Model-based Image Reconstruction Method Research Articles

Model-based reconstruction for looping-star MRI.

The aim of this study was to develop a reconstruction method that more fully models the signals and reconstructs gradient echo (GRE) images without sacrificing the signal to noise ratio and spatial resolution, compared to conventional gridding and model-based image reconstruction method. By modeling the trajectories for every spoke and simplifying the scenario to only echo-in and echo-out mixture, the approach explicitly models the overlapping echoes. After modeling the overlapping echoes with two system matrices, we use the conjugate gradient algorithm (CG-SENSE) with the nonuniform FFT (NUFFT) to optimize the image reconstruction cost function. The proposed method is demonstrated in phantoms and in-vivo volunteer experiments for three-dimensional, high-resolution T2*-weighted imaging and functional MRI tasks. Compared to the gridding method, the high resolution protocol exhibits improved spatial resolution and reduced signal loss as a result of less intra-voxel dephasing. The fMRI task shows that the proposed model-based method produced images with reduced artifacts and blurring as well as more stable and prominent time courses. The proposed model-based reconstruction results shows improved spatial resolution and reduced artifacts. The fMRI task shows improved time series and activation map due to the reduced overlapping echoes and under-sampling artifacts.

MMV-Net: A Multiple Measurement Vector Network for Multifrequency Electrical Impedance Tomography.

Multifrequency electrical impedance tomography (mfEIT) is an emerging biomedical imaging modality to reveal frequency-dependent conductivity distributions in biomedical applications. Conventional model-based image reconstruction methods suffer from low spatial resolution, unconstrained frequency correlation, and high computational cost. Deep learning has been extensively applied in solving the EIT inverse problem in biomedical and industrial process imaging. However, most existing learning-based approaches deal with the single-frequency setup, which is inefficient and ineffective when extended to the multifrequency setup. This article presents a multiple measurement vector (MMV) model-based learning algorithm named MMV-Net to solve the mfEIT image reconstruction problem. MMV-Net considers the correlations between mfEIT images and unfolds the update steps of the Alternating Direction Method of Multipliers for the MMV problem (MMV-ADMM). The nonlinear shrinkage operator associated with the weighted l2,1 regularization term of MMV-ADMM is generalized in MMV-Net with a cascade of a Spatial Self-Attention module and a Convolutional Long Short-Term Memory (ConvLSTM) module to better capture intrafrequency and interfrequency dependencies. The proposed MMV-Net was validated on our Edinburgh mfEIT Dataset and a series of comprehensive experiments. The results show superior image quality, convergence performance, noise robustness, and computational efficiency against the conventional MMV-ADMM and the state-of-the-art deep learning methods.

Efficient Approximation of Jacobian Matrices Involving a Non-Uniform Fast Fourier Transform (NUFFT).

There is growing interest in learning Fourier domain sampling strategies (particularly for magnetic resonance imaging, MRI) using optimization approaches. For non-Cartesian sampling, the system models typically involve non-uniform fast Fourier transform (NUFFT) operations. Commonly used NUFFT algorithms contain frequency domain interpolation, which is not differentiable with respect to the sampling pattern, complicating the use of gradient methods. This paper describes an efficient and accurate approach for computing approximate gradients involving NUFFTs. Multiple numerical experiments validate the improved accuracy and efficiency of the proposed approximation. As an application to computational imaging, the NUFFT Jacobians were used to optimize non-Cartesian MRI sampling trajectories via data-driven stochastic optimization. Specifically, the sampling patterns were learned with respect to various model-based image reconstruction (MBIR) algorithms. The proposed approach enables sampling optimization for image sizes that are infeasible with standard auto-differentiation methods due to memory limits. The synergistic acquisition and reconstruction design leads to remarkably improved image quality. In fact, we show that model-based image reconstruction methods with suitably optimized imaging parameters can perform nearly as well as CNN-based methods.

OTRE: Where Optimal Transport Guided Unpaired Image-to-Image Translation Meets Regularization by Enhancing.

