Task-Driven Optimization of Fluence Field and Regularization for Model-Based Iterative Reconstruction in Computed Tomography

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.

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.

Full-Spectrum-Knowledge-Aware Tensor Model for Energy-Resolved CT Iterative Reconstruction

Energy-resolved computed tomography (ErCT) with a photon counting detector concurrently produces multiple CT images corresponding to different photon energy ranges. It has the potential to generate energy-dependent images with improved contrast-to-noise ratio and sufficient material-specific information. Since the number of detected photons in one energy bin in ErCT is smaller than that in conventional energy-integrating CT (EiCT), ErCT images are inherently more noisy than EiCT images, which leads to increased noise and bias in the subsequent material estimation. In this work, we first deeply analyze the intrinsic tensor properties of two-dimensional (2D) ErCT images acquired in different energy bins and then present a F ull- S pectrum-knowledge-aware Tensor analysis and processing (FSTensor) method for ErCT reconstruction to suppress noise-induced artifacts to obtain high-quality ErCT images and high-accuracy material images. The presented method is based on three considerations: (1) 2D ErCT images obtained in different energy bins can be treated as a 3-order tensor with three modes, i.e., width, height and energy bin, and a rich global correlation exists among the three modes, which can be characterized by tensor decomposition. (2) There is a locally piecewise smooth property in the 3-order ErCT images, and it can be captured by a tensor total variation regularization. (3) The images from the full spectrum are much better than the ErCT images with respect to noise variance and structural details and serve as external information to improve the reconstruction performance. We then develop an alternating direction method of multipliers algorithm to numerically solve the presented FSTensor method. We further utilize a genetic algorithm to tackle the parameter selection in ErCT reconstruction, instead of manually determining parameters. Simulation, preclinical and synthesized clinical ErCT results demonstrate that the presented FSTensor method leads to significant improvements over the filtered back-projection, robust principal component analysis, tensor-based dictionary learning and low-rank tensor decomposition with spatial-temporal total variation methods.

C-arm orbits for metal artifact avoidance (MAA) in cone-beam CT

Metal artifacts present a challenge to cone-beam CT (CBCT) image-guided surgery, obscuring visualization of metal instruments and adjacent anatomy-often in the very region of interest pertinent to the imaging/surgical tasks. We present a method to reduce the influence of metal artifacts by prospectively defining an image acquisition protocol-viz., the C-arm source-detector orbit-that mitigates metal-induced biases in the projection data. The metal artifact avoidance (MAA) method is compatible with simple mobile C-arms, does not require exact prior information on the patient or metal implants, and is consistent with 3D filtered backprojection (FBP), more advanced (e.g. polyenergetic) model-based image reconstruction (MBIR), and metal artifact reduction (MAR) post-processing methods. The MAA method consists of: (i) coarse localization of metal objects in the field-of-view (FOV) via two or more low-dose scout projection views and segmentation (e.g. a simple U-Net) in coarse backprojection; (ii) model-based prediction of metal-induced x-ray spectral shift for all source-detector vertices accessible by the imaging system (e.g. gantry rotation and tilt angles); and (iii) identification of a circular or non-circular orbit that reduces the variation in spectral shift. The method was developed, tested, and evaluated in a series of studies presenting increasing levels of complexity and realism, including digital simulations, phantom experiment, and cadaver experiment in the context of image-guided spine surgery (pedicle screw implants). The MAA method accurately predicted tilted circular and non-circular orbits that reduced the magnitude of metal artifacts in CBCT reconstructions. Realistic distributions of metal instrumentation were successfully localized (0.71 median Dice coefficient) from 2-6 low-dose scout views even in complex anatomical scenes. The MAA-predicted tilted circular orbits reduced root-mean-square error (RMSE) in 3D image reconstructions by 46%-70% and 'blooming' artifacts (apparent width of the screw shaft) by 20-45%. Non-circular orbits defined by MAA achieved a further ∼46% reduction in RMSE compared to the best (tilted) circular orbit. The MAA method presents a practical means to predict C-arm orbits that minimize spectral bias from metal instrumentation. Resulting orbits-either simple tilted circular orbits or more complex non-circular orbits that can be executed with a motorized multi-axis C-arm-exhibited substantial reduction of metal artifacts in raw CBCT reconstructions by virtue of higher fidelity projection data, which are in turn compatible with subsequent MAR post-processing and/or polyenergetic MBIR to further reduce artifacts.

