Hyperspectral Image Restoration Using Low-Rank Tensor Recovery

Abstract

This paper studies the hyperspectral image (HSI) denoising problem under the assumption that the signal is low in rank. In this paper, a mixture of Gaussian noise and sparse noise is considered. The sparse noise includes stripes, impulse noise, and dead pixels. The denoising task is formulated as a low-rank tensor recovery (LRTR) problem from Gaussian noise and sparse noise. Traditional low-rank tensor decomposition methods are generally NP-hard to compute. Besides, these tensor decomposition based methods are sensitive to sparse noise. In contrast, the proposed LRTR method can preserve the global structure of HSIs and simultaneously remove Gaussian noise and sparse noise.The proposed method is based on a new tensor singular value decomposition and tensor nuclear norm. The NP-hard tensor recovery task is well accomplished by polynomial time algorithms. The convergence of the algorithm and the parameter settings are also described in detail. Preliminary numerical experiments have demonstrated that the proposed method is effective for low-rank tensor recovery from Gaussian noise and sparse noise. Experimental results also show that the proposed LRTR method outperforms other denoising algorithms on real corrupted hyperspectral data.