Xiaoqun Zhang

Qiaoqiao Ding, Yong Long, Xiaoqun Zhang et al.

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.

Martin Burger, Carolin Rossmanith, Xiaoqun Zhang

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.

Qiaoqiao Ding, Tianye Niu, Xiaoqun Zhang et al.

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.

Qiaoqiao Ding, Martin Burger, Xiaoqun Zhang

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.

Ziruo Cai, Junqi Tang, Subhadip Mukherjee et al.

Bayesian methods for solving inverse problems are a powerful alternative to classical methods since the Bayesian approach offers the ability to quantify the uncertainty in the solution. In recent years, data-driven techniques for solving inverse problems have also been remarkably successful, due to their superior representation ability. In this work, we incorporate data-based models into a class of Langevin-based sampling algorithms for Bayesian inference in imaging inverse problems. In particular, we introduce NF-ULA (Normalizing Flow-based Unadjusted Langevin algorithm), which involves learning a normalizing flow (NF) as the image prior. We use NF to learn the prior because a tractable closed-form expression for the log prior enables the differentiation of it using autograd libraries. Our algorithm only requires a normalizing flow-based generative network, which can be pre-trained independently of the considered inverse problem and the forward operator. We perform theoretical analysis by investigating the well-posedness and non-asymptotic convergence of the resulting NF-ULA algorithm. The efficacy of the proposed NF-ULA algorithm is demonstrated in various image restoration problems such as image deblurring, image inpainting, and limited-angle X-ray computed tomography (CT) reconstruction. NF-ULA is found to perform better than competing methods for severely ill-posed inverse problems.

Jae Kyu Choi, Chenglong Bao, Xiaoqun Zhang

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.

Qiaoqiao Ding, Hui Ji, Yuhui Quan et al.

Low-dose CT (LDCT) imaging attracted a considerable interest for the reduction of the object's exposure to X-ray radiation. In recent years, supervised deep learning (DL) has been extensively studied for LDCT image reconstruction, which trains a network over a dataset containing many pairs of normal-dose and low-dose images. However, the challenge on collecting many such pairs in the clinical setup limits the application of such supervised-learning-based methods for LDCT image reconstruction in practice. Aiming at addressing the challenges raised by the collection of training dataset, this paper proposed a unsupervised deep learning method for LDCT image reconstruction, which does not require any external training data. The proposed method is built on a re-parametrization technique for Bayesian inference via deep network with random weights, combined with additional total variational~(TV) regularization. The experiments show that the proposed method noticeably outperforms existing dataset-free image reconstruction methods on the test data.

Jae Kyu Choi, Bin Dong, Xiaoqun Zhang

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.

Hao Hao, Xiaoqun Zhang, Aimin Zhou

Surrogate-assisted evolutionary algorithms (SAEAs) hold significant importance in resolving expensive optimization problems~(EOPs). Extensive efforts have been devoted to improving the efficacy of SAEAs through the development of proficient model-assisted selection methods. However, generating high-quality solutions is a prerequisite for selection. The fundamental paradigm of evaluating a limited number of solutions in each generation within SAEAs reduces the variance of adjacent populations, thus impacting the quality of offspring solutions. This is a frequently encountered issue, yet it has not gained widespread attention. This paper presents a framework using unevaluated solutions to enhance the efficiency of SAEAs. The surrogate model is employed to identify high-quality solutions for direct generation of new solutions without evaluation. To ensure dependable selection, we have introduced two tailored relation models for the selection of the optimal solution and the unevaluated population. A comprehensive experimental analysis is performed on two test suites, which showcases the superiority of the relation model over regression and classification models in the selection phase. Furthermore, the surrogate-selected unevaluated solutions with high potential have been shown to significantly enhance the efficiency of the algorithm.

Zhe Xiong, Qiaoqiao Ding, Xiaoqun Zhang

Finding a transformation between two unknown probability distributions from finite samples is crucial for modeling complex data distributions and performing tasks such as sample generation, domain adaptation and statistical inference. One powerful framework for such transformations is normalizing flow, which transforms an unknown distribution into a standard normal distribution using an invertible network. In this paper, we introduce a novel model called SyMOT-Flow that trains an invertible transformation by minimizing the symmetric maximum mean discrepancy between samples from two unknown distributions, and an optimal transport cost is incorporated as regularization to obtain a short-distance and interpretable transformation. The resulted transformation leads to more stable and accurate sample generation. Several theoretical results are established for the proposed model and its effectiveness is validated with low-dimensional illustrative examples as well as high-dimensional bi-modality medical image generation through the forward and reverse flows.

Jian-Feng Cai, Jingyang Li, Xiaoqun Zhang et al.