Non-mydriatic retinal color fundus photography (CFP) is widely available due to the advantage of not requiring pupillary dilation, however, is prone to poor quality due to operators, systemic imperfections, or patient-related causes. Optimal retinal image quality is mandated for accurate medical diagnoses and automated analyses. Herein, we leveraged the Optimal Transport (OT) theory to propose an unpaired image-to-image translation scheme for mapping low-quality retinal CFPs to high-quality counterparts. Furthermore, to improve the flexibility, robustness, and applicability of our image enhancement pipeline in the clinical practice, we generalized a state-of-the-art model-based image reconstruction method, regularization by denoising, by plugging in priors learned by our OT-guided image-to-image translation network. We named it as regularization by enhancing (RE). We validated the integrated framework, OTRE, on three publicly available retinal image datasets by assessing the quality after enhancement and their performance on various downstream tasks, including diabetic retinopathy grading, vessel segmentation, and diabetic lesion segmentation. The experimental results demonstrated the superiority of our proposed framework over some state-of-the-art unsupervised competitors and a state-of-the-art supervised method.

Image reconstruction for endoscopic photoacoustic tomography including effects of detector responses.

In photoacoustic tomography (PAT), conventional image reconstruction methods are generally based on the assumption of an ideal point-like ultrasonic detector. This assumption is appropriate when the receiving surface of the detector is sufficiently small and/or the distance between the imaged object and the detector is large enough. However, it does not hold in endoscopic applications of PAT. In this study, we propose a model-based image reconstruction method for endoscopic photoacoustic tomography (EPAT), considering the effect of detector responses on image quality. We construct a forward model to physically describe the imaging process of EPAT, including the generation of the initial pressure due to optical absorption and thermoelastic expansion, the propagation of photoacoustic waves in tissues, and the acoustic measurement. The model outputs the theoretical sampling voltage signal, which is the response of the ultrasonic detector to the acoustic pressure reaching its receiving surface. The images representing the distribution map of the optical absorption energy density on cross-sections of the imaged luminal structures are reconstructed from the sampling voltage signals output by the detector through iterative inversion of the forward model. Compared with the conventional approaches based on back-projection and other imaging models, our method improved the quality and spatial resolution of the resulting images.

Unified Supervised-Unsupervised (SUPER) Learning for X-Ray CT Image Reconstruction.

Traditional model-based image reconstruction (MBIR) methods combine forward and noise models with simple object priors. Recent machine learning methods for image reconstruction typically involve supervised learning or unsupervised learning, both of which have their advantages and disadvantages. In this work, we propose a unified supervised-unsupervised (SUPER) learning framework for X-ray computed tomography (CT) image reconstruction. The proposed learning formulation combines both unsupervised learning-based priors (or even simple analytical priors) together with (supervised) deep network-based priors in a unified MBIR framework based on a fixed point iteration analysis. The proposed training algorithm is also an approximate scheme for a bilevel supervised training optimization problem, wherein the network-based regularizer in the lower-level MBIR problem is optimized using an upper-level reconstruction loss. The training problem is optimized by alternating between updating the network weights and iteratively updating the reconstructions based on those weights. We demonstrate the learned SUPER models' efficacy for low-dose CT image reconstruction, for which we use the NIH AAPM Mayo Clinic Low Dose CT Grand Challenge dataset for training and testing. In our experiments, we studied different combinations of supervised deep network priors and unsupervised learning-based or analytical priors. Both numerical and visual results show the superiority of the proposed unified SUPER methods over standalone supervised learning-based methods, iterative MBIR methods, and variations of SUPER obtained via ablation studies. We also show that the proposed algorithm converges rapidly in practice.

