Notice of Removal: Fourier Diffusion Models: A Method to Control MTF and NPS in Score-Based Stochastic Image Generation

Removed.

Tunable neural networks for CT image formation

Optimization of CT image quality typically involves balancing variance and bias. In traditional filtered back-projection, this trade-off is controlled by the filter cutoff frequency. In model-based iterative reconstruction, the regularization strength parameter often serves the same function. Deep neural networks (DNNs) typically do not provide this tunable control over output image properties. Models are often trained to minimize the expected mean squared error, which penalizes both variance and bias in image outputs but does not offer any control over the trade-off between the two. We propose a method for controlling the output image properties of neural networks with a new loss function called weighted covariance and bias (WCB). Our proposed method uses multiple noise realizations of the input images during training to allow for separate weighting matrices for the variance and bias penalty terms. Moreover, we show that tuning these weights enables targeted penalization of specific image features with spatial frequency domain penalties. To evaluate our method, we present a simulation study using digital anthropomorphic phantoms, physical simulation of CT measurements, and image formation with various algorithms. We show that the WCB loss function offers a greater degree of control over trade-offs between variance and bias, whereas mean-squared error provides only one specific image quality configuration. We also show that WCB can be used to control specific image properties including variance, bias, spatial resolution, and the noise correlation of neural network outputs. Finally, we present a method to optimize the proposed weights for a spiculated lung nodule shape discrimination task. Our results demonstrate this new image quality can control the image properties of DNN outputs and optimize image quality for task-specific performance.

Deep Learning CT Image Restoration using System Blur Models

Restoration of images contaminated by blur is an important processing tool across modalities including computed tomography where the blur induced by various system factors can be complex with dependencies on acquisition and reconstruction protocol, and even be patient-dependent. In many cases, such a blur can be modeled and predicted with high accuracy providing an important input to a classical deconvolution approach. While traditional deblurring methods tend to be highly noise magnifying, deep learning approaches have the potential to improve upon classic performance limits. However, most network architectures base their restoration on data inputs alone without knowledge of the system blur. In this work, we explore a deep learning approach that takes both image inputs as well as information that characterizes the system blur to combine modeling and deep learning approaches. We apply the approach to CT image restoration and compare with an image-only deep learning approach. We find that inclusion of the system blur model improves deblurring performance - suggesting the potential power of the combined modeling and deep learning technique.

Task-Driven CT Image Quality Optimization for Low-Contrast Lesion Detectability with Tunable Neural Networks

Low-contrast lesions are difficult to detect in noisy low-dose CT images. Improving CT image quality for this detection task has the potential to improve diagnostic accuracy and patient outcomes. In this work, we use tunable neural networks for CT image restoration with a hyperparameter to control the variance/bias tradeoff. We use clinical images from a super-high-resolution normal-dose CT scan to synthesize low-contrast low-dose CT images for supervised training of deep learning CT reconstruction models. Those models are trained using with multiple noise realizations so that variance and bias can be penalized separately. We use a training loss function with one hyperparameter called the denoising level, which controls the variance/bias tradeoff. Finally, we evaluate the CT image quality to find the optimal denoising level for low-contrast lesion detectability. We evaluate performance using a shallow neural network model classification model to represent a suboptimal image observer. Our results indicate that the optimal networks for low-contrast lesion detectability are those that prioritize bias reduction rather than mean-squared error, which demonstrates the potential clinical benefit of our proposed tunable neural networks.

Design Optimization of Spatial-Spectral Filters for Cone-Beam CT Material Decomposition

Spectral CT has shown promise for high-sensitivity quantitative imaging and material decomposition. This work presents a new device called a spatial-spectral filter (SSF) which consists of a tiled array of filter materials positioned near the x-ray source that is used to modulate the spectral shape of the x-ray beam. The filter is moved to obtain projection data that is sparse in each spectral channel. To process this sparse data, we employ a one-step direct model-based material decomposition (MBMD) to reconstruct basis material density images directly from the SSF CT data. To evaluate different possible SSF designs, we define a new Fisher-information-based predictive image quality metric called separability index which characterizes the ability of a spectral CT system to distinguish between the signals from two or more materials. This spectral CT performance metric can be used to optimize spectral CT system design. We conducted simulation-based design optimization study to find optimized combinations of filter materials, filter thicknesses, filter widths, and source settings. Finally, we present MBMD results using simulated SSF CT measurements from the optimized designs to demonstrate the ability to reconstruct basis material density images and to show the benefits of the optimized designs. Our results indicate that optimizing SSF CT for separability leads to high-performance at material discrimination tasks.

