In order to optimally reconstruct a point within a volume of interest (VOI), the Radon transform on all possible planes through that point should be measured. The authors quantified the extent to which this ideal condition is satisfied for the entire image volume. They first determined a Radon completeness number for each point in the VOI, as the percentage of possible planes that is actually measured. A completeness map is then defined as a 3D matrix of the completeness numbers for the entire VOI. The authors proposed algorithms to analyze the projection datasets in Radon space and compute the completeness number for a fixed point and apply these algorithms to various architectures and scan modes that they are evaluating. In this report, the authors consider four selected candidate architectures, operating with different scan modes, for a total of five system design alternatives. Each of these alternatives is evaluated using completeness map.

RESULTS

If the detector size and cone angle are large enough to cover the entire cardiac VOI, a single-source circular scan can have ≥99% completeness over the entire VOI. However, only the central z-slice can be exactly reconstructed, which corresponds to 100% completeness. For a typical single-source architecture, if the detector is limited to an axial dimension of 40 mm, a helical scan needs about five rotations to form an exact reconstruction region covering the cardiac VOI, while a triple-source helical scan only requires two rotations, leading to a 2.5x improvement in temporal resolution. If the source and detector of an inverse-geometry (IGCT) system have the same axial extent, and the spacing of source points in the axial and transaxial directions is sufficiently small, the IGCT can also form an exact reconstruction region for the cardiac VOI. If the VOI can be covered by the x-ray beam in any view, a composite-circling scan can generate an exact reconstruction region covering the VOI.

CONCLUSIONS

The completeness map evaluation provides useful information for selecting the next-generation cardiac CT system design. The proposed completeness map method provides a practical tool for analyzing complex scanning trajectories, where the theoretical image quality for some complex system designs is impossible to predict, without yet-undeveloped reconstruction algorithms.

Practical interior tomography with radial Hilbert filtering and a priori knowledge in a small round area

PURPOSES

Interior tomography problem can be solved using the so-called differentiated backprojection-projection onto convex sets (DBP-POCS) method, which requires a priori knowledge within a small area interior to the region of interest (ROI) to be imaged. In theory, the small area wherein the a priori knowledge is required can be in any shape, but most of the existing implementations carry out the Hilbert filtering either horizontally or vertically, leading to a vertical or horizontal strip that may be across a large area in the object. In this work, we implement a practical DBP-POCS method with radial Hilbert filtering and thus the small area with the a priori knowledge can be roughly round (e.g., a sinus or ventricles among other anatomic cavities in human or animal body). We also conduct an experimental evaluation to verify the performance of this practical implementation.

METHODS

We specifically re-derive the reconstruction formula in the DBP-POCS fashion with radial Hilbert filtering to assure that only a small round area with the a priori knowledge be needed (namely radial DBP-POCS method henceforth). The performance of the practical DBP-POCS method with radial Hilbert filtering and a priori knowledge in a small round area is evaluated with projection data of the standard and modified Shepp-Logan phantoms simulated by computer, followed by a verification using real projection data acquired by a computed tomography (CT) scanner.

RESULTS

The preliminary performance study shows that, if a priori knowledge in a small round area is available, the radial DBP-POCS method can solve the interior tomography problem in a more practical way at high accuracy.

CONCLUSIONS

In comparison to the implementations of DBP-POCS method demanding the a priori knowledge in horizontal or vertical strip, the radial DBP-POCS method requires the a priori knowledge within a small round area only. Such a relaxed requirement on the availability of a priori knowledge can be readily met in practice, because a variety of small round areas (e.g., air-filled sinuses or fluid-filled ventricles among other anatomic cavities) exist in human or animal body. Therefore, the radial DBP-POCS method with a priori knowledge in a small round area is more feasible in clinical and preclinical practice.

High-order total variation minimization for interior SPECT

Recently, we developed an approach for solving the computed tomography (CT) interior problem based on the high-order TV (HOT) minimization, assuming that a region-of-interest (ROI) is piecewise polynomial. In this paper, we generalize this finding from the CT field to the single-photon emission computed tomography (SPECT) field, and prove that if an ROI is piecewise polynomial, then the ROI can be uniquely reconstructed from the SPECT projection data associated with the ROI through the HOT minimization. Also, we propose a new formulation of HOT, which has an explicit formula for any n-order piecewise polynomial function, while the original formulation has no explicit formula for n ≥ 2. Finally, we verify our theoretical results in numerical simulation, and discuss relevant issues.