Photo-acoustic tomographic image reconstruction from reduced data using physically inspired regularization

We propose a model-based image reconstruction method for photoacoustic tomography (PAT) involving a novel form of regularization and demonstrate its ability to recover good quality images from significantly reduced size datasets. The regularization is constructed to suit the physical structure of typical PAT images. We construct it by combining second-order derivatives and intensity into a non-convex form to exploit a structural property of PAT images that we observe: in PAT images, high intensities and high second-order derivatives are jointly sparse. The specific form of regularization constructed here is a modification of the form proposed for fluorescence image restoration. This regularization is combined with a data fidelity cost, and the required image is obtained as the minimizer of this cost. As this regularization is non-convex, the efficiency of the minimization method is crucial in obtaining artifact-free reconstructions. We develop a custom minimization method for efficiently handling this non-convex minimization problem. Further, as non-convex minimization requires a large number of iterations and the PAT forward model in the data-fidelity term has to be applied in the iterations, we propose a computational structure for efficient implementation of the forward model with reduced memory requirements. We evaluate the proposed method on both simulated and real measured data sets and compare them with a recent reconstruction method that is based on a well-known fast iterative shrinkage threshold algorithm (FISTA).

Momentum-Net: Fast and Convergent Iterative Neural Network for Inverse Problems.

Iterative neural networks (INN) are rapidly gaining attention for solving inverse problems in imaging, image processing, and computer vision. INNs combine regression NNs and an iterative model-based image reconstruction (MBIR) algorithm, often leading to both good generalization capability and outperforming reconstruction quality over existing MBIR optimization models. This paper proposes the first fast and convergent INN architecture, Momentum-Net, by generalizing a block-wise MBIR algorithm that uses momentum and majorizers with regression NNs. For fast MBIR, Momentum-Net uses momentum terms in extrapolation modules, and noniterative MBIR modules at each iteration by using majorizers, where each iteration of Momentum-Net consists of three core modules: image refining, extrapolation, and MBIR. Momentum-Net guarantees convergence to a fixed-point for general differentiable (non)convex MBIR functions (or data-fit terms) and convex feasible sets, under two asymptomatic conditions. To consider data-fit variations across training and testing samples, we also propose a regularization parameter selection scheme based on the "spectral spread" of majorization matrices. Numerical experiments for light-field photography using a focal stack and sparse-view computational tomography demonstrate that, given identical regression NN architectures, Momentum-Net significantly improves MBIR speed and accuracy over several existing INNs; it significantly improves reconstruction quality compared to a state-of-the-art MBIR method in each application.

Improved Low-Count Quantitative PET Reconstruction With an Iterative Neural Network.

Image reconstruction in low-count PET is particularly challenging because gammas from natural radioactivity in Lu-based crystals cause high random fractions that lower the measurement signal-to-noise-ratio (SNR). In model-based image reconstruction (MBIR), using more iterations of an unregularized method may increase the noise, so incorporating regularization into the image reconstruction is desirable to control the noise. New regularization methods based on learned convolutional operators are emerging in MBIR. We modify the architecture of an iterative neural network, BCD-Net, for PET MBIR, and demonstrate the efficacy of the trained BCD-Net using XCAT phantom data that simulates the low true coincidence count-rates with high random fractions typical for Y-90 PET patient imaging after Y-90 microsphere radioembolization. Numerical results show that the proposed BCD-Net significantly improves CNR and RMSE of the reconstructed images compared to MBIR methods using non-trained regularizers, total variation (TV) and non-local means (NLM). Moreover, BCD-Net successfully generalizes to test data that differs from the training data. Improvements were also demonstrated for the clinically relevant phantom measurement data where we used training and testing datasets having very different activity distributions and count-levels.