Model-based three-material decomposition in dual-energy CT using the volume conservation constraint

Objective. We develop a model-based optimization algorithm for ‘one-step’ dual-energy (DE) CT decomposition of three materials directly from projection measurements. Approach. Since the three-material problem is inherently undetermined, we incorporate the volume conservation principle (VCP) as a pair of equality and nonnegativity constraints into the objective function of the recently reported model-based material decomposition (MBMD). An optimization algorithm (constrained MBMD, CMBMD) is derived that utilizes voxel-wise separability to partition the volume into a VCP-constrained region solved using interior-point iterations, and an unconstrained region (air surrounding the object, where VCP is violated) solved with conventional two-material MBMD. Constrained MBMD (CMBMD) is validated in simulations and experiments in application to bone composition measurements in the presence of metal hardware using DE cone-beam CT (CBCT). A kV-switching protocol with non-coinciding low- and high-energy (LE and HE) projections was assumed. CMBMD with decomposed base materials of cortical bone, fat, and metal (titanium, Ti) is compared to MBMD with (i) fat-bone and (ii) fat-Ti bases. Main results. Three-material CMBMD exhibits a substantial reduction in metal artifacts relative to the two-material MBMD implementations. The accuracies of cortical bone volume fraction estimates are markedly improved using CMBMD, with ∼5–10× lower normalized root mean squared error in simulations with anthropomorphic knee phantoms (depending on the complexity of the metal component) and ∼2–2.5× lower in an experimental test-bench study. Significance. In conclusion, we demonstrated one-step three-material decomposition of DE CT using volume conservation as an optimization constraint. The proposed method might be applicable to DE applications such as bone marrow edema imaging (fat-bone-water decomposition) or multi-contrast imaging, especially on CT/CBCT systems that do not provide coinciding LE and HE ray paths required for conventional projection-domain DE decomposition.

Local Linearity Analysis of Deep Learning CT Denoising Algorithms

The rapid development of deep-learning methods in medical imaging has called for an analysis method suitable for non-linear and data-dependent algorithms. In this work, we investigate a local linearity analysis where a complex neural network can be represented as piecewise linear systems. We recognize that a large number of neural networks consists of alternating linear layers and rectified linear unit (ReLU) activations, and are therefore strictly piecewise linear. We investigated the extent of these locally linear regions by gradually adding perturbations to an operating point. For this work, we explored perturbations based on image features of interest, including lesion contrast, background, and additive noise. We then developed strategies to extend these strictly locally linear regions to include neighboring linear regions with similar gradients. Using these approximately linear regions, we applied singular value decomposition (SVD) analysis to each local linear system to investigate and explain the overall nonlinear and data-dependent behaviors of neural networks. The analysis was applied to an example CT denoising algorithm trained on thorax CT scans. We observed that the strictly local linear regions are highly sensitive to small signal perturbations. Over a range of lesion contrast from 0.007 to 0.04 mm^-1, there is a total of 33992 linear regions. The Jacobians are also shift-variant. However, the Jacobians of neighboring linear regions are very similar. By combining linear regions with similar Jacobians, we narrowed down the number of approximately linear regions to four over lesion contrast from 0.001 to 0.08 mm^-1. The SVD analysis to different linear regions revealed denoising behavior that is highly dependent on the background intensity. Analysis further identified greater amount of noise reduction in uniform regions compared to lesion edges. In summary, the local linearity analysis framework we proposed has the potential for us to better characterize and interpret the non-linear and data-dependent behaviors of neural networks.

