Wenxing Zhang

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.

REPORT ON DISTRIBUTIONAL MATRIX COMPLETION VIA NEAREST NEIGHBORS IN THE WASSERSTEIN SPACE The authors proposed a very interesting generalization of matrix completion---distributional matrix completion. Instead of scalars as matrix entries, the 1D e...

Thin cloud removal for multispectral (MS) or hyperspectral (HS) images is a ubiquitous and fundamental problem in remote sensing. However, it is prohibitively challenging due to the ill-posedness and underdetermination of the image formation. The existing methods for cloud removal are dominated by either cirrus detection bands from satellite sensors or large-scale datasets from training. In this article, by vectorizing the MS/HS image of each band and stacking them columnwisely as a matrix, we develop a double rank-one prior (DROP) method for thin cloud removal. By leveraging some visible bands in satellite sensors, the proposed method is composed of cloud retrieval and removal phases. In brief, we first separate clouds from the observed image by formalizing the top-of-atmosphere (TOA) reflectance and then evaluate the thickness of clouds in each band by the independence of cloud-free and cloud images. Numerical experiments on various Landsat-8 and Sentinel-2 images demonstrate the compelling performances of the proposed method.

The blocky optimization has gained a significant amount of attention in far-reaching practical applications. Following the recent work (M. Nikolova and P. Tan [SIAM J. Optim. 29 (2019), pp. 2053–2078]) on solving a class of nonconvex nonsmooth optimization, we develop a stochastic alternating structure-adapted proximal (s-ASAP) gradient descent method for solving blocky optimization problems. By deploying some state-of-the-art variance reduced gradient estimators (rather than full gradient) in stochastic optimization, the s-ASAP method is applicable to nonconvex optimization whose objective is the sum of a nonsmooth data-fitting term and a finite number of differentiable functions. The sublinear convergence rate of s-ASAP is built upon the proximal point algorithmic framework, whilst the linear convergence rate of s-ASAP is achieved under the error bound condition. Furthermore, the convergence of the sequence produced by s-ASAP is established under the Kurdyka-Łojasiewicz property. Preliminary numerical simulations on some image processing applications demonstrate the compelling performance of the proposed method.

Blind deconvolution (BD), which aims to separate unknown convolved signals, is a fundamental problem in signal processing. Due to the ill-posedness and underdetermination of the convolution system, it is a challenging nonlinear inverse problem. This paper is devoted to the algorithmic studies of parametric BD, which is typically applied to recover images from ad hoc optical modalities. We propose a generalized variational framework for parametric BD with various priors and potential functions. By using the conjugate theory in convex analysis, the framework can be cast into a nonlinear saddle point problem. We employ the recent advances in minimax optimization to solve the parametric BD by the nonlinear primal-dual hybrid gradient method, with all subproblems admitting closed-form solutions. Numerical simulations on synthetic and real datasets demonstrate the compelling performance of the minimax optimization approach for solving parametric BD.