MO-DE-207A-02: A Feature-Preserving Image Reconstruction Method for Improved Pancreaticlesion Classification in Diagnostic CT Imaging

Purpose: To develop a feature-preserving model based image reconstruction (MBIR) method that improves performance in pancreatic lesion classification at equal or reduced radiation dose. Methods: A set of pancreatic lesion models was created with both benign and premalignant lesion types. These two classes of lesions are distinguished by their fine internal structures; their delineation is therefore crucial to the task of pancreatic lesion classification. To reduce image noise while preserving the features of the lesions, we developed a MBIR method with curvature-based regularization. The novel regularization encourages formation of smooth surfaces that model both the exterior shape and the internal features of pancreatic lesions. Given that the curvature depends on the unknown image, image reconstruction or denoising becomes a non-convex optimization problem; to address this issue an iterative-reweighting scheme was used to calculate and update the curvature using the image from the previous iteration. Evaluation was carried out with insertion of the lesion models into the pancreas of a patient CT image. Results: Visual inspection was used to compare conventional TV regularization with our curvature-based regularization. Several penalty-strengths were considered for TV regularization, all of which resulted in erasing portions of the septation (thin partition) in a premalignant lesion. At matched noise variance (50% noise reduction in the patient stomach region), the connectivity of the septation was well preserved using the proposed curvature-based method. Conclusion: The curvature-based regularization is able to reduce image noise while simultaneously preserving the lesion features. This method could potentially improve task performance for pancreatic lesion classification at equal or reduced radiation dose. The result is of high significance for longitudinal surveillance studies of patients with pancreatic cysts, which may develop into pancreatic cancer. The Senior Author receives financial support from Siemens GmbH Healthcare

Alternating dual updates algorithm for X-ray CT reconstruction on the GPU.

Model-based image reconstruction (MBIR) for X-ray computed tomography (CT) offers improved image quality and potential low-dose operation, but has yet to reach ubiquity in the clinic. MBIR methods form an image by solving a large statistically motivated optimization problem, and the long time it takes to numerically solve this problem has hampered MBIR's adoption. We present a new optimization algorithm for X-ray CT MBIR based on duality and group coordinate ascent that may converge even with approximate updates and can handle a wide range of regularizers, including total variation (TV). The algorithm iteratively updates groups of dual variables corresponding to terms in the cost function; these updates are highly parallel and map well onto the GPU. Although the algorithm stores a large number of variables, the "working size" for each of the algorithm's steps is small and can be efficiently streamed to the GPU while other calculations are being performed. The proposed algorithm converges rapidly on both real and simulated data and shows promising parallelization over multiple devices.

Low-dose preview for patient-specific, task-specific technique selection in cone-beam CT.

A method is presented for generating simulated low-dose cone-beam CT (CBCT) preview images from which patient- and task-specific minimum-dose protocols can be confidently selected prospectively in clinical scenarios involving repeat scans. In clinical scenarios involving a series of CBCT images, the low-dose preview (LDP) method operates upon the first scan to create a projection dataset that accurately simulates the effects of dose reduction in subsequent scans by injecting noise of proper magnitude and correlation, including both quantum and electronic readout noise as important components of image noise in flat-panel detector CBCT. Experiments were conducted to validate the LDP method in both a head phantom and a cadaveric torso by performing CBCT acquisitions spanning a wide dose range (head: 0.8-13.2 mGy, body: 0.8-12.4 mGy) with a prototype mobile C-arm system. After injecting correlated noise to simulate dose reduction, the projections were reconstructed using both conventional filtered backprojection (FBP) and an iterative, model-based image reconstruction method (MBIR). The LDP images were then compared to real CBCT images in terms of noise magnitude, noise-power spectrum (NPS), spatial resolution, contrast, and artifacts. For both FBP and MBIR, the LDP images exhibited accurate levels of spatial resolution and contrast that were unaffected by the correlated noise injection, as expected. Furthermore, the LDP image noise magnitude and NPS were in strong agreement with real CBCT images acquired at the corresponding, reduced dose level across the entire dose range considered. The noise magnitude agreed within 7% for both the head phantom and cadaveric torso, and the NPS showed a similar level of agreement up to the Nyquist frequency. Therefore, the LDP images were highly representative of real image quality across a broad range of dose and reconstruction methods. On the other hand, naïve injection ofuncorrelated noise resulted in strong underestimation of the true noise, which would lead to overly optimistic predictions of dose reduction. Correlated noise injection is essential to accurate simulation of CBCT image quality at reduced dose. With the proposed LDP method, the user can prospectively select patient-specific, minimum-dose protocols (viz., acquisition technique and reconstruction method) suitable to a particular imaging task and to the user's own observer preferences for CBCT scans following the first acquisition. The method could provide dose reduction in common clinical scenarios involving multiple CBCT scans, such as image-guided surgery and radiotherapy.