Tunable Neural Networks for Multi-Material Image Formation from Spectral CT Measurements

Quantitative estimation of multi-material density images is an important goal for Spectral CT imaging. However, material decomposition is a poorly-conditioned nonlinear inverse problem. Maximum-likelihood model-based material decomposition results in very noisy material density image estimates. One increasingly popular strategy for noise reduction is to apply deep neural networks for multi-material image formation. The most common loss function is mean squared error with respect to supervised target images such as ground truth or higher-dose cases. However, we believe that the mean-squared error loss function has several issues for multi-material image formation. In this work, we present a new loss function which includes multiple noise realizations with separate weights on covariance and bias for joint denoising of all material bases. By modulating these weights, it is possible to tune the image quality of neural network output images. To demonstrate our proposed approach, we conducted a simulation of a water/calcium/gadolinium spectral CT imaging scenario using a deep neural network for multi-material image denoising. Our results show that by changing the weights of our proposed loss function, it is possible to control the tradeoff between variance and bias for individual materials as well as the control over the bias coupling between materials.

Performance Assessment Framework for Neural Network Denoising

The proliferation of deep learning image processing calls for a quantitative image quality assessment framework that is suitable for nonlinear, data-dependent algorithms. In this work, we propose a method to systematically evaluate the system and noise responses such that the nonlinear transfer properties can be mapped out. The method involves sampling of lesion perturbations as a function of size, contrast, as well as clinically relevant features such as shape and texture that may be important for diagnosis. We embed the perturbations in backgrounds of varying attenuation levels, noise magnitude and correlation that are associated with different patient anatomies and imaging protocols. The range of system and noise response are further used to evaluate performance for clinical tasks such as signal detection and classification. We performed the assessment for an example CNN-denoising algorithm for low does lung CT screening. The system response of the CNN-denoising algorithm exhibits highly nonlinear behavior where both contrast and higher order lesion features such as spiculated boundaries are not reliably represented for lesions perturbations with small size and low contrast. The noise properties are potentially highly nonstationary, and should be assumed to be the same between the signal-present and signal-absent images. Furthermore, we observer a high degree dependency of both system and noise response on the background attenuation levels. Inputs around zeros are effectively imposed a non-negativity constraint; transfer properties for higher background levels are highly variable. For a detection task, CNN-denoised images improved detectability index by 16-18% compared to low dose CT inputs. For classification task between spiculated and smooth lesions, CNN-denoised images result in a much larger improvement up to 50%. The performance assessment framework propose in this work can systematically map out the nonlinear transfer functions for deep learning algorithms and can potentially enable robust deployment of such algorithms in medical imaging applications.

Data-dependent Nonlinearity Analysis in CT Denoising CNNs

Recent years have seen the increasing application of deep learning methods in medical imaging formation, processing, and analysis. These methods take advantage of the flexibility of nonlinear neural network models to encode information and features in ways that can outperform conventional approaches. However, because of the nonlinear nature of this processing, images formed by neural networks have properties that are highly data-dependent and difficult to analyze. In particular, the generalizability and robustness of these approaches can be difficult to ascertain. In this work, we analyze a class of neural networks that use only piece-wise linear activation functions. This class of networks can be represented by locally linear systems where the linear properties are highly data-dependent - allowing, for example, estimation of noise in image output via standard propagation methods. We propose a nonlinearity index metric that quantifies the fidelity of a local linear approximation of trained models based on specific input data. We applied this analysis to three example CT denoising CNNs to analytically predict the noise properties in the output images. We found that the proposed nonlinearity metric highly correlates with the accuracy of noise predictions. The analysis proposed in this work provides theoretical understanding of the nonlinear behavior of neural networks and enables performance prediction and quantitation under certain conditions.

