arXiv subjects

Wengu Chen

Publications and source records attributed to Wengu Chen.

At least 19 recordsLinked to original sources

arXiv2026

Stable Image Reconstruction via Two-Parameter Power-Scale Variation Minimization

In this article, we introduce a power-scale variation (PSV$_{a,p}$) with two tunable parameters: the sparsity-inducing exponent $p\in(0,1]$ and the scaling factor $a\in(0,\infty)$. By minimizing the PSV$_{a,p}$, we establish stable reconstructions in both the gradient and the image domains under the restricted isometry property (RIP) framework. Furthermore, we design an iteratively re-weighted least squares algorithm IRLSPSV to solve the unconstrained PSV$_{a,p}$ minimization. Numerical experiments demonstrate its superior performance and broad applicability. The main novelties are: (i) the PSV$_{a,p}$ minimization enjoys great flexibility and wide applicability due to its two tunable parameters $a$ and $p$, (ii) as $a\to\infty$, the PSV$_{a,p}$ minimization reduces to the $p$-th power total variation (TV$_p$) minimization and, even in this limiting case, the established RIP condition for image reconstruction is also new, (iii) the derived RIP upper bound $\overline{\delta}$ is proved to be asymptotically optimal in $a$ for gradient recovery, (iv) sensitivity analysis confirms the distinct roles of $a$ and $p$, thereby motivating a practical parameter tuning scheme for the proposed model.

cs.IT↗

arXiv2026

A Novel Two-Parameter Penalty: Relaxation Degree Analysis and Sparse Signal Recovery

In this article, we introduce a nonconvex two-parameter penalty function $P_{a,p}$, parameterized by $a\in(0,\infty)$ and $p\in(0,1]$, and the relaxation degree RD$_P$ for a separable nonconvex penalty function $P$. Based on $P_{a,p}$, we further propose the $P_{a,p}$ minimization framework for sparse signal recovery. This framework generalizes the TL1 minimization model established by S. Zhang and J. Xin (corresponding to the special case $p=1$) and provides a unified and flexible family of nonconvex penalty functions for sparse signal recovery. Using the sparse convex-combination technique, we establish both exact and stable sparse signal recovery under the restricted isometry property (RIP). To efficiently solve the resulting nonconvex optimization problem, we apply a modified iteratively re-weighted least squares method and the difference of convex functions algorithm (DCA) to develop the IRLSTLp algorithm for unconstrained $P_{a,p}$ minimization and prove some convergence results. Finally, some numerical experiments are conducted to show the flexibility of the $P_{a,p}$ minimization framework, the robustness of the IRLSTLp, and also the utility of the relaxation degree.

math.FA↗

arXiv2025

BF-APNN: A Low-Memory Method for Accelerating the Solution of Radiative Transfer Equations

The Radiative Transfer Equations (RTEs) exhibit high dimensionality and multiscale characteristics, rendering conventional numerical methods computationally intensive. Existing deep learning methods perform well in low-dimensional or linear RTEs, but still face many challenges with high-dimensional or nonlinear RTEs. To overcome these challenges, we propose the Basis Function Asymptotically Preserving Neural Network (BF-APNN), a framework that inherits the advantages of Radiative Transfer Asymptotically Preserving Neural Network (RT-APNN) and accelerates the solution process. By employing basis function expansion on the microscopic component, derived from micro-macro decomposition, BF-APNN effectively mitigates the computational burden associated with evaluating high-dimensional integrals during training. Numerical experiments, which involve challenging RTE scenarios featuring, nonlinearity, discontinuities, and multiscale behavior, demonstrate that BF-APNN substantially reduces training time compared to RT-APNN while preserving high solution accuracy. Moreover, BF-APNN exhibits superior performance in addressing complex, high-dimensional RTE problems, underscoring its potential as a robust tool for radiative transfer computations.

physics.comp-ph↗

arXiv2025

RT-APNN for Solving Gray Radiative Transfer Equations

The Gray Radiative Transfer Equations (GRTEs) are high-dimensional, multiscale problems that pose significant computational challenges for traditional numerical methods. Current deep learning approaches, including Physics-Informed Neural Networks (PINNs) and Asymptotically Preserving Neural Networks (APNNs), are largely restricted to low-dimensional or linear GRTEs. To address these challenges, we propose the Radiative Transfer Asymptotically Preserving Neural Network (RT-APNN), an innovative framework extending APNNs. RT-APNN integrates multiple neural networks into a cohesive architecture, reducing training time while ensuring high solution accuracy. Advanced techniques such as pre-training and Markov Chain Monte Carlo (MCMC) adaptive sampling are employed to tackle the complexities of long-term simulations and intricate boundary conditions. RT-APNN is the first deep learning method to successfully simulate the Marshak wave problem. Numerical experiments demonstrate its superiority over existing methods, including APNNs and MD-APNNs, in both accuracy and computational efficiency. Furthermore, RT-APNN excels at solving high-dimensional, nonlinear problems, underscoring its potential for diverse applications in science and engineering.

