Polychromatic X-ray CT Image Reconstruction and Mass-Attenuation Spectrum Estimation

We develop a method for sparse image reconstruction from polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident-energy spectrum are unknown. We obtain a parsimonious measurement-model parameterization by changing the integral variable from photon energy to mass attenuation, which allows us to combine the variations brought by the unknown incident spectrum and mass attenuation into a single unknown mass-attenuation spectrum function; the resulting measurement equation has the Laplace integral form. The mass-attenuation spectrum is then expanded into first order B-spline basis functions. We derive a block coordinate-descent algorithm for constrained minimization of a penalized negative log-likelihood (NLL) cost function, where penalty terms ensure nonnegativity of the spline coefficients and nonnegativity and sparsity of the density map. The image sparsity is imposed using total-variation (TV) and $\ell_1$ norms, applied to the density-map image and its discrete wavelet transform (DWT) coefficients, respectively. This algorithm alternates between Nesterov's proximal-gradient (NPG) and limited-memory Broyden-Fletcher-Goldfarb-Shanno with box constraints (L-BFGS-B) steps for updating the image and mass-attenuation spectrum parameters. To accelerate convergence of the density-map NPG step, we apply a step-size selection scheme that accounts for varying local Lipschitz constant of the NLL. We consider lognormal and Poisson noise models and establish conditions for biconvexity of the corresponding NLLs. We also prove the Kurdyka-{\L}ojasiewicz property of the objective function, which is important for establishing local convergence of the algorithm. Numerical experiments with simulated and real X-ray CT data demonstrate the performance of the proposed scheme

General Phase Regularized Reconstruction using Phase Cycling

Purpose: To develop a general phase regularized image reconstruction method, with applications to partial Fourier imaging, water-fat imaging and flow imaging. Theory and Methods: The problem of enforcing phase constraints in reconstruction was studied under a regularized inverse problem framework. A general phase regularized reconstruction algorithm was proposed to enable various joint reconstruction of partial Fourier imaging, water-fat imaging and flow imaging, along with parallel imaging (PI) and compressed sensing (CS). Since phase regularized reconstruction is inherently non-convex and sensitive to phase wraps in the initial solution, a reconstruction technique, named phase cycling, was proposed to render the overall algorithm invariant to phase wraps. The proposed method was applied to retrospectively under-sampled in vivo datasets and compared with state of the art reconstruction methods. Results: Phase cycling reconstructions showed reduction of artifacts compared to reconstructions with- out phase cycling and achieved similar performances as state of the art results in partial Fourier, water-fat and divergence-free regularized flow reconstruction. Joint reconstruction of partial Fourier + water-fat imaging + PI + CS, and partial Fourier + divergence-free regularized flow imaging + PI + CS were demonstrated. Conclusion: The proposed phase cycling reconstruction provides an alternative way to perform phase regularized reconstruction, without the need to perform phase unwrapping. It is robust to the choice of initial solutions and encourages the joint reconstruction of phase imaging applications

DIMENSION: Dynamic MR Imaging with Both K-space and Spatial Prior Knowledge Obtained via Multi-Supervised Network Training

Dynamic MR image reconstruction from incomplete k-space data has generated great research interest due to its capability in reducing scan time. Nevertheless, the reconstruction problem is still challenging due to its ill-posed nature. Most existing methods either suffer from long iterative reconstruction time or explore limited prior knowledge. This paper proposes a dynamic MR imaging method with both k-space and spatial prior knowledge integrated via multi-supervised network training, dubbed as DIMENSION. Specifically, the DIMENSION architecture consists of a frequential prior network for updating the k-space with its network prediction and a spatial prior network for capturing image structures and details. Furthermore, a multisupervised network training technique is developed to constrain the frequency domain information and reconstruction results at different levels. The comparisons with classical k-t FOCUSS, k-t SLR, L+S and the state-of-the-art CNN-based method on in vivo datasets show our method can achieve improved reconstruction results in shorter time.Comment: 11 pages, 12 figure

Altered functional and structural brain network organization in autism.