Control of Variance and Bias in CT Image Processing with Variational Training of Deep Neural Networks

Optimization of CT image quality typically involves balancing noise and bias. In filtered back-projection, this trade-off is controlled by the particular filter and cutoff frequency. In penalized-likelihood iterative reconstruction, the penalty weight serves the same function. Deep neural networks typically do not provide this tuneable control over output image properties. Models are often trained to minimize mean squared error which penalizes both variance and bias in image outputs but does not offer any control over the trade-off between the two. In this work, we propose a method for controlling the output image properties of neural networks with a new loss function called weighted covariance and bias (WCB). Our proposed method includes separate weighting parameters to control the relative importance of noise or bias reduction. Moreover, we show that tuning these weights enables targeted penalization of specific image features (e.g. spatial frequencies). To evaluate our method, we present a simulation study using digital anthropormorphic phantoms, physical simulation of non-ideal CT data, and image formation with various algorithms. We show that WCB offers a greater degree of control over trade-offs between variance and bias whereas MSE has only one configuration. We also show that WCB can be used to control specific image properties including variance, bias, spatial resolution, and the noise correlation of neural network outputs. Finally, we present a method to optimize the proposed weights for stimulus detectability. Our results demonstrate the potential for this new capability to control the image properties of DNN outputs and optimize image quality for the task-specific applications.

Manifold Reconstruction of Differences: A Model-Based Iterative Statistical Estimation Algorithm With a Data-Driven Prior

Manifold learning using deep neural networks been shown to be an effective tool for building sophisticated prior image models that can be applied to noise reduction in low-close CT. A manifold is a low-dimensional space that captures most of the variation in a class of data (e.g. chest CT images). This nonlinear reduction in dimensionality is one way to build up a sophisticated model of the features and structures present in image data. This nonlinear dimensionality reduction tends to learn features associated with the signal rather than the noise when provided with a large training dataset. However, the internal workings operation are typically not easy to understand. The results can be highly nonlinear and object-dependent. After training the model is fixed and during reconstruction is typically no check for fitness between the image estimates and the measured data. We propose a new iterative CT reconstruction algorithm, called Manifold Reconstruction of Differences (MRoD), which combines physical and statistical models with a data-driven prior based on manifold learning. The MRoD algorithm involves estimating a manifold component, approximating common features among all patients, and the difference component which has the freedom to fit the measured data. By applying a sparsity-promoting penalty to the difference image rather than a hard constraint to the manifold, the MRoD algorithm is able to reconstruct features which are not present in the training data. The difference component itself may be independently useful. While the manifold captures typical patient features (e.g. healthy anatomy), the difference image highlights patient-specific elements (e.g. pathology). In this work, we present a description of an optimization framework which combines trained manifold-based modules with physical modules. We present a simulation study using anthropomorphic lung data showing that the MRoD algorithm can both isolate differences between a particular patient and the typical distribution, but also provide significant noise reduction with less bias than a typical penalized likelihood estimator in composite manifold plus difference reconstructions.

Spectral CT using a fine grid structure and varying x-ray incidence angle

PURPOSE

Interest in spectral computed tomography (CT) for diagnostics and therapy evaluation has been growing. Data acquisitions with distinct spectral sensitivities provide the ability to discriminate multiple materials, quantitative density estimates, and reduced artifacts due to energy dependencies. We introduce a novel spectral CT concept that includes a fine-pitch grid structure for prefiltration of the x-ray beam.

METHODS

We develop physical models for grid designs and illustrate the basic operating principles wherein small angulations of the incident x rays results significant filtration and spectral shaping of the beam. We fabricate a prototype grid with tungsten lamellae. We compare x-ray spectra induced by this filter as a function of incidence angle in both simulation students and in physical measurements. The grid is also integrated onto a CT test bench where we scanned an iodinated phantom with clinically relevant concentrations (5, 10, 20, and 50 mgI/mL) to demonstrate the ability to perform spectral CT acquisitions and material decomposition.

RESULTS

X-ray spectrometer measurements reveal diverse and controllable spectral shaping with small angle changes that are in agreement with simulation studies. Critical angles where the characteristics of the induced spectrum changes dramatically are identified. Reconstructions of projection data for two angulations separated by 2° was reconstructed and material decomposition into iodine and water images shows good agreement with the known iodine concentrations.

CONCLUSIONS

This work demonstrates the feasibility of the grid-based approach to enable spectral CT data acquisitions and accurate material decompositions. On-going and future studies will investigate the potential of this novel concept as a relatively simple upgrade to standard energy-integrating CT.