A Statistical Model for Rigid Image Registration Performance: The Influence of Soft-Tissue Deformation as a Confounding Noise Source

Soft-tissue deformation presents a confounding factor to rigid image registration by introducing image content inconsistent with the underlying motion model, presenting non-correspondent structure with potentially high power, and creating local minima that challenge iterative optimization. In this paper, we introduce a model for registration performance that includes deformable soft tissue as a power-law noise distribution within a statistical framework describing the Cramer-Rao lower bound (CRLB) and root-mean-squared error (RMSE) in registration performance. The model incorporates both cross-correlation and gradient-based similarity metrics, and the model was tested in application to 3D-2D (CT-to-radiograph) and 3D-3D (CT-to-CT) image registration. Predictions accurately reflect the trends in registration error as a function of dose (quantum noise), and the choice of similarity metrics for both registration scenarios. Incorporating soft-tissue deformation as a noise source yields important insight on the limits of registration performance with respect to algorithm design and the clinical application or anatomical context. For example, the model quantifies the advantage of gradient-based similarity metrics in 3D-2D registration, identifies the low-dose limits of registration performance, and reveals the conditions for which the registration performance is fundamentally limited by soft-tissue deformation.

Dynamic fluence field modulation in computed tomography using multiple aperture devices

A novel beam filter consisting of multiple aperture devices (MADs) has been developed for dynamic fluence field modulation (FFM) in CT. Each MAD achieves spatial modulation of x-ray through fine-scale, highly attenuating tungsten bars of varying widths and spacings. Moiré patterns produced by relative motions between two MADs provide versatile classes of modulation profiles. The dual-MAD filter can be designed to achieve specific classes of target profiles. The designed filter was manufactured through a laser-sintering process and integrated to an experimental imaging system that enables linear actuation of the MADs. Dynamic FFM was achieved through a combination of beam shape modulation (by relative MAD motion) and amplitude modulation (by view-dependent mAs). To correct for gains associated with the MADs, we developed an algorithm to account for possible focal spot changes during/between scans and spectral effects introduced by the MADs. We performed FFM designs for phantoms following two imaging objectives: (1) to achieve minimum mean variance in filtered backprojection (FBP) reconstruction, and (2) to flatten the fluence behind the phantom. Comparisons with conventional FFM strategies involving a static bowtie and pulse width modulation were performed. The dual-MAD filter produced modulation profiles closely matched with the design target, providing varying beam widths not achievable by the static bowtie. The entire range of modulation profiles was achieved by 0.373 mm of MAD displacement. The correction algorithm effectively alleviated ring artifacts as a result of MADs while preserving phantom details such as wires and tissue boundaries. Dynamic FFM enabled by the MADs were effective in achieving the imaging objectives and demonstrated superior FFM capabilities compared to the static bowtie. In an ellipse phantom, the FFM of objective 1 achieved the lowest mean variance in all cases investigated. The FFM of objective 2 produce nearly isotropic local noise power spectrum and homogeneous noise magnitude. The dual-MAD filter provides an effective tool for fluence control in CT to overcome limitations of conventional static bowties and to further enable patient-specific FFM studies for a wide range of dose and image quality objectives.

Task-driven source-detector trajectories in cone-beam computed tomography: I. Theory and methods

We develop a mathematical framework for the design of orbital trajectories that are optimal to a particular imaging task (or tasks) in advanced cone-beam computed tomography systems that have the capability of general source-detector positioning. The framework allows various parameterizations of the orbit as well as constraints based on imaging system capabilities. To accommodate nonstandard system geometries, a model-based iterative reconstruction method is applied. Such algorithms generally complicate the assessment and prediction of reconstructed image properties; however, we leverage efficient implementations of analytical predictors of local noise and spatial resolution that incorporate dependencies of the reconstruction algorithm on patient anatomy, x-ray technique, and geometry. These image property predictors serve as inputs to a task-based performance metric defined by detectability index, which is optimized with respect to the orbital parameters of data acquisition. We investigate the framework of the task-driven trajectory design in several examples to examine the dependence of optimal source-detector trajectories on the imaging task (or tasks), including location and spatial-frequency dependence. A variety of multitask objectives are also investigated, and the advantages to imaging performance are quantified in simulation studies.

Multi-energy computed tomography reconstruction using a nonlocal spectral similarity model

Multi-energy computed tomography (MECT) is able to acquire simultaneous multi-energy measurements from one scan. In addition, it allows material differentiation and quantification effectively. However, due to the limited energy bin width, the number of photons detected in an energy-specific channel is smaller than that in traditional CT, which results in image quality degradation. To address this issue, in this work, we develop a statistical iterative reconstruction algorithm to acquire high-quality MECT images and high-accuracy material-specific images. Specifically, this algorithm fully incorporates redundant self-similarities within nonlocal regions in the MECT image at one bin and rich spectral similarities among MECT images at all bins. For simplicity, the presented algorithm is referred to as 'MECT-NSS'. Moreover, an efficient optimization algorithm is developed to solve the MECT-NSS objective function. Then, a comprehensive evaluation of parameter selection for the MECT-NSS algorithm is conducted. In the experiment, the datasets include images from three phantoms and one patient to validate and evaluate the MECT-NSS reconstruction performance. The qualitative and quantitative results demonstrate that the presented MECT-NSS can successfully yield better MECT image quality and more accurate material estimation than the competing algorithms.

