Hyperspectral Image Denoising With Group Sparse and Low-Rank Tensor Decomposition

Abstract

Hyperspectral image (HSI) is usually corrupted by various types of noise, including Gaussian \nnoise, impulse noise, stripes, deadlines, and so on. Recently, sparse and low-rank matrix decomposition \n(SLRMD) has demonstrated to be an effective tool in HSI denoising. However, the matrix-based SLRMD \ntechnique cannot fully take the advantage of spatial and spectral information in a 3-D HSI data. In this paper, \na novel group sparse and low-rank tensor decomposition (GSLRTD) method is proposed to remove different \nkinds of noise in HSI, while still well preserving spectral and spatial characteristics. Since a clean 3-D HSI \ndata can be regarded as a 3-D tensor, the proposed GSLRTD method formulates a HSI recovery problem \ninto a sparse and low-rank tensor decomposition framework. Specifically, the HSI is first divided into a set \nof overlapping 3-D tensor cubes, which are then clustered into groups by K-means algorithm. Then, each \ngroup contains similar tensor cubes, which can be constructed as a new tensor by unfolding these similar \ntensors into a set of matrices and stacking them. Finally, the SLRTD model is introduced to generate noisefree \nestimation for each group tensor. By aggregating all reconstructed group tensors, we can reconstruct a \ndenoised HSI. Experiments on both simulated and real HSI data sets demonstrate the effectiveness of the \nproposed method.