arXiv subjects

Xiaoqun Zhang

Publications and source records attributed to Xiaoqun Zhang.

50 records · Page 3Linked to original sources

arXiv2019

Low-Dose CT with Deep Learning Regularization via Proximal Forward Backward Splitting

Low dose X-ray computed tomography (LDCT) is desirable for reduced patient dose. This work develops image reconstruction methods with deep learning (DL) regularization for LDCT. Our methods are based on unrolling of proximal forward-backward splitting (PFBS) framework with data-driven image regularization via deep neural networks. In contrast with PFBS-IR that utilizes standard data fidelity updates via iterative reconstruction (IR) method, PFBS-AIR involves preconditioned data fidelity updates that fuse analytical reconstruction (AR) method and IR in a synergistic way, I.e. fused analytical and iterative reconstruction (AIR). The results suggest that DL-regularized methods (PFBS-IR and PFBS-AIR) provided better reconstruction quality from conventional wisdoms (AR or IR), and DL-based postprocessing method (FBPConvNet). In addition, owing to AIR, PFBS-AIR noticeably outperformed PFBS-IR.

eess.IV↗

arXiv2019

A greedy algorithm for sparse precision matrix approximation

Precision matrix estimation is an important problem in statistical data analysis. This paper introduces a fast sparse precision matrix estimation algorithm, namely GISS$^{ρ}$, which is originally introduced for compressive sensing. The algorithm GISS$^{ρ}$ is derived based on $l_1$ minimization while with the computation advantage of greedy algorithms. We analyze the asymptotic convergence rate of the proposed GISS$^{ρ}$ for sparse precision matrix estimation and sparsity recovery properties with respect to the stopping criteria. Finally, we numerically compare GISS$^ρ$ to other sparse recovery algorithms, such as ADMM and HTP in three settings of precision matrix estimation. The numerical results show the advantages of the proposed algorithm.

math.ST↗

arXiv2019

NLTG Priors in Medical Image: Nonlocal TV-Gaussian (NLTG) prior for Bayesian inverse problems with applications to Limited CT Reconstruction

Bayesian inference methods have been widely applied in inverse problems, {largely due to their ability to characterize the uncertainty associated with the estimation results.} {In the Bayesian framework} the prior distribution of the unknown plays an essential role in the Bayesian inference, {and a good prior distribution can significantly improve the inference results.} In this paper, we extend the total~variation-Gaussian (TG) prior in \cite{Z.Yao2016}, and propose a hybrid prior distribution which combines the nonlocal total variation regularization and the Gaussian (NLTG) distribution. The advantage of the new prior is two-fold. The proposed prior models both texture and geometric structures present in images through the NLTV. The Gaussian reference measure also provides a flexibility of incorporating structure information from a reference image. Some theoretical properties are established for the NLTG prior. The proposed prior is applied to limited-angle tomography reconstruction problem with difficulties of severe data missing. We compute both MAP and CM estimates through two efficient methods and the numerical experiments validate the advantages and feasibility of the proposed NLTG prior.

math.OC↗

arXiv2018

Dynamic SPECT reconstruction with temporal edge correlation

In dynamic imaging, a key challenge is to reconstruct image sequences with high temporal resolution from strong undersampling projections due to a relatively slow data acquisition speed. In this paper, we propose a variational model using the infimal convolution of Bregman distance with respect to total variation to model edge dependence of sequential frames. The proposed model is solved via an alternating iterative scheme, for which each subproblem is convex and can be solved by existing algorithms. The proposed model is formulated under both Gaussian and Poisson noise assumption and the simulation on two sets of dynamic images shows the advantage of the proposed method compared to previous methods.

math.NA↗

arXiv2018

Statistical Image Reconstruction Using Mixed Poisson-Gaussian Noise Model for X-Ray CT

