Wenxing Zhang (张文星)

Wenxing Zhang (张文星)

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Extended alternating structure-adapted proximal gradient algorithm for nonconvex nonsmooth optimization

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.

Unsupervised diffusion method with null space learning for cloud removal in remote sensing images

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.

A variable metric Douglas-Rachford splitting method for nonconvex composite optimization

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.

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