Abstract: Hyperspectral image(HSI) has good spectral recognition capabilities and is widely used in various fields.However,HSI is susceptible to mixed noise pollution during imaging,which will seriously weaken the accuracy of subsequent tasks,and how to recover HSI with high quality is the first problem that needs to be solved.At present,the HSI denoising methods based on the combination of low-rank prior and total variational regularization have achieved good performance.On the one hand,these methods ignore the characteristics of high-intensity stripe noise in spatial structure and spectral distribution,so that the noise cannot be completely removed,and on the other hand,they do not consider the information of low-rank subspace of HSI differential images,then cannot explore the potential local spatial smooth structure.In order to solve these problems,an HSI recovery model based on bi-smoothing function rank approximation and group sparse is proposed.Firstly,the bi-smoothing function rank approximation model is used to explore the low-rank structure of clean HSI and stripe noise,which can remove high-intensity mixed noise such as structured stripe noise.Secondly,the group sparse regularization based on E3DTV is integrated into the bi-smoothing function rank approximation model,which can fully exploit the sparse prior information of HSI differential images and further improves the performance of images in spatial recovery and spectral feature retention.Finally,an alternating direction multiplier method(ADMM) is designed to solve the proposed BSRAGS model.Simulation and real data experiments show that the proposed model can effectively improve the image restoration quality.

Key words: Hyperspectral image, Smoothing function, Group sparse, Low-rank constraint, Stripe noise, E3DTV