Statistical image reconstruction (SIR) methods for X-ray CT produce high-quality and accurate images, while greatly reducing patient exposure to radiation. When further reducing X-ray dose to an ultra-low level by lowering the tube current, photon starvation happens and electronic noise starts to dominate, which introduces negative or zero values into the raw measurements. These non-positive values pose challenges to post-log SIR methods that require taking the logarithm of the raw data, and causes artifacts in the reconstructed images if simple correction methods are used to process these non-positive raw measurements. The raw data at ultra-low dose deviates significantly from Poisson or shifted Poisson statistics for pre-log data and from Gaussian statistics for post-log data. This paper proposes a novel SIR method called MPG (mixed Poisson-Gaussian). MPG models the raw noisy measurements using a mixed Poisson-Gaussian distribution that accounts for both the quantum noise and electronic noise. MPG is able to directly use the negative and zero values in raw data without any pre-processing. MPG cost function contains a reweighted least square data-fit term, an edge preserving regularization term and a non-negativity constraint term. We use Alternating Direction Method of Multipliers (ADMM) to separate the MPG optimization problem into several sub-problems that are easier to solve. Our results on 3D simulated cone-beam data set and synthetic helical data set generated from clinical data indicate that the proposed MPG method reduces noise and decreases bias in the reconstructed images, comparing with the conventional filtered back projection (FBP), penalized weighted least-square (PWLS) and shift Poisson (SP) method for ultra-low dose CT (ULDCT) imaging.

physics.med-ph↗

arXiv2018

PET-MRI Joint Reconstruction by Joint Sparsity Based Tight Frame Regularization

Recent technical advances lead to the coupling of PET and MRI scanners, enabling to acquire functional and anatomical data simultaneously. In this paper, we propose a tight frame based PET-MRI joint reconstruction model via the joint sparsity of tight frame coefficients. In addition, a non-convex balanced approach is adopted to take the different regularities of PET and MRI images into account. To solve the nonconvex and nonsmooth model, a proximal alternating minimization algorithm is proposed, and the global convergence is present based on Kurdyka-Lojasiewicz property. Finally, the numerical experiments show that the our proposed models achieve better performance over the existing PET-MRI joint reconstruction models.

math.NA↗

arXiv2018

An accelerated proximal iterative hard thresholding method for $\ell_0$ minimization

In this paper, we consider a non-convex problem which is the sum of $\ell_0$-norm and a convex smooth function under box constraint. We propose one proximal iterative hard thresholding type method with extrapolation step used for acceleration and establish its global convergence results. In detail, the sequence generated by the proposed method globally converges to a local minimizer of the objective function. Finally, we conduct numerical experiments to show the proposed method's effectiveness on comparison with some other efficient methods.

math.OC↗

arXiv2017

Image-domain multi-material decomposition for dual-energy CT based on correlation and sparsity of material images

Dual energy CT (DECT) enhances tissue characterization because it can produce images of basis materials such as soft-tissue and bone. DECT is of great interest in applications to medical imaging, security inspection and nondestructive testing. Theoretically, two materials with different linear attenuation coefficients can be accurately reconstructed using DECT technique. However, the ability to reconstruct three or more basis materials is clinically and industrially important. Under the assumption that there are at most three materials in each pixel, there are a few methods that estimate multiple material images from DECT measurements by enforcing sum-to-one and a box constraint ([0 1]) derived from both the volume and mass conservation assumption. The recently proposed image-domain multi-material decomposition (MMD) method introduces edge-preserving regularization for each material image which neglects the relations among material images, and enforced the assumption that there are at most three materials in each pixel using a time-consuming loop over all possible material-triplet in each iteration of optimizing its cost function. We propose a new image-domain MMD method for DECT that considers the prior information that different material images have common edges and encourages sparsity of material composition in each pixel using regularization.

physics.med-ph↗

arXiv2017

An Edge Driven Wavelet Frame Model for Image Restoration

Wavelet frame systems are known to be effective in capturing singularities from noisy and degraded images. In this paper, we introduce a new edge driven wavelet frame model for image restoration by approximating images as piecewise smooth functions. With an implicit representation of image singularities sets, the proposed model inflicts different strength of regularization on smooth and singular image regions and edges. The proposed edge driven model is robust to both image approximation and singularity estimation. The implicit formulation also enables an asymptotic analysis of the proposed models and a rigorous connection between the discrete model and a general continuous variational model. Finally, numerical results on image inpainting and deblurring show that the proposed model is compared favorably against several popular image restoration models.

