Hyperspectral Images Denoising via Nonconvex Regularized Low-Rank and Sparse Matrix Decomposition

Hyperspectral images (HSIs) are often degraded by a mixture of various types of noise during the imaging process, including Gaussian noise, impulse noise, and stripes. Such complex noise could plague the subsequent HSIs processing. Generally, most HSI denoising methods formulate sparsity optimization problems with convex norm constraints, which over-penalize large entries of vectors, and may result in a biased solution. In this paper, a nonconvex regularized low-rank and sparse matrix decomposition (NonRLRS) method is proposed for HSI denoising, which can simultaneously remove the Gaussian noise, impulse noise, dead lines, and stripes. The NonRLRS aims to decompose the degraded HSI, expressed in a matrix form, into low-rank and sparse components with a robust formulation. To enhance the sparsity in both the intrinsic low-rank structure and the sparse corruptions, a novel nonconvex regularizer named as normalized ε-penalty, is presented, which can adaptively shrink each entry. In addition, an effective algorithm based on the majorization minimization (MM) is developed to solve the resulting nonconvex optimization problem. Specifically, the MM algorithm first substitutes the nonconvex objective function with the surrogate upper-bound in each iteration, and then minimizes the constructed surrogate function, which enables the nonconvex problem to be solved in the framework of reweighted technique. Experimental results on both simulated and real data demonstrate the effectiveness of the proposed method.