High-resolution model-based material decomposition in dual-layer flat-panel CBCT

PURPOSE

Spectral CT uses energy-dependent measurements that enable material discrimination in addition to reconstruction of structural information. Flat-panel detectors (FPDs) have been widely used in dedicated and interventional systems to deliver high spatial resolution, volumetric cone-beam CT (CBCT) in compact and OR-friendly designs. In this work, we derive a model-based method that facilitates high-resolution material decomposition in a spectral CBCT system equipped with a prototype dual-layer FPD. Through high-fidelity modeling of multilayer detector, we seek to avoid resolution loss that is present in more traditional processing and decomposition approaches.

METHOD

A physical model for spectral measurements in dual-layer flat-panel CBCT is developed including layer-dependent differences in system geometry, spectral sensitivities, and detector blur (e.g., due to varied scintillator thicknesses). This forward model is integrated into a model-based material decomposition (MBMD) method based on minimization of a penalized weighted least-squared (PWLS) objective function. The noise and resolution performance of this approach was compared with traditional projection-domain decomposition (PDD) and image-domain decomposition (IDD) approaches as well as one-step MBMD with lower-fidelity models that use approximated geometry, projection interpolation, or an idealized system geometry without system blur model. Physical studies using high-resolution three-dimensional (3D)-printed water-iodine phantoms were conducted to demonstrate the high-resolution imaging performance of the compared decomposition methods in iodine basis images and synthetic monoenergetic images.

RESULTS

Physical experiments demonstrate that the MBMD methods incorporating an accurate geometry model can yield higher spatial resolution iodine basis images and synthetic monoenergetic images than PDD and IDD results at the same noise level. MBMD with blur modeling can further improve the spatial-resolution compared with the decomposition results obtained with IDD, PDD, and MBMD methods with lower-fidelity models. Using the MBMD without or with blur model can increase the absolute modulation at 1.75 lp/mm by 10% and 22% compared with IDD at the same noise level.

CONCLUSION

The proposed model-based material decomposition method for a dual-layer flat-panel CBCT system has demonstrated an ability to extend high-resolution performance through sophisticated detector modeling including the layer-dependent blur. The proposed work has the potential to not only facilitate high-resolution spectral CT in interventional and dedicated CBCT systems, but may also provide the opportunity to evaluate different flat-panel design trade-offs including multilayer FPDs with mismatched geometries, scintillator thicknesses, and spectral sensitivities.

A prototype spatial-spectral CT system for material decomposition with energy-integrating detectors

PURPOSE

Spectral CT has great potential for a variety of clinical applications due to improved tissue and material discrimination over conventional single-energy CT. Many clinical and preclinical spectral CT systems have two spectral channels enabling dual-energy CT. Strategies include split filtration, dual-layer detectors, photon-counting detectors, and kVp switching. The motivation for this work is the development of an x-ray source spectral modulation device with three or more spectral channels to enable high-sensitivity multi-material decomposition with energy-integrating detectors.

MATERIALS AND METHODS

We present spatial-spectral filters which are a new x-ray source modulation technology with the potential for additional channel diversity. The filtering device consists of an array of K-edge materials which divide the x-ray beam into spectrally varied beamlets. This design allows for an arbitrary number of spectral channels-trading off spatial and spectral information. We use a one-step model-based material decomposition (MBMD) algorithm to iteratively estimate material density images directly from the spatial-spectral CT data. In this work, we present a prototype spatial-spectral filter integrated with an x-ray CT test bench. The filter is composed of an array of tin, erbium, tantalum, and lead filter tiles which spatially modulate the system spectral sensitivity pattern. In a simulation study, we investigate the particular problem of mis-calibration between the data acquisition and the reconstruction model. With an understanding of the required model accuracy, we present a spectral calibration method to estimate the critical model parameters. To demonstrate feasibility of the spatial-spectral filter with a calibrated beamlet model, we collected a spatial-spectral CT scan of a multicontrast-enhanced phantom containing water, iodine, and gadolinium solutions.

