Hyperspectral images (HSIs) are often corrupted by a mixture of several types of noise during the acquisition process, e.g., Gaussian noise, impulse noise, dead lines, stripes, etc. Such complex noise could degrade the quality of the acquired HSIs, limiting the precision of the subsequent processing. In this paper, we present a novel tensor-based HSI restoration approach by fully identifying the intrinsic structures of the clean HSI part and the mixed noise part. Specifically, for the clean HSI part, we use tensor Tucker decomposition to describe the global correlation among all bands, and an anisotropic spatial–spectral total variation regularization to characterize the piecewise smooth structure in both spatial and spectral domains. For the mixed noise part, we adopt the $\ell _1$ norm regularization to detect the sparse noise, including stripes, impulse noise, and dead pixels. Despite that TV regularization has the ability of removing Gaussian noise, the Frobenius norm term is further used to model heavy Gaussian noise for some real-world scenarios. Then, we develop an efficient algorithm for solving the resulting optimization problem by using the augmented Lagrange multiplier method. Finally, extensive experiments on simulated and real-world noisy HSIs are carried out to demonstrate the superiority of the proposed method over the existing state-of-the-art ones.

The total variation (TV) is a powerful regularization term encoding the local smoothness prior structure underlying images. By combining the TV regularization term with low rank prior, the 3D total variation (3DTV) regularizer has achieved advanced performance in general hyperspectral image (HSI) processing tasks. Intrinsically, 3DTV assumes i.i.d. sparsity structures on all bands of the gradient maps calculated along the spectrum and space of an HSI. This, however, largely deviates from the real-world cases, where the gradient maps generally have different while correlated gradient map structures across all bands. To alleviate this issue, we propose an enhanced 3DTV (E-3DTV) regularization term beyond the conventional. Instead of imposing sparsity on gradient maps themselves, the new term calculates sparsity on the subspace bases on gradient maps along all bands of an HSI, which naturally encodes the correlation and difference among all these bands, and thus more faithfully reflects the insightful configurations of an HSI. The E-3DTV term can easily replace the conventional 3DTV term and be embedded into an HSI processing model to ameliorate its performance. We made such attempts on two typical related tasks: HSI denoising and compressed sensing. The superiority of our proposed method is substantiated by extensive experiments on synthetic and real HSI data, visually and quantitatively on both tasks, as compared with current state-of-the-arts. The code of our algorithm is released at https://github.com/andrew-pengjj/Enhanced-3DTV.git .

Background subtraction has been a fundamental and widely studied task in video analysis, with a wide range of applications in video surveillance, teleconferencing, and 3D modeling. Recently, motivated by compressive imaging, background subtraction from compressive measurements (BSCM) is becoming an active research task in video surveillance. In this paper, we propose a novel tensor-based robust principal component analysis (TenRPCA) approach for BSCM by decomposing video frames into backgrounds with spatial-temporal correlations and foregrounds with spatio-temporal continuity in a tensor framework. In this approach, we use 3D total variation to enhance the spatio-temporal continuity of foregrounds, and Tucker decomposition to model the spatio-temporal correlations of video background. Based on this idea, we design a basic tensor RPCA model over the video frames, dubbed as the holistic TenRPCA model. To characterize the correlations among the groups of similar 3D patches of video background, we further design a patch-group-based tensor RPCA model by joint tensor Tucker decompositions of 3D patch groups for modeling the video background. Efficient algorithms using the alternating direction method of multipliers are developed to solve the proposed models. Extensive experiments on simulated and real-world videos demonstrate the superiority of the proposed approaches over the existing state-of-the-art approaches.

Hyperspectral image (HSI) possesses three intrinsic characteristics: the global correlation across spectral domain, the nonlocal self-similarity across spatial domain, and the local smooth structure across both spatial and spectral domains. This paper proposes a novel tensor based approach to handle the problem of HSI spatial super-resolution by modeling such three underlying characteristics. Specifically, a noncovex tensor penalty is used to exploit the former two intrinsic characteristics hidden in several 4D tensors formed by nonlocal similar patches within the 3D HSI. In addition, the local smoothness in both spatial and spectral modes of the HSI cube is characterized by a 3D total variation (TV) term. Then, we develop an effective algorithm for solving the resulting optimization by using the local linear approximation (LLA) strategy and the alternative direction method of multipliers (ADMM). A series of experiments are carried out to illustrate the superiority of the proposed approach over some state-of-the-art approaches.

It is known that the decomposition in low-rank and sparse matrices ( L+S for short) can be achieved by several Robust PCA techniques. Besides the low rankness, the local smoothness ( LSS ) is a vitally essential prior for many real-world matrix data such as hyperspectral images and surveillance videos, which makes such matrices have low-rankness and local smoothness property at the same time. This poses an interesting question: Can we make a matrix decomposition in terms of L&LSS +S form exactly? To address this issue, we propose in this paper a new RPCA model based on three-dimensional correlated total variation regularization (3DCTV-RPCA for short) by fully exploiting and encoding the prior expression underlying such joint low-rank and local smoothness matrices. Specifically, using a modification of Golfing scheme, we prove that under some mild assumptions, the proposed 3DCTV-RPCA model can decompose both components exactly, which should be the first theoretical guarantee among all such related methods combining low rankness and local smoothness. In addition, by utilizing Fast Fourier Transform (FFT), we propose an efficient ADMM algorithm with a solid convergence guarantee for solving the resulting optimization problem. Finally, a series of experiments on both simulations and real applications are carried out to demonstrate the general validity of the proposed 3DCTV-RPCA model.