Hyperspectral images (HSIs) are usually corrupted by various noises, e.g., Gaussian noise, impulse noise, stripes, dead lines, and many others. In this article, motivated by the good performance of the L₁₋₂ nonconvex metric in image sparse structure exploitation, we first develop a 3-D L₁₋₂ spatial-spectral total variation (L₁₋₂SSTV) regularization to globally represent the sparse prior in the gradient domain of HSIs. Then, we divide HSIs into local overlapping 3-D patches, and low-rank tensor recovery (LTR) is locally used to effectively separate the low-rank clean HSI patches from complex noise. The patchwise LTR can not only adapt to the local low-rank property of HSIs well but also significantly reduce the information loss caused by the global LTR. Finally, integrating the advantages of both the global L₁₋₂SSTV regularization and local LTR model, we propose a L₁₋₂SSTV regularized local LTR model for hyperspectral restoration. In the framework of the alternating direction method of multipliers, the difference of convex algorithm, the split Bregman iteration method, and tensor singular value decomposition method are adopted to solve the proposed model efficiently. Simulated and real HSI experiments show that the proposed model can reduce the dependence on noise independent and identical distribution hypotheses, and simultaneously remove various types of noise, even structure-related noise.

Hyperspectral images (HSIs) are usually corrupted by various noises during the image acquisition process, e.g., Gaussian noise, impulse noise, stripes, deadlines and many others. Such complex noise severely degrades the data quality, reduces the interpretation accuracy of HSIs, and restricts the subsequent HSI applications. In this paper, a spatial non-local and local rank-constrained low-rank regularized Plug-and-Play (NLRPnP) model is presented for mixed noise removal in HSIs. Specifically, we first divide HSIs into local overlapping patches. Local rank-constrained low-rank matrix recovery is adopted to effectively separate the low-rank clean HSI patches from the sparse noise and a part of Gaussian noise, and to significantly preserve local structure and detail information in HSIs. Then the spatial non-local based denoiser is introduced to promote the non-local self-similarity and obviously depress the Gaussian noise. Without increasing the difficulty of solving optimization problems, we combine the local and non-local based methods into the Plug-and-Play framework, and develop an efficient algorithm for solving the proposed NLRPnP model by using the alternating direction method of multipliers method. Finally, several experiments are conducted in both simulated and real data conditions to illustrate the better performance of the proposed NLRPnP model than the existing state-of-the-art denoising models.

Higher-order low-rank tensor arises in many data processing applications and has attracted great interests. Inspired by low-rank approximation theory, researchers have proposed a series of effective tensor completion methods. However, most of these methods directly consider the global low-rankness of underlying tensors, which is not sufficient for a low sampling rate; in addition, the single nuclear norm or its relaxation is usually adopted to approximate the rank function, which would lead to suboptimal solution deviated from the original one. To alleviate the above problems, in this paper, we propose a novel low-rank approximation of tensor multi-modes (LRATM), in which a double nonconvex L _γ norm is designed to represent the underlying joint-manifold drawn from the factorization factors of each mode in the underlying tensor. A block successive upper-bound minimization method-based algorithm is designed to efficiently solve the proposed model, and it can be demonstrated that our numerical scheme converges to the coordinate-wise minimizers. Numerical results on three types of public multi-dimensional datasets have tested and shown that our algorithm can recover a variety of low-rank tensors with significantly fewer samples than the compared methods.

The noise in a tomographic synthetic aperture radar (Tomo-SAR) model is normally assumed to be independent and identically distributed (i.i.d.) Gaussian. In this paper, the correlated Tomo-SAR model is introduced by studying the effect of random residual phase and correlated additive Gaussian noise, and a realistic and general hybrid Cramér-Rao bound (HCRB) on elevation estimation is derived for such a model. Then, a simplified calculation of the HCRB is proposed when the bound of elevation is the main focus. Computer simulations are performed to analyze the proposed HCRB for elevation estimation. The results obtained from estimators based on compressive sensing and distributed compressive sensing show that the proposed HCRB can provide a more realistic bound than the CRB derived with the white additive noise and perfect phase compensation assumption. This is also validated through processing results on real data acquired by TerraSAR-X/Tandem-X sensors.