  Hyperspectral images (HSIs) are often contaminated by a mixture of noises
such as Gaussian noise, dead lines, stripes, and so on. In this paper, we
propose a novel approach for HSI denoising and destriping, called NLTL2p, which
consists of an orthogonal constrained minimization model and an iterative
algorithm with convergence guarantees. The model of the proposed NLTL2p
approach is built based on a new sparsity-enhanced Nonlocal Low-rank Tensor
regularization and a tensor $\ell_{2,p}$ norm with $p\in(0,1)$. The low-rank
constraints for HSI denoising utilize the spatial nonlocal self-similarity and
spectral correlation of HSIs and are formulated based on independent
higher-order singular value decomposition with sparsity enhancement on its core
tensor to prompt more low-rankness. The tensor $\ell_{2,p}$ norm for HSI
destriping is extended from the matrix $\ell_{2,p}$ norm. A proximal block
coordinate descent algorithm is proposed in the NLTL2p 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 NLTL2p method
demonstrates outperformance in terms of metrics such as mean peak
signal-to-noise ratio as well as visual quality.