RESULTS

With simulations, we show that material decomposition is possible with spatial-spectral-filtered CT data, and we demonstrate the importance of a well-calibrated physical model. We find a 50% increase in error for focal spot model mismatch of 0.27mm and gap width model mismatch of 16 mμ. With physical results, we demonstrate that the calibrated system model is in close agreement with the measured data, and that the reconstructed material density images match the ground truth concentrations for the multicontrast phantom. Empirical results indicate gadolinium density estimation had an error of 17-58% mostly due to a systematic constant bias of 0.30-0.60 mg/ml. Water density estimates are within 1% and iodine estimates are within 10% of ground truth.

CONCLUSION

These preliminary results demonstrate the potential of spatial-spectral filters to enable multicontrast imaging. Moreover, this device is compatible with energy-integrating detectors and so provides a feasible modification to enable spectral CT imaging with existing single-energy systems.

Model-based dual-energy tomographic image reconstruction of objects containing known metal components

Dual-energy (DE) decomposition has been adopted in orthopedic imaging to measure bone composition and visualize intraarticular contrast enhancement. One of the potential applications involves monitoring of callus mineralization for longitudinal assessment of fracture healing. However, fracture repair usually involves internal fixation hardware that can generate significant artifacts in reconstructed images. To address this challenge, we develop a novel algorithm that combines simultaneous reconstruction-decomposition using a previously reported method for model-based material decomposition (MBMD) augmented by the known-component (KC) reconstruction framework to mitigate metal artifacts. We apply the proposed algorithm to simulated DE data representative of a dedicated extremity cone-beam CT (CBCT) employing an x-ray unit with three vertically arranged sources. The scanner generates DE data with non-coinciding high- and low-energy projection rays when the central source is operated at high tube potential and the peripheral sources at low potential. The proposed algorithm was validated using a digital extremity phantom containing varying concentrations of Ca-water mixtures and Ti implants. Decomposition accuracy was compared to MBMD without the KC model. The proposed method suppressed metal artifacts and yielded estimated Ca concentrations that approached the reconstructions of an implant-free phantom for most mixture regions. In the vicinity of simple components, the errors of Ca density estimates obtained by incorporating KC in MBMD were ∼1.5-5× lower than the errors of conventional MBMD; for cases with complex implants, the errors were ∼3-5× lower. In conclusion, the proposed method can achieve accurate bone mineral density measurements in the presence of metal implants using non-coinciding DE projections acquired on a multisource CBCT system.

Grating-based Spectral CT using Small Angle X-ray Beam Deflections

Interest in spectral CT for diagnostics and therapy evaluation has been growing. Acquisitions of data from distinct energy spectra provide, among other advantages, quantitative density estimations for multiple materials. We introduce a novel spectral CT concept that includes a fine-pitch grating for prefiltration of the x-ray beam. The attenuation behavior of this grating changes significantly if x-rays are slightly angled in relation to the grating structures. To apply such an angle (i.e. switch between the different filtrations) we propose a fast, controllable, and precise solution by moving the focal spot of the x-ray tube. In this work, we performed preliminary evaluations with a grating prototype on a CT test bench. Our results include x-ray spectrometer measurements that reveal diverse and controllable spectral shaping between 4° and 6° for a specific grating design. Additional experiments with a contrast agent phantom illustrated the capability to decompose clinically relevant iodine concentrations (5, 10, 20, and 50mg/mL) - demonstrating the feasibility of the grating-based approach. Ongoing and future studies will investigate the potential of this novel concept as a relatively simple upgrade to standard energy-integrating CT.

Perturbation Response of Model-based Material Decomposition with Edge-Preserving Penalties

Spectral CT permits material discrimination beyond the structural information in conventional single-energy CT. Model-based material decomposition facilitates direct estimation of material density from spectral measurements, incorporating a general forward model for arbitrary spectral CT system, a statistical model of spectral CT measurements, and flexible regularization schemes. Such one-step approaches are promising for superior image quality, but the relationship between regularization parameters, imaging conditions, and reconstructed image properties is complicated. More specifically, the estimator is inherently nonlinear and may include additional nonlinearities like edge-preserving regularization, making image quality metrics intended for linear system evaluation difficult to apply. In this work, we seek approaches to quantify the image properties of this inherently nonlinear process through an investigation of perturbation response - the generalized system response to a local perturbation of arbitrary shape, location, and contrast. Such responses include cross-talk between material density channels, and we investigate the application of this metric in a sample spectral CT system. Inspired by the prior work under assumptions of local linearity and shift-invariant we also propose a prediction framework for perturbation response using a perceptron neural network. The proposed prediction framework offers an alternative to exhaustive evaluation and is a potential tool that can be used to prospectively choose optimal regularization parameters based on imaging conditions and diagnostic task.