physics.comp-ph↗

arXiv2025

Asymptotic-Preserving Neural Networks based on Even-odd Decomposition for Multiscale Gray Radiative Transfer Equations

We present a novel Asymptotic-Preserving Neural Network (APNN) approach utilizing even-odd decomposition to tackle the nonlinear gray radiative transfer equations (GRTEs). Our AP loss demonstrates consistent stability concerning the small Knudsen number, ensuring the neural network solution uniformly converges to the diffusion limit solution. This APNN method alleviates the rigorous conservation requirements while simultaneously incorporating an auxiliary deep neural network, distinguishing it from the APNN method based on micro-macro decomposition for GRTE. Several numerical problems are examined to demonstrate the effectiveness of our proposed APNN technique.

math.NA↗

arXiv2020

Inertial Proximal ADMM for Separable Multi-Block Convex Optimizations and Compressive Affine Phase Retrieval

Separable multi-block convex optimization problem appears in many mathematical and engineering fields. In the first part of this paper, we propose an inertial proximal ADMM to solve a linearly constrained separable multi-block convex optimization problem, and we show that the proposed inertial proximal ADMM has global convergence under mild assumptions on the regularization matrices. Affine phase retrieval arises in holography, data separation and phaseless sampling, and it is also considered as a nonhomogeneous version of phase retrieval that has received considerable attention in recent years. Inspired by convex relaxation of vector sparsity and matrix rank in compressive sensing and by phase lifting in phase retrieval, in the second part of this paper, we introduce a compressive affine phase retrieval via lifting approach to connect affine phase retrieval with multi-block convex optimization, and then based on the proposed inertial proximal ADMM for multi-block convex optimization, we propose an algorithm to recover sparse real signals from their (noisy) affine quadratic measurements. Our numerical simulations show that the proposed algorithm has satisfactory performance for affine phase retrieval of sparse real signals.

math.NA↗

arXiv2018

Efficient and Robust Recovery of Signal and Image in Impulsive Noise via $\ell_1-α\ell_2$ Minimization

In this paper, we consider the efficient and robust reconstruction of signals and images via $\ell_{1}-α\ell_{2}~(0<α\leq 1)$ minimization in impulsive noise case. To achieve this goal, we introduce two new models: the $\ell_1-α\ell_2$ minimization with $\ell_1$ constraint, which is called $\ell_1-α\ell_2$-LAD, the $\ell_1-α\ell_2$ minimization with Dantzig selector constraint, which is called $\ell_1-α\ell_2$-DS. We first show that sparse signals or nearly sparse signals can be exactly or stably recovered via $\ell_{1}-α\ell_{2}$ minimization under some conditions based on the restricted $1$-isometry property ($\ell_1$-RIP). Second, for $\ell_1-α\ell_2$-LAD model, we introduce unconstrained $\ell_1-α\ell_2$ minimization model denoting $\ell_1-α\ell_2$-PLAD and propose $\ell_1-α\ell_2$LA algorithm to solve the $\ell_1-α\ell_2$-PLAD. Last, numerical experiments %on success rates of sparse signal recovery demonstrate that when the sensing matrix is ill-conditioned (i.e., the coherence of the matrix is larger than 0.99), the $\ell_1-α\ell_2$LA method is better than the existing convex and non-convex compressed sensing solvers for the recovery of sparse signals. And for the magnetic resonance imaging (MRI) reconstruction with impulsive noise, we show that the $\ell_1-α\ell_2$LA method has better performance than state-of-the-art methods via numerical experiments.

math.OC↗

arXiv2018

CAPRL: Signal Recovery from Compressive Affine Phase Retrieval via Lifting

In this paper, we consider compressive/sparse affine phase retrieval proposed in [B. Gao B, Q. Sun, Y. Wang and Z. Xu, Adv. in Appl. Math., 93(2018), 121-141]. By the lift technique, and heuristic nuclear norm for convex relaxation of rank and $\ell$ one norm convex relaxation of sparsity, we establish convex models , which are called compressive affine phase retrieval via lifting (CAPRL). In order to compute these models, we develop inertial proximal ADMM for multiple separated operators and also give out its convergence analysis. Our numerical experiments via proposed algorithm show that sparse signal can be exactly and stably recovered via CAPRL. We also list some other applications of our proposed algorithm.

