Publications
Journal Articles
Published in manuscript, 2025
The Douglas-Rachford splitting method (DRSM) has been highly successful in solving composite optimization and structured inclusions over the last decades and it has continued its success in recent years. However, DRSM usually suffers from the slow convergence for ill-posed problems. To ameliorate the efficiency of DRSM, we develop a variable metric DRSM (VMDR) with provable convergence by deploying the second-order oracle. Under the Kurdyka-{\L}ojasiewicz assumption, we analyze the global convergence of VMDR and establish its convergence rate from two different viewpoints. Alternatively, a latent pitfall of VMDR is the computational effort on solving the weighted proximity, which is often handled by internally nested subroutines. Thereby, we develop an inexact VMDR (iVMDR) algorithmic framework by devising two inexact criteria (one involves the summable error sequence, and the other exploits the verifiable functional residual). Numerical experiments on binary classification and image reconstruction demonstrate the compelling performance of the proposed method.
Recommended citation: Z.H. Jia, W.X. Zhang, X.J. Cai, D.R. Han. (2025). manuscript. 1-28.
Published in Inverse Problem Imaging, 2024
Clouds are ubiquitous in remote sensing images, and most of the existing methods for cloud removal are limited to either implementing multispectral images or exploiting supervised learning techniques. In this paper, we propose an unsupervised diffusion method by adapting the null space learning. The proposed method is built upon two trained denoising diffusion probabilistic models on diverse remote sensing datasets so as to cope with the mixed data from different sources. The matrices involving simplified degradation and ``self-adaptive’’ generalized inverse are devised for the null space decomposition. For the diffusion model with null space decomposition, we derive its continuous reverse-time stochastic differential equation (SDE) and prove its variance-preserving property. Furthermore, we formulate explicitly the expectation of reverse-time SDE, which expedites the numerical efficiency of the proposed method. Numerical experiments on some remote sensing images are implemented to demonstrate the performance of the proposed method.
Recommended citation: Y.X. Zhang, L.W. Xu, J.P. Yin, W.X. Zhang. (2025). Inverse Problem Imaging. to appear.
Published in under review, 2024
Alternating structure-adapted proximal (ASAP) gradient algorithm (M. Nikolova and P. Tan, SIAM J Optim, 29:2053-2078) has drawn much attention due to its efficiency in solving nonconvex nonsmooth optimization. However, the multiblock nonseparable structure confines the applications of ASAP to far-reaching practical problems, e.g., coupled tensor decomposition. In this paper, we propose an extended ASAP (eASAP) algorithm for nonconvex nonsmooth optimization whose objective is the sum of two nonseparable functions and a coupling one. By exploiting the blockwise restricted prox-regularity property, eASAP is capable of minimizing the objective whose coupling function is multiblock nonseparable. Moreover, we analyze the global convergence of eASAP by virtue of the Aubin property on partial subdifferential mapping and the Kurdyka-{\L}ojasiewicz property on the objective. Furthermore, the sublinear convergence rate of eASAP is built upon the proximal point algorithmic framework under some mild conditions. Numerical simulations on multimodal data fusion demonstrate the compelling performance of the proposed method.
Recommended citation: Y. Gao, C.F. Cui, W.X. Zhang, D.R. Han. (2024). under review. 1-25.