Matrix product operators (MPOs) provide a scalable approach for quantum state tomography (QST) by offering a compact representation of many-body mixed states with limited entanglement, using only a number of parameters that scales polynomially with the system size. In this paper, we study QST for quantum density matrices that can be represented by MPOs. We first derive an equivalent characterization of Hermiticity in terms of the MPO core tensors and show that the coefficient tensor of an MPO under the Pauli or generalized Gell-Mann basis admits a real-valued low tensor-train (TT) rank structure. This establishes an explicit connection between MPO-based QST and noisy low-rank tensor completion. Motivated by this formulation, we develop an online Riemannian gradient descent (oRGD) algorithm that sequentially incorporates measurement data during the reconstruction process. With a proper initialization, we prove that oRGD converges linearly to the target MPO and succeeds with a number of distinct measurement settings that scales quadratically with the system size. As a byproduct, our analysis also yields a significantly improved sample complexity bound for the low TT rank tensor completion task. Furthermore, we propose a tailored spectral initialization method and establish its theoretical guarantee. Numerical experiments on several classes of quantum states validate the effectiveness and scalability of the proposed method.

Zhe Xiong, Qiaoqiao Ding, Xiaoqun Zhang

Recently, medical image synthesis gains more and more popularity, along with the rapid development of generative models. Medical image synthesis aims to generate an unacquired image modality, often from other observed data modalities. Synthesized images can be used for clinical diagnostic assistance, data augmentation for model training and validation or image quality improving. In the meanwhile, the flow-based models are among the successful generative models for the ability of generating realistic and high-quality synthetic images. However, most flow-based models require to calculate flow ordinary different equation (ODE) evolution steps in synthesis process, for which the performances are significantly limited by heavy computation time due to a large number of time iterations. In this paper, we propose a novel flow-based model, namely bi-directional Discrete Process Matching (Bi-DPM) to accomplish the bi-modality image synthesis tasks. Different to other flow matching based models, we propose to utilize both forward and backward ODE flows and enhance the consistency on the intermediate images over a few discrete time steps, resulting in a synthesis process maintaining high-quality generations for both modalities under the guidance of paired data. Our experiments on three datasets of MRI T1/T2 and CT/MRI demonstrate that Bi-DPM outperforms other state-of-the-art flow-based methods for bi-modality image synthesis, delivering higher image quality with accurate anatomical regions.

Xiang Cao, Qiaoqiao Ding, Xinliang Liu et al.

Ultrasound Computed Tomography (USCT) constitutes a nonlinear inverse problem with inherent ill-posedness that can benefit from regularization through diffusion generative priors. However, traditional approaches for solving Helmholtz equation-constrained USCT face three fundamental challenges when integrating these priors: PDE-constrained gradient computation, discretization-induced approximation errors, and computational imbalance between neural networks and numerical PDE solvers. In this work, we introduce \textbf{Diff-ANO} (\textbf{Diff}usion-based Models with \textbf{A}djoint \textbf{N}eural \textbf{O}perators), a novel framework that combines conditional consistency models with adjoint operator learning to address these limitations. Our two key innovations include: (1) a \textit{conditional consistency model} that enables measurement-conditional few-step sampling by directly learning a self-consistent mapping from diffusion trajectories, and (2) an \textit{adjoint operator learning} module that replaces traditional PDE solvers with neural operator surrogates for efficient adjoint-based gradient computation. To enable practical deployment, we introduce the batch-based Convergent Born Series (BCBS)--a memory-efficient strategy for online generation of neural operator training pairs. Comprehensive experiments demonstrate that Diff-ANO significantly improves both computational efficiency and reconstruction quality, especially under sparse-view and partial-view measurement scenarios.

Chaozhi Zhang, Lin Liu, Xiaoqun Zhang

Data scarcity poses a serious threat to modern machine learning and artificial intelligence, as their practical success typically relies on the availability of big datasets. One effective strategy to mitigate the issue of insufficient data is to first harness information from other data sources possessing certain similarities in the study design stage, and then employ the multi-task or meta learning framework in the analysis stage. In this paper, we focus on multi-task (or multi-source) linear models whose coefficients across tasks share an invariant low-rank component, a popular structural assumption considered in the recent multi-task or meta learning literature. Under this assumption, we propose a new algorithm, called Meta Subspace Pursuit (abbreviated as Meta-SP), that provably learns this invariant subspace shared by different tasks. Under this stylized setup for multi-task or meta learning, we establish both the algorithmic and statistical guarantees of the proposed method. Extensive numerical experiments are conducted, comparing Meta-SP against several competing methods, including popular, off-the-shelf model-agnostic meta learning algorithms such as ANIL. These experiments demonstrate that Meta-SP achieves superior performance over the competing methods in various aspects.

Hao Hao, Xiaoqun Zhang, Aimin Zhou

Black-box optimization problems, which are common in many real-world applications, require optimization through input-output interactions without access to internal workings. This often leads to significant computational resources being consumed for simulations. Bayesian Optimization (BO) and Surrogate-Assisted Evolutionary Algorithm (SAEA) are two widely used gradient-free optimization techniques employed to address such challenges. Both approaches follow a similar iterative procedure that relies on surrogate models to guide the search process. This paper aims to elucidate the similarities and differences in the utilization of model uncertainty between these two methods, as well as the impact of model inaccuracies on algorithmic performance. A novel model-assisted strategy is introduced, which utilizes unevaluated solutions to generate offspring, leveraging the population-based search capabilities of evolutionary algorithm to enhance the effectiveness of model-assisted optimization. Experimental results demonstrate that the proposed approach outperforms mainstream Bayesian optimization algorithms in terms of accuracy and efficiency.