Multi-Contrast CT Imaging with a Prototype Spatial-Spectral Filter

Spectral CT has great potential for a variety of clinical applications due to the improved material discrimination with respect to conventional CT. Many clinical and preclinical spectral CT systems have two spectral channels for dual-energy CT using strategies such as split-filtration, dual-layer detectors, or kVp-switching. However, there are emerging clinical imaging applications which would require three or more spectral sensitivity channels, for example, multiple exogenous contrast agents in a single scan. Spatial-spectral filters are a new spectral CT technology which use x-ray beam modulation to offer greater spectral diversity. The device consists of an array of k-edge filters which divide the x-ray beam into spectrally varied beamlets. This design allows for an arbitrary number of spectral channels; however, traditional two-step reconstruction-decomposition schemes are typically not effective because the measured data for any individual spectral channel is sparse in the projection domain. Instead, we use a one-step model-based material decomposition algorithm to iteratively estimate material density images directly from spectral CT data. In this work, we present a prototype spatial-spectral filter integrated with an x-ray CT test-bench. The filter is composed of an array of tin, erbium, tantalum, and lead filter tiles which spatially modulate the system spectral sensitivity pattern. After the system was characterized and modeled, we conducted a spectral CT scan of a multi-contrast-enhanced phantom containing water, iodine, and gadolinium solutions. We present the resulting spectral CT data as well as the material density images estimated by model-based material decomposition. The calibrated system model is in close agreement with the measured data, and the reconstructed material density images match the ground truth concentrations for the multi-contrast phantom. These preliminary results demonstrate the potential of spatial-spectral filters to enable multi-contrast imaging and other new clinical applications of spectral CT.

Combining Spectral CT Acquisition Methods for High-Sensitivity Material Decomposition

Quantitative estimation of contrast agent concentration is made possible by spectral CT and material decomposition. There are several approaches to modulate the sensitivity of the imaging system to obtain the different spectral channels required for decomposition. Spectral CT technologies that enable this varied sensitivity include source kV-switching, dual-layer detectors, and source-side filtering (e.g., tiled spatial-spectral filters). In this work, we use an advanced physical model to simulate these three spectral CT strategies as well as hybrid acquisitions using all combinations of two or three strategies. We apply model-based material decomposition to a water-iodine phantom with iodine concentrations from 0.1 to 5.0 mg/mL. We present bias-noise plots for the different combinations of spectral techniques and show that combined approaches permit diversity in spectral sensitivity and improve low concentration imaging performance relative to the those strategies applied individually. Better ability to estimate low concentrations of contrast agent has the potential to reduce risks associated with contrast administration (by lowering dosage) or to extend imaging applications into targets with much lower uptake.

Model-based Material Decomposition with System Blur Modeling

In this work, we present a novel model-based material decomposition (MBMD) approach for x-ray CT that includes system blur in the measurement model. Such processing has the potential to extend spatial resolution in material density estimates - particularly in systems where different spectral channels exhibit different spatial resolutions. We illustrate this new approach for a dual-layer detector x-ray CT and compare MBMD algorithms with and without blur in the reconstruction forward model. Both qualitative and quantitative comparisons of performance with and without blur modeling are reported. We find that blur modeling yields images with better recovery of high-resolution structures in an investigation of reconstructed line pairs as well as lower cross-talk bias between material bases that is ordinarily found due to mismatches in spatial resolution between spectral channels. The extended spatial resolution of the material decompositions has potential application in a range of high-resolution clinical tasks and spectral CT systems where spectral channels exhibit different spatial resolutions.