Evaluation of metal artifacts in MVCT systems using a model based correction method

To evaluate the performance of a model based image reconstruction method in reducing metal artifacts in the megavoltage computed tomography (MVCT) images of a phantom representing bilateral hip prostheses and to compare with the filtered-backprojection (FBP) technique. An iterative maximum likelihood polychromatic algorithm for CT (IMPACT) is used with an additional model for the pair∕triplet production process and the energy dependent response of the detectors. The beam spectra for an in-house bench-top and TomoTherapy™ MVCTs are modeled for use in IMPACT. The empirical energy dependent response of detectors is calculated using a constrained optimization technique that predicts the measured attenuation of the beam by various thicknesses (0-24 cm) of solid water slabs. A cylindrical (19.1 cm diameter) plexiglass phantom containing various cylindrical inserts of relative electron densities 0.295-1.695 positioned between two steel rods (2.7 cm diameter) is scanned in the bench-top MVCT that utilizes the bremsstrahlung radiation from a 6 MeV electron beam passed through 4 cm solid water on the Varian Clinac 2300C and in the imaging beam of the TomoTherapy™ MVCT. The FBP technique in bench-top MVCT reconstructs images from raw signal normalized to air scan and corrected for beam hardening using a uniform plexiglass cylinder (20 cm diameter). The IMPACT starts with a FBP reconstructed seed image and reconstructs the final image in 150 iterations. In both MVCTs, FBP produces visible dark shading in the image connecting the steel rods. In the IMPACT reconstructed images this shading is nearly removed and the uniform background is restored. The average attenuation coefficients of the inserts and the background are very close to the corresponding values in the absence of the steel inserts. In the FBP images of the bench-top MVCT, the shading causes 4%-9.5% underestimation of electron density at the central inserts with an average of (6.3 ± 1.8)% for the range of electron densities studied. In the uniform plexiglass background, the shadow creates 0.8%-4.7% underestimation of electron density with an average of (2.9 ± 1.2)%. In the corresponding IMPACT images, the underestimation in the shaded plexiglass background is 0.3%-1.8% with an average of (0.9 ± 0.5)% and 1.4%-6.8% with an average of (2.8 ± 2.7)% in the central insert region. In the FBP images of the TomoTherapy™ MVCT, this shading creates 2.6%-6.7% underestimation of electron density with an average of (3.7 ± 1.4)% at the central inserts and 5.9%-7.2% underestimation in the background with an average of (6.4 ± 0.5)%. In the IMPACT images, the uniform background between the steel rods is restored with 0.3%-1.0% underestimation of electron density with an average of (0.7 ± 0.3)%. The corresponding underestimation at the central inserts of the IMPACT images is -0.4%-0.1% with an average of (-0.1 ± 0.2)%. The shading metal artifact has been nearly removed in MVCT images using the IMPACT algorithm with the accurate geometry of the system, proper modeling of energy dependent response of detectors, and all relevant photon interaction processes. This results less than 1% difference in electron density in the background plexiglass and less than 3% averaged over the range of electron densities investigated.

SU-E-J-17: Evaluation of Metal Artifact Reduction in MVCTs Using a Model Based Image Reconstruction Method.