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Some of my previous publications:
[1] W.X. Zhang, D.R. Han*, Z.B. Li, A self-adaptive projection method for multiple-sets split feasibility problem, Inverse Problems, 25 (2009) 115001
[2] W.X. Zhang, D.R. Han, X.M. Yuan*, An efficient simultaneous method for constrained multiple-sets split feasibility problem, Comput Optim Appl, 52 (2012) 825-843
[3] R.H. Chan*, X.M. Yuan, W.X. Zhang, Point spread function reconstruction in ground-based astronomy by l1-lp model, J Opt Soc Ame A, 29 (2012) 2263-2271
[4] D.R. Han, X.M. Yuan*, W.X. Zhang, X.J. Cai, An ADM-based splitting method for separable convex programming, Comput Optim Appl, 54 (2013) 343-369
[5] M.K. Ng*, X.M. Yuan, W.X. Zhang, Coupled variational image decomposition and restoration model for blurred cartoon-plus-texture images with missing pixels, IEEE Trans Image Process, 22 (2013) 2233-2246
[6] B.S. He, X.M. Yuan*, W.X. Zhang, A customized proximal point algorithm for convex minimization with linear constraints, Comput Optim Appl, 56 (2013) 559-572
[7] R.H. Chan*, X.M. Yuan, W.X. Zhang, A phase model for point spread function estimation in ground-based astronomy, Sci China Ser A, 56 (2013) 2701-2710
[8]D.R. Han, X.M. Yuan*, W.X. Zhang, An augmented Lagrangian based parallel splitting method for separable convex minimization with applications to image processing, Math Comput, 83 (2014) 2263-2291
[9]M.K. Ng*, H.Y.T. Ngan, X.M. Yuan, W.X. Zhang, Patterned fabric inspection and visualization by texture and defect decomposition method, IEEE Trans Autom Sci Eng,11 (2014) 943-947
[10]D.R. Han*, W.W. Kong, W.X. Zhang, A partial splitting augmented Lagrangian method for low-patch-rank image decomposition, J Math Imaging Vision, 51 (2015) 145-160
[11]W.X. Zhang*, X.J. Cai, Z.H. Jia, A proximal alternating linearization method for minimizing the sum of two convex functions, Sci China Ser A, 58 (2015) 2225-2244
[12]W.X. Zhang, J. Fehrenbach, A. Desmaison, V. Lobjois, B. Ducommun, P. Weiss*, Structure tensor based analysis of cells and nuclei organization in tissues, IEEE Trans Med Imag, 35, (2016) 294-306
[13]Y.H. Dai, D.R. Han, X.M. Yuan*, W.X. Zhang, A sequential updating scheme of Lagrange multiplier for separable convex programming, Math Comput, 86 (2017) 315-343
[14]P. Escande, P. Weiss, W.X. Zhang, A variational model for multiplicative structured noise removal, J Math Imaging Vision, 57, (2017) 43-55
[15]M.K. Ng, H.Y.T. Ngan, X.M. Yuan, W.X. Zhang, Lattice-based patterned fabric inspection by using total variation and sparsity with low-rank representations, SIAM J Imaging Sci, 10, (2017), 2140-2164
[16]W.Y. Ding, M.K. Ng, W.X. Zhang*, A Peaceman-Rachford splitting method with monotone plus skew-symmetric splitting for nonlinear saddle point problems, J Sci Comput, 81 (2019), 763-788
[17]X.F. Wang, J.P. Zhang, W.X. Zhang*, The distance between convex sets with Minkowski sum structure: application to collision detection, Comput Optim Appl,77 (2020), 465-490
[18]L.Y. Hu, W.X. Zhang, X.J. Cai, D.R. Han*, A parallel operator splitting algorithm for solving constrained total-variation retinex, Inverse Prob Imag, 14 (2020) 1135-1156
[19]W.X. Zhang*, A phase model using the Huber norm for estimating point spread function under frozen flow hypothesis, J Comput Appl Math, 397 (2021)11357
[20]Y. Gao, W.X. Zhang*, An alternative extrapolation scheme of PDHGM for saddle point problem with nonlinear function, Comput Optim Appl, 85 (2023) 263-291
[21]Z.H. Jia, W.X. Zhang, X.J. Cai, D.R. Han, Stochastic alternating structure-adapted proximal gradient descent with variance reduction for nonconvex nonsmooth problem, Math Comput, 93 (2024), 1677-1714
[22]Q.C. Cao, D.R. Han, X.F. Wang, W.X. Zhang*, Generalized variational framework with minimax optimization for parametric blind deconvolution, Inverse Problems, 40 (2024) 045019
[23]何炳生, 张文星，图像处理中一些典型凸优化问题及其求解方法,《医学图像计算中的数学理论与方法》(孔德兴等著), 北京: 科学出版社, (2025)
[24]Y.X. Zhang, W.X. Zhang, J. Zhang, J.P. Yin*, Double rank-one prior: thin cloud removal by visible bands, IEEE Trans Geoscience Remote Sens, 62 (2024), 1-10
[25]W.Y. Ding, M.K. Ng, W.X. Zhang*, A generalized alternating direction implicit method for consensus optimization: application to distributed sparse logistic regression, J Global Optim, 90 (2024), 727-753
[26]Y.X. Zhang, W.X. Zhang*, J.P. Yin, Image dejittering on the perspective of spatially-varying mixed noise removal, Signal Process, 226 (2025), 109671
[27]Y.M. Li, H.W. Xu, W.X. Zhang*, A balanced augmented Lagrangian method with correction for linearly constrained optimization, J Sci Comput, 104 (2025), to appear
[28]Y.X. Zhang, L.W. Xu, J.P. Yin*, W.X. Zhang, Unsupervised diffusion method with null space learning for cloud removal in remote sensing images, Inverse Prob Imag, (2025), to appear
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