Fluid-filled dynamic bowtie filter: Description and comparison with other modulators

PURPOSE

A dynamic bowtie filter can modulate flux along both fan and view angles for reduced patient dose, scatter, and required photon flux, which is especially important for photon counting detectors (PCDs). Among the proposed dynamic bowtie designs, the piecewise-linear attenuator (Hsieh and Pelc, Med Phys. 2013;40:031910) offers more flexibility than conventional filters, but relies on analog positioning of a limited number of wedges. In this work, we study our previously proposed dynamic attenuator design, the fluid-filled dynamic bowtie filter (FDBF) that has digital control. Specifically, we use computer simulations to study fluence modulation, reconstructed image noise, and radiation dose and to compare it to other attenuators. FDBF is an array of small channels each of which, if it can be filled with dense fluid or emptied quickly, has a binary effect on the flux. The cumulative attenuation from each channel along the x-ray path contributes to the FDBF total attenuation.

METHODS

An algorithm is proposed for selecting which FDBF channels should be filled. Two optimization metrics are considered: minimizing the maximum-count-rate for PCDs and minimizing peak-variance for energy-integrating detectors (EIDs) at fixed radiation dose (for optimizing dose efficiency). Using simulated chest, abdomen, and shoulder data, the performance is compared with a conventional bowtie and a piecewise-linear attenuator. For minimizing peak-variance, a perfect-attenuator (hypothetical filter capable of adjusting the fluence of each ray individually) and flat-variance attenuator are also included in the comparison. Two possible fluids, solutions of zinc bromide and gadolinium chloride, were tested.

RESULTS

To obtain the same SNR as routine clinical protocols, the proposed FDBF reduces the maximum-count-rate (across projection data, averaged over the test objects) of PCDs to 1.2 Mcps/mm² , which is 55.8 and 3.3 times lower than the max-count-rate of the conventional bowtie and the piecewise-linear bowtie, respectively. (Averaged across objects for FDBF, the max-count-rate without object and FDBF is 2063.5 Mcps/mm² , and the max-count-rate with object without FDBF is 749.8 Mcps/mm² .) Moreover, for the peak-variance analysis, the FDBF can reduce entrance-energy-fluence (sum of energy incident on objects, used as a surrogate for dose) to 34% of the entrance-energy-fluence from the conventional filter on average while achieving the same peak noise level. Its entrance-energy-fluence reduction performance is only 7% worse than the perfect-attenuator on average and is 13% better than the piecewise-linear filter for chest and shoulder. Furthermore, the noise-map in reconstructed image domain from the FDBF is more uniform than the piecewise-linear filter, with 3 times less variation across the object. For the dose reduction task, the zinc bromide solution performed slightly poorer than stainless steel but was better than the gadolinium chloride solution.

CONCLUSIONS

The FDBF allows finer control over flux distribution compared to piecewise-linear and conventional bowtie filters. It can reduce the required maximum-count-rate for PCDs to a level achievable by current detector designs and offers a high dose reduction factor.

Statistical CT reconstruction using region-aware texture preserving regularization learning from prior normal-dose CT image

In some clinical applications, prior normal-dose CT (NdCT) images are available, and the valuable textures and structure features in them may be used to promote follow-up low-dose CT (LdCT) reconstruction. This study aims to learn texture information from the NdCT images and leverage it for follow-up LdCT image reconstruction to preserve textures and structure features. Specifically, the proposed reconstruction method first learns the texture information from those patches with similar structures in NdCT image, and the similar patches can be clustered by searching context features efficiently from the surroundings of the current patch. Then it utilizes redundant texture information from the similar patches as a priori knowledge to describe specific regions in the LdCT image. The advanced region-aware texture preserving prior is termed as 'RATP'. The main advantage of the PATP prior is that it can properly learn the texture features from available NdCT images and adaptively characterize the region-specific structures in the LdCT image. The experiments using patient data were performed to evaluate the performance of the proposed method. The proposed RATP method demonstrated superior performance in LdCT imaging compared to the filtered back projection (FBP) and statistical iterative reconstruction (SIR) methods using Gaussian regularization, Huber regularization and the original texture preserving regularization.