math.NA↗

arXiv2016

Simultaneous Reconstruction and Segmentation for Dynamic SPECT Imaging

This work deals with the reconstruction of dynamic images that incorporate characteristic dynamics in certain subregions, as arising for the kinetics of many tracers in emission tomography (SPECT, PET). We make use of a basis function approach for the unknown tracer concentration by assuming that the region of interest can be divided into subregions with spatially constant concentration curves. Applying a regularized variational framework reminiscent of the Chan-Vese model for image segmentation we simultaneously reconstruct both the labelling functions of the subregions as well as the subconcentrations within each region. Our particular focus is on applications in SPECT with Poisson noise model, resulting in a Kullback-Leibler data fidelity in the variational approach. We present a detailed analysis of the proposed variational model and prove existence of minimizers as well as error estimates. The latter apply to a more general class of problems and generalize existing results in literature since we deal with a nonlinear forward operator and a nonquadratic data fidelity. A computational algorithm based on alternating minimization and splitting techniques is developed for the solution of the problem and tested on appropriately designed synthetic data sets. For those we compare the results to those of standard EM reconstructions and investigate the effects of Poisson noise in the data.

math.NA↗

arXiv2016

Limited Tomography Reconstruction via Tight Frame and Sinogram Extrapolation

X-ray computed tomography (CT) is one of widely used diagnostic tools for medical and dental tomographic imaging of the human body. However, the standard filtered backprojection reconstruction method requires the complete knowledge of the projection data. In the case of limited data, the inverse problem of CT becomes more ill-posed, which makes the reconstructed image deteriorated by the artifacts. In this paper, we consider two dimensional CT reconstruction using the horizontally truncated projections. Over the decades, the numerous results including the sparsity model based approach has enabled the reconstruction of the image inside the region of interest (ROI) from the limited knowledge of the data. However, unlike these existing methods, we try to reconstruct the entire CT image from the limited knowledge of the sinogram via the tight frame regularization and the simultaneous sinogram extrapolation. Our proposed model shows more promising numerical simulation results compared with the existing sparsity model based approach.

math.NA↗

arXiv2016

A primal-dual fixed point algorithm for multi-block convex minimization

We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP algorithm to multi-block problems and illustrate how practical and fully decoupled schemes can be derived, especially for parallel implementation of large scale problems. The connections and comparisons to the alternating direction method of multiplier (ADMM) are also present. We demonstrate how different algorithms can be obtained by splitting the problems in different ways through the classic example of sparsity regularized least square model with constraint. In particular, for a class of linearly constrained problems, which are of great interest in the context of multi-block ADMM, can be solved by PDFP with a guarantee of convergence. Finally, some experiments are provided to illustrate the performance of several schemes derived by the PDFP algorithm.

math.OC↗

arXiv2015

A primal-dual fixed-point algorithm for minimization of the sum of three convex separable functions

Many problems arising in image processing and signal recovery with multi-regularization can be formulated as minimization of a sum of three convex separable functions. Typically, the objective function involves a smooth function with Lipschitz continuous gradient, a linear composite nonsmooth function and a nonsmooth function. In this paper, we propose a primal-dual fixed-point (PDFP) scheme to solve the above class of problems. The proposed algorithm for three block problems is a fully splitting symmetric scheme, only involving explicit gradient and linear operators without inner iteration, when the nonsmooth functions can be easily solved via their proximity operators, such as $\ell_1$ type regularization. We study the convergence of the proposed algorithm and illustrate its efficiency through examples on fused LASSO and image restoration with non-negative constraint and sparse regularization.

math.OC↗

arXiv2015

A Hybrid Segmentation and D-bar Method for Electrical Impedance Tomography

The Regularized D-bar method for Electrical Impedance Tomography provides a rigorous mathematical approach for solving the full nonlinear inverse problem directly, i.e. without iterations. It is based on a low-pass filtering in the (nonlinear) frequency domain. However, the resulting D-bar reconstructions are inherently smoothed leading to a loss of edge distinction. In this paper, a novel approach that combines the rigor of the D-bar approach with the edge-preserving nature of Total Variation regularization is presented. The method also includes a data-driven contrast adjustment technique guided by the key functions (CGO solutions) of the D-bar method. The new TV-Enhanced D-bar Method produces reconstructions with sharper edges and improved contrast while still solving the full nonlinear problem. This is achieved by using the TV-induced edges to increase the truncation radius of the scattering data in the nonlinear frequency domain thereby increasing the radius of the low pass filter. The algorithm is tested on numerically simulated noisy EIT data and demonstrates significant improvements in edge preservation and contrast which can be highly valuable for absolute EIT imaging.

math.NA↗