To evaluate the performance of a model based image reconstruction in reducing metal artifacts in MVCT systems, and to compare with filtered-back projection (FBP) technique. Iterative maximum likelihood polychromatic algorithm for CT (IMPACT) is used with pair/triplet production process and the energy dependent response of detectors. The beam spectra for in-house bench-top and TomotherapyTM MVCT are modelled for use in IMPACT. The energy dependent gain of detectors is calculated using a constrained optimization technique and measured attenuation produced by 0 - 24 cm thick solid water slabs. A cylindrical (19 cm diameter) plexiglass phantom containing various central cylindrical inserts (relative electron density of 0.28-1.69) between two steel rods (2 cm diameter) is scanned in the bench-top [the bremsstrahlung radiation from 6 MeV electron beam passed through 4 cm solid water on the Varian Clinac 2300C] and TomotherapyTM MVCTs. The FBP reconstructs images from raw signal normalised to air scan and corrected for beam hardening using a uniform plexi-glass cylinder (20 cm diameter). IMPACT starts with FBP reconstructed seed image and reconstructs final image at 1.25 MeV in 150 iterations. FBP produces a visible dark shading in the image between two steel rods that becomes darker with higher density central insert causing 5-8 % underestimation of electron density compared to the case without the steel rods. In the IMPACT image the dark shading connecting the steel rods is nearly removed and the uniform background restored. The average attenuation coefficients of the inserts and the background are very close to the corresponding theoretical values at 1.25 MeV. The dark shading metal artifact due to beam hardening can be removed in MVCT using the iterative reconstruction algorithm such as IMPACT. However, the accurate modelling of detectors' energy dependent response and physical processes are crucial for successful implementation. Funding support for the research is obtained from "Vanier Canada Graduate Scholarship" and "Canadian Institute of Health Research".

K -space propagation models for acoustically heterogeneous media: Application to biomedical photoacoustics

Biomedical applications of photoacoustics, in particular photoacoustic tomography, require efficient models of photoacoustic propagation that can incorporate realistic properties of soft tissue, such as acoustic inhomogeneities both for purposes of simulation and for use in model-based image reconstruction methods. k-space methods are well suited to modeling high-frequency acoustics applications as they require fewer mesh points per wavelength than conventional finite element and finite difference models, and larger time steps can be taken without a loss of stability or accuracy. They are also straightforward to encode numerically, making them appealing as a general tool. The rationale behind k-space methods and the k-space approach to the numerical modeling of photoacoustic waves in fluids are covered in this paper. Three existing k-space models are applied to photoacoustics and demonstrated with examples: an exact model for homogeneous media, a second-order model that can take into account heterogeneous media, and a first-order model that can incorporate absorbing boundary conditions.

Three-dimensional bioluminescence tomography with model-based reconstruction

A model-based image reconstruction method, bioluminescence tomography (BLT), is described. BLT has the potential to spatially resolve bioluminescence associated with gene expression in vivo, thus, offering a tomographic molecular imaging method. The three-dimensional spatial map of reporter genes is recovered using a diffusion equation model-based, finite element reconstruction algorithm. The imaging method is demonstrated using both numerical simulations and phantom experiments.

Model-based normalization for iterative 3D PET image reconstruction

We describe a method for normalization in 3D PET for use with maximum a posteriori (MAP) or other iterative model-based image reconstruction methods. This approach is an extension of previous factored normalization methods in which we include separate factors for detector sensitivity, geometric response, block effects and deadtime. Since our MAP reconstruction approach already models some of the geometric factors in the forward projection, the normalization factors must be modified to account only for effects not already included in the model. We describe a maximum likelihood approach to joint estimation of the count-rate independent normalization factors, which we apply to data from a uniform cylindrical source. We then compute block-wise and block-profile deadtime correction factors using singles and coincidence data, respectively, from a multiframe cylindrical source. We have applied this method for reconstruction of data from the Concorde microPET P4 scanner. Quantitative evaluation of this method using well-counter measurements of activity in a multicompartment phantom compares favourably with normalization based directly on cylindrical source measurements.

Improved parametric reconstruction using variable projection optimization

This paper addresses the problem of image reconstruction from limited Fourier data. An improved parameter estimation algorithm is proposed for use with a polynomial model-based image reconstruction method. Results from magnetic resonance imaging data are shown to demonstrate the performance of the proposed algorithm.