A Unified Framework of Cloud Detection and Removal Based on Low-Rank and Group Sparse Regularizations for Multitemporal Multispectral Images

The existing cloud removal methods either need a cloud mask as prior knowledge or detect clouds before cloud removal processing, i.e., the detection and removal processes are separate. In this article, we propose a box-constrained (BC) smooth low-rank plus group sparse model to simultaneously detect and remove clouds, by formulating the degraded data as the summation of image and cloud components. For the cloud component, we propose a group sparse function along the spectral dimension. This is motivated by our observations that: 1) one tube is contaminated by clouds if any pixels of this tube are contaminated by clouds; 2) the positions of tubes, which are taken at different times, contaminated by clouds are different. For the image component, we propose to use a tensor rank based on the tensor singular value decomposition. The tensor rank characterizes the global property of the image component and could not keep the cloud-free information unchanged. To address the problem, we introduce a BC on the image component to force its cloud-free information to be equal to the corresponding values of observed data. Owing to the BC, the proposed model integrates the cloud detection and removal processes so that the two processes could promote each other and result in a promising result. To solve the proposed model, we develop an efficient algorithm that can generate the cloud mask, image component, and cloud component alternately. Extensive experiments on synthetic and real data show that the proposed method is competitive compared with the completion and other cloud removal methods.