Dynamic fluence field modulation for miscentered patients in computed tomography

Traditional CT image acquisition uses bowtie filters to reduce dose, x-ray scatter, and detector dynamic range requirements. However, accurate patient centering within the bore of the CT scanner takes time and is often difficult to achieve precisely. Patient miscentering combined with a static bowtie filter can result in significant increases in dose, reconstruction noise, and CT number variations, and consequently raise overall exposure requirements. Approaches to estimate the patient position from scout scans and perform dynamic spatial beam filtration during acquisition are developed and applied in physical experiments on a CT test bench using different beam filtration strategies. While various dynamic beam modulation strategies have been developed, we focus on two approaches: (1) a simple approach using attenuation-based beam modulation using a translating bowtie filter and (2) dynamic beam modulation using multiple aperture devices (MADs)-an emerging beam filtration strategy based on binary filtration of the x-ray beam using variable width slits in a high-density beam blocker. Improved dose utilization and more consistent image performance with respect to an unmodulated baseline (static filter) are demonstrated for miscentered objects and dynamic beam filtration in physical experiments. For a homogeneous object miscentered by 4 cm, the dynamic filter reduced the maximum regional noise and dose penalties (compared with a centered object) from 173% to 16% and 42% to 14%, respectively, for a traditional bowtie, 29% to 8% and 24% to 15%, respectively, for a single MAD, and 275% to 11% and 56% to 18%, respectively, for a dual-MAD filter. The proposed methodology has the potential to relax patient centering requirements within the scanner, reduce setup time, and facilitate additional CT dose reduction.

Implementation and Assessment of Dynamic Fluence Field Modulation with Multiple Aperture Devices

This work reports experimental results of dynamic fluence field modulation (FFM) using a dual multiple aperture devices (MAD) system. MAD filters use Moiré patterns produced by relative motions between two sets of thin, highly attenuating tungsten bars of varying widths and spacings. Each MAD was affixed to a linear actuator and installed on an experimental cone-beam CT bench. Phantom-specific FFM profiles were designed based on a flatness and minimum mean variance objectives and realized through a combination of MAD translations and pulse width modulation at a constant tube current. To properly correct for gains associated with the MAD filters, a correction algorithm was designed to account for focal spot shifts during scanning, as well as spectral effects from incomplete blockage of x-rays by the tungsten bars. The FFM designs were demonstrated in an elliptical phantom (25.8×14.1 cm). Variance and noise power spectrum (NPS) analysis was performed on the resulting reconstructions. While conventionalgain correction produced reconstructions with high frequency ring artifacts in axial slices, the proposed correction algorithm effectively removed such artifacts while preserving phantom details. Fluence field designs for the elliptical phantom were achievedusing relative MAD motions over a 0.44 mm range, and measured beam profiles closely approximated the theoretically computed target profiles. The noise properties of the resulting reconstructions behave as expected: a flat detected fluence criterion yields nearly isotropic NPS and more homogeneous variance across the reconstruction as compared to an unmodulated scan; the minimum mean variance FFM results in lower mean variance compared to both the unmodulated and flat-field patterns at approximately matched total bare-beam fluence. These results suggest that a dual-MAD CT is an effective approach to provide fluence and image quality control and that can potentially accommodate a wide range of phantoms and design objectives.

Joint Optimization of Fluence Field Modulation and Regularization for Multi-Task Objectives

This work investigates task-driven optimization of fluence field modulation (FFM) and regularization for model-based iterative reconstruction (MBIR) when different imaging tasks are presented by different organs. Example applications of the design framework were demonstrated in an abdomen phantom where the task of interest in the liver is a low-contrast, low-frequency detection task while that in the kidney is a high-contrast, high-frequency discrimination task. The global performance objective is based on maximizing local detectability index (d') at a discrete set of locations. Two objective functions were formulated based on different imaging needs: 1) a maxi-min objective where all tasks are equally important, and 2) a region-of-interest (ROI) objective to maximize imaging performance in an ROI while maintaining a minimum level of performance elsewhere. The FFM pattern for the maxi-min objective is determined by the most challenging task in the liver where both angular and spatial modulation resulted in a ~35% improvement in d' compared to an unmodulated case. The FFM for the ROI objective prescribes the most fluence to the organs of interest, boosting d' by ~59%, but manages to achieve the minimum d' target elsewhere. A spatially varying regularization was found to be important when tasks of different frequency content are present in different parts of the image - the optimal regularization strength for the two studied tasks differed by two orders of magnitude. Initial investigations in this work demonstrated that a multi-task objective is potentially important in shaping the optimal FFM and MBIR regularization, and that these tools may help to generalize task-based acquisition and reconstruction design for more complex diagnostic scenarios.