Orthogonal Constrained Minimization with Tensor l_2,p, Regularization for HSI Denoising and Destriping

Hyperspectral images (HSIs) are often contaminated by a mixture of noise such as Gaussian noise, dead lines, stripes, and so on. In this paper, we propose a multiscale low-rank tensor regularized l_2,p (MLTL2p) approach for HSI denoising and destriping, which consists of an orthogonal constrained minimization model and an iterative algorithm with convergence guarantees. The model of the proposed MLTL2p approach is built based on a new sparsity-enhanced Multiscale Low-rank Tensor regularization and a tensor l_2,p norm with p ∈ (0, 1). The multiscale low-rank regularization for HSI denoising utilizes the global and local spectral correlation as well as the spatial nonlocal self-similarity priors of HSIs. The corresponding low-rank constraints are formulated based on independent higherorder singular value decomposition with sparsity enhancement on its core tensor to prompt more lowrankness. The tensor l_2,p norm for HSI destriping is extended from the matrix l_2,p norm. A proximal block coordinate descent algorithm is proposed in the MLTL2p approach to solve the resulting nonconvex nonsmooth minimization with orthogonal constraints. We show any accumulation point of the sequence generated by the proposed algorithm converges to a first-order stationary point, which is defined using three equalities of substationarity, symmetry, and feasibility for orthogonal constraints. In the numerical experiments, we compare the proposed method with state-of-the-art methods, including a deep learning based method, and test the methods on both simulated and real HSI datasets. Our proposed MLTL2p method demonstrates outperformance in terms of metrics such as mean peak signal-to-noise ratio as well as visual quality.