math.OC↗

arXiv2018

Signal Recovery under Mutual Incoherence Property and Oracle Inequalities

This paper considers signal recovery through an unconstrained minimization in the framework of mutual incoherence property. A sufficient condition is provided to guarantee the stable recovery in the noisy case. And we give a lower bound for the $\ell_2$ norm of difference of reconstructed signals and the original signal, in the sense of expectation and probability. Furthermore, oracle inequalities of both sparse signals and non-sparse signals are derived under the mutual incoherence condition in the case of Gaussian noises. Finally, we investigate the relationship between mutual incoherence property and robust null space property and find that robust null space property can be deduced from the mutual incoherence property.

cs.IT↗

arXiv2018

Matrix Recovery from Rank-One Projection Measurements via Nonconvex Minimization

In this paper, we consider the matrix recovery from rank-one projection measurements proposed in [Cai and Zhang, Ann. Statist., 43(2015), 102-138], via nonconvex minimization. We establish a sufficient identifiability condition, which can guarantee the exact recovery of low-rank matrix via Schatten-$p$ minimization $\min_{X}\|X\|_{S_p}^p$ for $0<p<1$ under affine constraint, and stable recovery of low-rank matrix under $\ell_q$ constraint and Dantzig selector constraint. Our condition is also sufficient to guarantee low-rank matrix recovery via least $q$ minimization $\min_{X}\|\mathcal{A}(X)-b\|_{q}^q$ for $0<q\leq1$. And we also extend our result to Gaussian design distribution, and show that any matrix can be stably recovered for rank-one projection from Gaussian distributions via least $1$ minimization with high probability.

cs.IT↗

arXiv2018

Truncated Sparse Approximation Property and Truncated $q$-Norm Minimization

This paper considers approximately sparse signal and low-rank matrix's recovery via truncated norm minimization $\min_{x}\|x_T\|_q$ and $\min_{X}\|X_T\|_{S_q}$ from noisy measurements. We first introduce truncated sparse approximation property, a more general robust null space property, and establish the stable recovery of signals and matrices under the truncated sparse approximation property. We also explore the relationship between the restricted isometry property and truncated sparse approximation property. And we also prove that if a measurement matrix $A$ or linear map $\mathcal{A}$ satisfies truncated sparse approximation property of order $k$, then the first inequality in restricted isometry property of order $k$ and of order $2k$ can hold for certain different constants $\delta_{k}$ and $\delta_{2k}$, respectively. Last, we show that if $\delta_{t(k+|T^c|)}<\sqrt{(t-1)/t}$ for some $t\geq 4/3$, then measurement matrix $A$ and linear map $\mathcal{A}$ satisfy truncated sparse approximation property of order $k$. Which should point out is that when $T^c=\emptyset$, our conclusion implies that sparse approximation property of order $k$ is weaker than restricted isometry property of order $tk$.

cs.IT↗

arXiv2018

Signal Recovery under Cumulative Coherence

This paper considers signal recovery in the framework of cumulative coherence. First, we show that the Lasso estimator and the Dantzig selector exhibit similar behavior under the cumulative coherence. Then we estimate the approximation equivalence between the Lasso and the Dantzig selector by calculating prediction loss difference under the condition of cumulative coherence. And we also prove that the cumulative coherence implies the restricted eigenvalue condition. Last, we illustrate the advantages of cumulative coherence condition for three class matrices, in terms of the recovery performance of sparse signals via extensive numerical experiments.

cs.IT↗

arXiv2017

A sharp recovery condition for sparse signals with partial support information via orthogonal matching pursuit

This paper considers the exact recovery of $k$-sparse signals in the noiseless setting and support recovery in the noisy case when some prior information on the support of the signals is available. This prior support consists of two parts. One part is a subset of the true support and another part is outside of the true support. For $k$-sparse signals $\mathbf{x}$ with the prior support which is composed of $g$ true indices and $b$ wrong indices, we show that if the restricted isometry constant (RIC) $δ_{k+b+1}$ of the sensing matrix $\mathbf{A}$ satisfies \begin{eqnarray*} δ_{k+b+1}<\frac{1}{\sqrt{k-g+1}}, \end{eqnarray*} then orthogonal matching pursuit (OMP) algorithm can perfectly recover the signals $\mathbf{x}$ from $\mathbf{y}=\mathbf{Ax}$ in $k-g$ iterations. Moreover, we show the above sufficient condition on the RIC is sharp. In the noisy case, we achieve the exact recovery of the remainder support (the part of the true support outside of the prior support) for the $k$-sparse signals $\mathbf{x}$ from $\mathbf{y}=\mathbf{Ax}+\mathbf{v}$ under appropriate conditions. For the remainder support recovery, we also obtain a necessary condition based on the minimum magnitude of partial nonzero elements of the signals $\mathbf{x}$.

cs.IT↗

arXiv2017

Recovery of signals by a weighted $\ell_2/\ell_1$ minimization under arbitrary prior support information