Image reconstruction from limited angle projections collected by multisource interior x-ray imaging systems

A multisource x-ray interior imaging system with limited angle scanning is investigated to study the possibility of building an ultrafast micro-CT for dynamic small animal imaging, and two methods are employed to perform interior reconstruction from a limited number of projections collected by the multisource interior x-ray system. The first is total variation minimization with the steepest descent search (TVM-SD) and the second is total difference minimization with soft-threshold filtering (TDM-STF). Comprehensive numerical simulations and animal studies are performed to validate the associated reconstructed methods and demonstrate the feasibility and application of the proposed system configuration. The image reconstruction results show that both of the two reconstruction methods can significantly improve the image quality and the TDM-SFT is slightly superior to the TVM-SD. Finally, quantitative image analysis shows that it is possible to make an ultrafast micro-CT using a multisource interior x-ray system scheme combined with the state-of-the-art interior tomography.

Newer CT applications and their alternatives: what is appropriate in children?

Innovations in image acquisition and reconstruction technologies have greatly expanded the range of CT applications available in the routine clinical setting. CT images of sub-millimeter resolution can now be acquired of entire body regions in a few seconds or even sub-second time, allowing depiction of fine anatomical detail uncompromised by motion artifact. With sophisticated visualization software, image data can be processed into multiplanar, volume-rendered, cine and other formats to better display anatomical abnormalities and facilitate newer applications such as CT angiography, enterography, urography, tracheobronchography and cardiac CT. Newer applications including dual-energy material decomposition CT are furthering the transition of CT from a purely morphological to a combined anatomical, functional and metabolic imaging technique. These newer applications have largely been pioneered in adult populations, and heightened concern of the risk of carcinogenesis from ionizing radiation tempers dissemination of their use in children. Similar information can often be gleaned from alternative imaging modalities without ionizing radiation exposure, such as MRI and US, and what is most appropriate in children will depend on relative diagnostic efficacy, cost, availability and local expertise.

Robust principal component analysis-based four-dimensional computed tomography

The purpose of this paper for four-dimensional (4D) computed tomography (CT) is threefold. (1) A new spatiotemporal model is presented from the matrix perspective with the row dimension in space and the column dimension in time, namely the robust PCA (principal component analysis)-based 4D CT model. That is, instead of viewing the 4D object as a temporal collection of three-dimensional (3D) images and looking for local coherence in time or space independently, we perceive it as a mixture of low-rank matrix and sparse matrix to explore the maximum temporal coherence of the spatial structure among phases. Here the low-rank matrix corresponds to the 'background' or reference state, which is stationary over time or similar in structure; the sparse matrix stands for the 'motion' or time-varying component, e.g., heart motion in cardiac imaging, which is often either approximately sparse itself or can be sparsified in the proper basis. Besides 4D CT, this robust PCA-based 4D CT model should be applicable in other imaging problems for motion reduction or/and change detection with the least amount of data, such as multi-energy CT, cardiac MRI, and hyperspectral imaging. (2) A dynamic strategy for data acquisition, i.e. a temporally spiral scheme, is proposed that can potentially maintain similar reconstruction accuracy with far fewer projections of the data. The key point of this dynamic scheme is to reduce the total number of measurements, and hence the radiation dose, by acquiring complementary data in different phases while reducing redundant measurements of the common background structure. (3) An accurate, efficient, yet simple-to-implement algorithm based on the split Bregman method is developed for solving the model problem with sparse representation in tight frames.

Statistical interior tomography

This paper presents a statistical interior tomography (SIT) approach making use of compressed sensing (CS) theory. With the projection data modeled by the Poisson distribution, an objective function with a total variation (TV) regularization term is formulated in the maximization of a posteriori (MAP) framework to solve the interior problem. An alternating minimization method is used to optimize the objective function with an initial image from the direct inversion of the truncated Hilbert transform. The proposed SIT approach is extensively evaluated with both numerical and real datasets. The results demonstrate that SIT is robust with respect to data noise and down-sampling, and has better resolution and less bias than its deterministic counterpart in the case of low count data.

Compressive sampling based interior reconstruction for dynamic carbon nanotube micro-CT

In the computed tomography (CT) field, one recent invention is the so-called carbon nanotube (CNT) based field emission x-ray technology. On the other hand, compressive sampling (CS) based interior tomography is a new innovation. Combining the strengths of these two novel subjects, we apply the interior tomography technique to local mouse cardiac imaging using respiration and cardiac gating with a CNT based micro-CT scanner. The major features of our method are: (1) it does not need exact prior knowledge inside an ROI; and (2) two orthogonal scout projections are employed to regularize the reconstruction. Both numerical simulations and in vivo mouse studies are performed to demonstrate the feasibility of our methodology.