Chaozhi Zhang, Wenxiang Ding, Roy Y. He et al.

The reconstruction of dynamic positron emission tomography (PET) images from noisy projection data is a significant but challenging problem. In this paper, we introduce an unsupervised learning approach, Non-negative Implicit Neural Representation Factorization (\texttt{NINRF}), based on low rank matrix factorization of unknown images and employing neural networks to represent both coefficients and bases. Mathematically, we demonstrate that if a sequence of dynamic PET images satisfies a generalized non-negative low-rank property, it can be decomposed into a set of non-negative continuous functions varying in the temporal-spatial domain. This bridges the well-established non-negative matrix factorization (NMF) with continuous functions and we propose using implicit neural representations (INRs) to connect matrix with continuous functions. The neural network parameters are obtained by minimizing the KL divergence, with additional sparsity regularization on coefficients and bases. Extensive experiments on dynamic PET reconstruction with Poisson noise demonstrate the effectiveness of the proposed method compared to other methods, while giving continuous representations for object's detailed geometric features and regional concentration variation.

Fengmiao Bian, Jian-Feng Cai, Xiaoqun Zhang et al.

Low-rank tensor completion aims to recover a tensor from partially observed entries, and it is widely applicable in fields such as quantum computing and image processing. Due to the significant advantages of the tensor train (TT) format in handling structured high-order tensors, this paper investigates the low-rank tensor completion problem based on the TT-format. We proposed a preconditioned Riemannian gradient descent algorithm (PRGD) to solve low TT-rank tensor completion and establish its linear convergence. Experimental results on both simulated and real datasets demonstrate the effectiveness of the PRGD algorithm. On the simulated dataset, the PRGD algorithm reduced the computation time by two orders of magnitude compared to existing classical algorithms. In practical applications such as hyperspectral image completion and quantum state tomography, the PRGD algorithm significantly reduced the number of iterations, thereby substantially reducing the computational time.

Xiang Cao, Qiaoqiao Ding, Xiaoqun Zhang

The regularized D-bar method is a popular method for solving Electrical Impedance Tomography (EIT) problems due to its efficiency and simplicity. It utilizes the low-pass truncated scattering data in the non-linear Fourier domain to solve the associated D-bar integral equations, yielding a smooth conductivity approximation. However, the D-bar reconstruction often presents low contrast and resolution due to the absence of accurate high-frequency information and the ill-posedness of the problem. In this paper, we propose a deep learning-based supervised approach for real-time EIT reconstruction. Based on the D-bar method, we propose to utilize both multi-scale frequency enhancement and spatial consistency for a high image quality reconstruction. Additionally, we propose a fixed-point iteration for solving discrete D-bar systems on GPUs for fast computation. Numerical results are performed for both the continuum model and complete electrode model simulation on KIT4 and ACT4 datasets to demonstrate notable improvements in absolute EIT imaging quality.

Bingxin Zhou, Yuanhong Jiang, Yu Guang Wang et al.

The performance of graph representation learning is affected by the quality of graph input. While existing research usually pursues a globally smoothed graph embedding, we believe the rarely observed anomalies are as well harmful to an accurate prediction. This work establishes a graph learning scheme that automatically detects (locally) corrupted feature attributes and recovers robust embedding for prediction tasks. The detection operation leverages a graph autoencoder, which does not make any assumptions about the distribution of the local corruptions. It pinpoints the positions of the anomalous node attributes in an unbiased mask matrix, where robust estimations are recovered with sparsity promoting regularizer. The optimizer approaches a new embedding that is sparse in the framelet domain and conditionally close to input observations. Extensive experiments are provided to validate our proposed model can recover a robust graph representation from black-box poisoning and achieve excellent performance.

Ren Liu, Xiaoqun Zhang

Neural network has attracted great attention for a long time and many researchers are devoted to improve the effectiveness of neural network training algorithms. Though stochastic gradient descent (SGD) and other explicit gradient-based methods are widely adopted, there are still many challenges such as gradient vanishing and small step sizes, which leads to slow convergence and instability of SGD algorithms. Motivated by error back propagation (BP) and proximal methods, we propose a semi-implicit back propagation method for neural network training. Similar to BP, the difference on the neurons are propagated in a backward fashion and the parameters are updated with proximal mapping. The implicit update for both hidden neurons and parameters allows to choose large step size in the training algorithm. Finally, we also show that any fixed point of convergent sequences produced by this algorithm is a stationary point of the objective loss function. The experiments on both MNIST and CIFAR-10 demonstrate that the proposed semi-implicit BP algorithm leads to better performance in terms of both loss decreasing and training/validation accuracy, compared to SGD and a similar algorithm ProxBP.

Jae Kyu Choi, Bin Dong, Xiaoqun Zhang

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.