Structural and functional underconnectivity have been reported for multiple brain regions, functional systems, and white matter tracts in individuals with autism spectrum disorders (ASD). Although recent developments in complex network analysis have established that the brain is a modular network exhibiting small-world properties, network level organization has not been carefully examined in ASD. Here we used resting-state functional MRI (n = 42 ASD, n = 37 typically developing; TD) to show that children and adolescents with ASD display reduced short and long-range connectivity within functional systems (i.e., reduced functional integration) and stronger connectivity between functional systems (i.e., reduced functional segregation), particularly in default and higher-order visual regions. Using graph theoretical methods, we show that pairwise group differences in functional connectivity are reflected in network level reductions in modularity and clustering (local efficiency), but shorter characteristic path lengths (higher global efficiency). Structural networks, generated from diffusion tensor MRI derived fiber tracts (n = 51 ASD, n = 43 TD), displayed lower levels of white matter integrity yet higher numbers of fibers. TD and ASD individuals exhibited similar levels of correlation between raw measures of structural and functional connectivity (n = 35 ASD, n = 35 TD). However, a principal component analysis combining structural and functional network properties revealed that the balance of local and global efficiency between structural and functional networks was reduced in ASD, positively correlated with age, and inversely correlated with ASD symptom severity. Overall, our findings suggest that modeling the brain as a complex network will be highly informative in unraveling the biological basis of ASD and other neuropsychiatric disorders

Sparse signal reconstruction from polychromatic X-ray CT measurements via mass attenuation discretization

We propose a method for reconstructing sparse images from polychromatic x-ray computed tomography (ct) measurements via mass attenuation coefficient discretization. The material of the inspected object and the incident spectrum are assumed to be unknown. We rewrite the Lambert-Beer’s law in terms of integral expressions of mass attenuation and discretize the resulting integrals. We then present a penalized constrained least-squares optimization approach forreconstructing the underlying object from log-domain measurements, where an active set approach is employed to estimate incident energy density parameters and the nonnegativity and sparsity of the image density map are imposed using negative-energy and smooth ℓ1-norm penalty terms. We propose a two-step scheme for refining the mass attenuation discretization grid by using higher sampling rate over the range with higher photon energy, and eliminating the discretization points that have little effect on accuracy of the forward projection model. This refinement allows us to successfully handle the characteristic lines (Dirac impulses) in the incident energy density spectrum. We compare the proposed method with the standard filtered backprojection, which ignores the polychromatic nature of the measurements and sparsity of theimage density map. Numerical simulations using both realistic simulated and real x-ray ct data are presented

Under-Sampled Reconstruction Techniques for Accelerated Magnetic Resonance Imaging

Due to physical and biological constraints and requirements on the minimum resolution and SNR, the acquisition time is relatively long in magnetic resonance imaging (MRI). Consequently, a limited number of pulse sequences can be run in a clinical MRI session because of constraints on the total acquisition time due to patient comfort and cost considerations. Therefore, it is strongly desired to reduce the acquisition time without compromising the reconstruction quality. This thesis concerns under-sampled reconstruction techniques for acceleration of MRI acquisitions, i.e., parallel imaging and compressed sensing. While compressed sensing MRI reconstructions are commonly regularized by penalizing the decimated wavelet transform coefficients, it is shown in this thesis that the visual artifacts, associated with the lack of translation-invariance of the wavelet basis in the decimated form, can be avoided by penalizing the undecimated wavelet transform coefficients, i.e., the stationary wavelet transform (SWT). An iterative SWT thresholding algorithm for combined SWT-regularized compressed sensing and parallel imaging reconstruction is presented. Additionally, it is shown that in MRI applications involving multiple sequential acquisitions, e.g., quantitative T1/T2 mapping, the correlation between the successive acquisitions can be incorporated as an additional constraint for joint under-sampled reconstruction, resulting in improved reconstruction performance. While quantitative measures of quality, e.g., reconstruction error with respect to the fully-sampled reference, are commonly used for performance evaluation and comparison of under-sampled reconstructions, this thesis shows that such quantitative measures do not necessarily correlate with the subjective quality of reconstruction as perceived by radiologists and other expert end users. Therefore, unless accompanied by subjective evaluations, quantitative quality measurements/comparisons will be of limited clinical impact. The results of experiments aimed at subjective evaluation/comparison of different under-sampled reconstructions for specific clinical neuroimaging MRI applications are presented in this thesis. One motivation behind the current work was to reduce the acquisition time for relaxation mapping techniques DESPOT1 and DESPOT2. This work also includes a modification to the Driven Equilibrium Single Pulse Observation of T1 with high-speed incorporation of RF field inhomogeneities (DESPOT1-HIFI), resulting in more accurate estimation of T1 values at high strength (3T and higher) magnetic fields

Disease Prediction based on Functional Connectomes using a Scalable and Spatially-Informed Support Vector Machine

