Double Low-Rank Matrix Decomposition for Hyperspectral Image Denoising and Destriping

Hyperspectral images (HSIs) have a wealth of applications in many areas, due to their fine spectral discrimination ability. However, in the practical imaging process, HSIs are often degraded by a mixture of various types of noise, for example, Gaussian noise, impulse noise, dead pixels, dead lines, and stripe noise. Low-rank matrix decomposition theory has been widely used in HSI denoising, and has achieved competitive results by modeling the impulse noise, dead pixels, dead lines, and stripe noise as sparse components. However, the existing low-rank-based methods for HSI denoising cannot completely remove stripe noise when the stripe noise is no longer sparse. In this article, we extend the HSI observation model and propose a double low-rank (DLR) matrix decomposition method for HSI denoising and destriping. By simultaneously exploring the low-rank characteristic of the lexicographically ordered noise-free HSI and the low-rank structure of the stripe noise on each band of the HSI, the two low-rank constraints are formulated into one unified framework, to achieve separation of the noise-free HSI, stripe noise, and other mixed noise. The proposed DLR model is then solved by the augmented Lagrange multiplier (ALM) algorithm efficiently. Both simulation and real HSI data experiments were carried out to verify the superiority of the proposed DLR method.