Prospective Prediction and Control of Image Properties in Model-based Material Decomposition for Spectral CT

Model-based material decomposition (MBMD) directly estimates the material densities from the spectral CT data and has found opportunities for dose reduction via physical and statistical modeling and advanced regularization. However, image properties such as spatial resolution, noise, and cross-basis response in the context of material decomposition are dependent on regularization, and high-dimensional exhaustive sweeping of regularization parameters is suboptimal. In this work, we proposed a set of prediction tools for generalized local impulse response (LIR) that characterizes both in-basis spatial resolution and cross-basis response, and noise correlation prospectively. The accuracy of noise predictor was validated in a simulation study, comparing predicted and measured in- and cross-basis noise correlations. Employing these predictors, we composed a specialized regularization for cross-talk reduction and showed that such prediction tools are promising for task-based optimization in spectral CT applications.

Local response prediction in model-based CT material decomposition

Spectral CT is an emerging modality that permits material decomposition and density estimation through the use of energy-dependent information in measurements. Direct model-based material decomposition algorithms have been developed that incorporate statistical models and advanced regularization schemes to improve density estimates and lower exposure requirements. However, understanding and control of the relationship between regularization and image properties is complex with interactions between spectral channels and material bases. In particular, regularization in one material basis can affect the image properties of other material bases, and vice versa. In this work, we derived a closed-form set of local impulse responses for the solutions to a general, regularized, model-based material decomposition (MBMD) objective. These predictors quantify both the spatial resolution in each material image as well as the influence of regularization of one material basis on other material images. This information can be used prospectively to tune regularization parameters for specific imaging goals.

Optimized Spatial-Spectral CT for Multi-Material Decomposition

Spectral CT is an emerging modality that uses a data acquisition scheme with varied spectral responses to provide enhanced material discrimination in addition to the structural information of conventional CT. Existing clinical and preclinical designs with this capability include kV-switching, split-filtration, and dual-layer detector systems to provide two spectral channels of projection data. In this work, we examine an alternate design based on a spatial-spectral filter. This source-side filter is made up a linear array of materials that divide the incident x-ray beam into spectrally varied beamlets. This design allows for any number of spectral channels; however, each individual channel is sparse in the projection domain. Model-based iterative reconstruction methods can accommodate such sparse spatial-spectral sampling patterns and allow for the incorporation of advanced regularization. With the goal of an optimized physical design, we characterize the effects of design parameters including filter tile order and filter tile width and their impact on material decomposition performance. We present results of numerical simulations that characterize the impact of each design parameter using a realistic CT geometry and noise model to demonstrate feasibility. Results for filter tile order show little change indicating that filter order is a low-priority design consideration. We observe improved performance for narrower filter widths; however, the performance drop-off is relatively flat indicating that wider filter widths are also feasible designs.

Physical Modeling and Performance of Spatial-Spectral Filters for CT Material Decomposition

Material decomposition for imaging multiple contrast agents in a single acquisition has been made possible by spectral CT: a modality which incorporates multiple photon energy spectral sensitivities into a single data collection. This work presents an investigation of a new approach to spectral CT which does not rely on energy-discriminating detectors or multiple x-ray sources. Instead, a tiled pattern of K-edge filters are placed in front of the x-ray to create spatially encoded spectra data. For improved sampling, the spatial-spectral filter is moved continuously with respect to the source. A model-based material decomposition algorithm is adopted to directly reconstruct multiple material densities from projection data that is sparse in each spectral channel. Physical effects associated with the x-ray focal spot size and motion blur for the moving filter are expected to impact overall performance. In this work, those physical effects are modeled and a performance analysis is conducted. Specifically, experiments are presented with simulated focal spot widths between 0.2 mm and 4.0 mm. Additionally, filter motion blur is simulated for a linear translation speeds between 50 mm/s and 450 mm/s. The performance differential between a 0.2 mm and a 1.0 mm focal spot is less than 15% suggesting feasibility of the approach with realistic x-ray tubes. Moreover, for reasonable filter actuation speeds, higher speeds are shown to decrease error (due to improved sampling) despite motion-based spectral blur.