In this paper, we introduce a weighted $\ell_2/\ell_1$ minimization to recover block sparse signals with arbitrary prior support information. When partial prior support information is available, a sufficient condition based on the high order block RIP is derived to guarantee stable and robust recovery of block sparse signals via the weighted $\ell_2/\ell_1$ minimization. We then show if the accuracy of arbitrary prior block support estimate is at least $50\%$, the sufficient recovery condition by the weighted $\ell_2/\ell_{1}$ minimization is weaker than that by the $\ell_2/\ell_{1}$ minimization, and the weighted $\ell_2/\ell_{1}$ minimization provides better upper bounds on the recovery error in terms of the measurement noise and the compressibility of the signal. Moreover, we illustrate the advantages of the weighted $\ell_2/\ell_1$ minimization approach in the recovery performance of block sparse signals under uniform and non-uniform prior information by extensive numerical experiments. The significance of the results lies in the facts that making explicit use of block sparsity and partial support information of block sparse signals can achieve better recovery performance than handling the signals as being in the conventional sense, thereby ignoring the additional structure and prior support information in the problem.

cs.IT↗

arXiv2016

The high order block RIP condition for signal recovery

In this paper, we consider the recovery of block sparse signals, whose nonzero entries appear in blocks (or clusters) rather than spread arbitrarily throughout the signal, from incomplete linear measurement. A high order sufficient condition based on block RIP is obtained to guarantee the stable recovery of all block sparse signals in the presence of noise, and robust recovery when signals are not exactly block sparse via mixed $l_{2}/l_{1}$ minimization. Moreover, a concrete example is established to ensure the condition is sharp. The significance of the results presented in this paper lies in the fact that recovery may be possible under more general conditions by exploiting the block structure of the sparsity pattern instead of the conventional sparsity pattern.

cs.IT↗

arXiv2016

A sharp recovery condition for block sparse signals by block orthogonal multi-matching pursuit

We consider the block orthogonal multi-matching pursuit (BOMMP) algorithm for the recovery of block sparse signals. A sharp bound is obtained for the exact reconstruction of block $K$-sparse signals via the BOMMP algorithm in the noiseless case, based on the block restricted isometry constant (block-RIC). Moreover, we show that the sharp bound combining with an extra condition on the minimum $\ell_2$ norm of nonzero blocks of block $K-$sparse signals is sufficient to recover the true support of block $K$-sparse signals by the BOMMP in the noise case. The significance of the results we obtain in this paper lies in the fact that making explicit use of block sparsity of block sparse signals can achieve better recovery performance than ignoring the additional structure in the problem as being in the conventional sense.

cs.IT↗

arXiv2016

A sharp bound on RIC in generalized orthogonal matching pursuit

Generalized orthogonal matching pursuit (gOMP) algorithm has received much attention in recent years as a natural extension of orthogonal matching pursuit. It is used to recover sparse signals in compressive sensing. In this paper, a new bound is obtained for the exact reconstruction of every $K$-sparse signal via the gOMP algorithm in the noiseless case. That is, if the restricted isometry constant (RIC) $\delta_{NK+1}$ of the sensing matrix $A$ satisfies \begin{eqnarray*} \delta_{NK+1}<\frac{1}{\sqrt{\frac{K}{N}+1}}, \end{eqnarray*} then the gOMP can perfectly recover every $K$-sparse signal $x$ from $y=Ax$. Furthermore, the bound is proved to be sharp in the following sense. For any given positive integer $K$, we construct a matrix $A$ with the RIC \begin{eqnarray*} \delta_{NK+1}=\frac{1}{\sqrt{\frac{K}{N}+1}} \end{eqnarray*} such that the gOMP may fail to recover some $K$-sparse signal $x$. In the noise case, an extra condition on the minimum magnitude of the nonzero components of every $K-$sparse signal combining with the above bound on RIC of the sensing matrix $A$ is sufficient to recover the true support of every $K$-sparse signal by the gOMP.

cs.IT↗

arXiv2016

Recovery of signals under the high order RIP condition via prior support information

In this paper we study the recovery conditions of weighted $l_{1}$ minimization for signal reconstruction from incomplete linear measurements when partial prior support information is available. We obtain that a high order RIP condition can guarantee stable and robust recovery of signals in bounded $l_{2}$ and Dantzig selector noise settings. Meanwhile, we not only prove that the sufficient recovery condition of weighted $l_{1}$ minimization method is weaker than that of standard $l_{1}$ minimization method, but also prove that weighted $l_{1}$ minimization method provides better upper bounds on the reconstruction error in terms of the measurement noise and the compressibility of the signal, provided that the accuracy of prior support estimate is at least $50\%$. Furthermore, the condition is proved sharp.

cs.IT↗