Abstract: In the process of hyperspectral image(HSI) acquisition,there will produce many kinds of noise,and the more the number of noise,the less effective information HSI has.In order to recover HSI's effective messages more effectively from a large number of mixed noises,a constrained smoothing rank approximation for HSI recovery method based on group sparse regularization is proposed in this paper.Among them,the group sparse regularization is defined as the spacial-spectral total variation(SSTV) which based on weighted $\ell_{2,1}$-norm.This regularization not only utilizes the information of spacial-spectral dimension,but also considers the group sparsity inside HSI,which enhances the model's removal effect of mixed noise and the smoothness of spacial-spectral dimension.In addition,the constrained smoothing function is used to approximate the rank function,which makes better use of the low-rank property of HSI and improves the efficiency of the algorithm.The optimization problem is solved by iterative algorithm based on alternating direction multiplier.The results of two simulated data expe-riments and one real data experiment show that compared with the five current mainstream methods,the proposed method has obvious improvement in visual effect and evaluation index.

Key words: Hyperspectral images, Denoising, Group sparse, Rank approximation, ADMM