Substantial evidence indicates that major psychiatric disorders are associated with distributed neural dysconnectivity, leading to strong interest in using neuroimaging methods to accurately predict disorder status. In this work, we are specifically interested in a multivariate approach that uses features derived from whole-brain resting state functional connectomes. However, functional connectomes reside in a high dimensional space, which complicates model interpretation and introduces numerous statistical and computational challenges. Traditional feature selection techniques are used to reduce data dimensionality, but are blind to the spatial structure of the connectomes. We propose a regularization framework where the 6-D structure of the functional connectome is explicitly taken into account via the fused Lasso or the GraphNet regularizer. Our method only restricts the loss function to be convex and margin-based, allowing non-differentiable loss functions such as the hinge-loss to be used. Using the fused Lasso or GraphNet regularizer with the hinge-loss leads to a structured sparse support vector machine (SVM) with embedded feature selection. We introduce a novel efficient optimization algorithm based on the augmented Lagrangian and the classical alternating direction method, which can solve both fused Lasso and GraphNet regularized SVM with very little modification. We also demonstrate that the inner subproblems of the algorithm can be solved efficiently in analytic form by coupling the variable splitting strategy with a data augmentation scheme. Experiments on simulated data and resting state scans from a large schizophrenia dataset show that our proposed approach can identify predictive regions that are spatially contiguous in the 6-D "connectome space," offering an additional layer of interpretability that could provide new insights about various disease processes

Data-Driven Learning of a Union of Sparsifying Transforms Model for Blind Compressed Sensing

Compressed sensing is a powerful tool in applications such as magnetic resonance imaging (MRI). It enables accurate recovery of images from highly undersampled measurements by exploiting the sparsity of the images or image patches in a transform domain or dictionary. In this work, we focus on blind compressed sensing (BCS), where the underlying sparse signal model is a priori unknown, and propose a framework to simultaneously reconstruct the underlying image as well as the unknown model from highly undersampled measurements. Specifically, our model is that the patches of the underlying image(s) are approximately sparse in a transform domain. We also extend this model to a union of transforms model that better captures the diversity of features in natural images. The proposed block coordinate descent type algorithms for blind compressed sensing are highly efficient, and are guaranteed to converge to at least the partial global and partial local minimizers of the highly non-convex BCS problems. Our numerical experiments show that the proposed framework usually leads to better quality of image reconstructions in MRI compared to several recent image reconstruction methods. Importantly, the learning of a union of sparsifying transforms leads to better image reconstructions than a single adaptive transform.Comment: Appears in IEEE Transactions on Computational Imaging, 201

Deep Convolutional Framelets: A General Deep Learning Framework for Inverse Problems

Recently, deep learning approaches with various network architectures have achieved significant performance improvement over existing iterative reconstruction methods in various imaging problems. However, it is still unclear why these deep learning architectures work for specific inverse problems. To address these issues, here we show that the long-searched-for missing link is the convolution framelets for representing a signal by convolving local and non-local bases. The convolution framelets was originally developed to generalize the theory of low-rank Hankel matrix approaches for inverse problems, and this paper further extends the idea so that we can obtain a deep neural network using multilayer convolution framelets with perfect reconstruction (PR) under rectilinear linear unit nonlinearity (ReLU). Our analysis also shows that the popular deep network components such as residual block, redundant filter channels, and concatenated ReLU (CReLU) do indeed help to achieve the PR, while the pooling and unpooling layers should be augmented with high-pass branches to meet the PR condition. Moreover, by changing the number of filter channels and bias, we can control the shrinkage behaviors of the neural network. This discovery leads us to propose a novel theory for deep convolutional framelets neural network. Using numerical experiments with various inverse problems, we demonstrated that our deep convolution framelets network shows consistent improvement over existing deep architectures.This discovery suggests that the success of deep learning is not from a magical power of a black-box, but rather comes from the power of a novel signal representation using non-local basis combined with data-driven local basis, which is indeed a natural extension of classical signal processing theory.Comment: This will appear in SIAM Journal on Imaging Science

Fast Multi-Layer Laplacian Enhancement

A novel, fast and practical way of enhancing images is introduced in this paper. Our approach builds on Laplacian operators of well-known edge-aware kernels, such as bilateral and nonlocal means, and extends these filter's capabilities to perform more effective and fast image smoothing, sharpening and tone manipulation. We propose an approximation of the Laplacian, which does not require normalization of the kernel weights. Multiple Laplacians of the affinity weights endow our method with progressive detail decomposition of the input image from fine to coarse scale. These image components are blended by a structure mask, which avoids noise/artifact magnification or detail loss in the output image. Contributions of the proposed method to existing image editing tools are: (1) Low computational and memory requirements, making it appropriate for mobile device implementations (e.g. as a finish step in a camera pipeline), (2) A range of filtering applications from detail enhancement to denoising with only a few control parameters, enabling the user to apply a combination of various (and even opposite) filtering effects