Hyperspectral imaging, providing abundant spatial and spectral information simultaneously, has attracted a lot of interest in recent years. Unfortunately, due to the hardware limitations, the hyperspectral image (HSI) is vulnerable to various degradations, such noises (random noise, HSI denoising), blurs (Gaussian and uniform blur, HSI deblurring), and down-sampled (both spectral and spatial downsample, HSI super-resolution). Previous HSI restoration methods are designed for one specific task only. Besides, most of them start from the 1-D vector or 2-D matrix models and cannot fully exploit the structurally spectral-spatial correlation in 3-D HSI. To overcome these limitations, in this work, we propose a unified low-rank tensor recovery model for comprehensive HSI restoration tasks, in which non-local similarity between spectral-spatial cubic and spectral correlation are simultaneously captured by 3-order tensors. Further, to improve the capability and flexibility, we formulate it as a weighted low-rank tensor recovery (WLRTR) model by treating the singular values differently, and study its analytical solution. We also consider the exclusive stripe noise in HSI as the gross error by extending WLRTR to robust principal component analysis (WLRTR-RPCA). Extensive experiments demonstrate the proposed WLRTR models consistently outperform state-of-the-arts in typical low level vision HSI tasks, including denoising, destriping, deblurring and super-resolution.
Image denoising is a test bed for the various technique. Consequently, numerous approaches for HSI denoising have been proposed @cite_18 @cite_21 @cite_76 . The spectral correlation and nonlocal self-similarity are two kinds of intrinsic characteristic underlying a HSI. Most of previous HSI denoising methods focus on the spectral correlation such as the wavelet methods @cite_6 , total variational methods @cite_79 , the low-rank matrix recovery methods @cite_38 @cite_87 @cite_62 @cite_46 , or the nonlocal self-similarity such as BM4D @cite_12 , HOSVD @cite_92 individually. Recently, @cite_94 firstly modeled them simultaneously in tensor format. However, the TDL @cite_94 is quite heuristic and short of a concise formulation, thus lacking of the flexibility to other HSI restoration tasks. Several tensor works @cite_52 @cite_31 @cite_70 followed the research line of @cite_94 , and model the sparsity of the core tensor coefficients in a principled manner. Interested readers could refer to @cite_99 for detailed background of HSI denoising. In this work, we further take the fine-grained intrinsic sparsity of the core tensor coefficients into consideration with the reweighting strategy, so as to better encode the structural correlation. Moreover, our WLRTR model can be well extended to other HSI issues.
@cite_99 @cite_38 @cite_18 @cite_62 @cite_31 @cite_87 @cite_70 @cite_92 @cite_21 @cite_52 @cite_6 @cite_79 @cite_94 @cite_46 @cite_76 @cite_12
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Hyperspectral imaging is beneficial in a diverse range of applications from diagnostic medicine, to agriculture, to surveillance to name a few. However, hyperspectral images often suffer from degradation such as noise and low resolution. In this paper, we propose an effective model for hyperspectral image (HSI) restoration, specifically image denoising and super-resolution. Our model considers three underlying characteristics of HSIs: sparsity across the spatial-spectral domain, high correlation across spectra, and non-local self-similarity over space. We first exploit high correlation across spectra and non-local self-similarity over space in the degraded HSI to learn an adaptive spatial-spectral dictionary. Then, we employ the local and non-local sparsity of the HSI under the learned spatial-spectral dictionary to design an HSI restoration model, which can be effectively solved by an iterative numerical algorithm with parameters that are adaptively adjusted for different clusters and different noise levels. In experiments on HSI denoising, we show that the proposed method outperforms many state-of-the-art methods under several comprehensive quantitative assessments. We also show that our method performs well on HSI super-resolution. Patch-based low-rank models have shown effective in exploiting spatial redundancy of natural images especially for the application of image denoising. However, two-dimensional low-rank model can not fully exploit the spatio-temporal correlation in larger data sets such as multispectral images and 3D MRIs. In this work, we propose a novel low-rank tensor approximation framework with Laplacian Scale Mixture (LSM) modeling for multi-frame image denoising. First, similar 3D patches are grouped to form a tensor of d-order and high-order Singular Value Decomposition (HOSVD) is applied to the grouped tensor. Then the task of multiframe image denoising is formulated as a Maximum A Posterior (MAP) estimation problem with the LSM prior for tensor coefficients. Both unknown sparse coefficients and hidden LSM parameters can be efficiently estimated by the method of alternating optimization. Specifically, we have derived closed-form solutions for both subproblems. Experimental results on spectral and dynamic MRI images show that the proposed algorithm can better preserve the sharpness of important image structures and outperform several existing state-of-the-art multiframe denoising methods (e.g., BM4D and tensor dictionary learning). Hyperspectral image (HSI) super-resolution, which fuses a low-resolution (LR) HSI with a high-resolution (HR) multispectral image (MSI), has recently attracted much attention. Most of the current HSI super-resolution approaches are based on matrix factorization, which unfolds the three-dimensional HSI as a matrix before processing. In general, the matrix data representation obtained after the matrix unfolding operation makes it hard to fully exploit the inherent HSI spatial-spectral structures. In this paper, a novel HSI super-resolution method based on non-local sparse tensor factorization (called as the NLSTF) is proposed. The sparse tensor factorization can directly decompose each cube of the HSI as a sparse core tensor and dictionaries of three modes, which reformulates the HSI super-resolution problem as the estimation of sparse core tensor and dictionaries for each cube. To further exploit the non-local spatial self-similarities of the HSI, similar cubes are grouped together, and they are assumed to share the same dictionaries. The dictionaries are learned from the LR-HSI and HR-MSI for each group, and corresponding sparse core tensors are estimated by spare coding on the learned dictionaries for each cube. Experimental results demonstrate the superiority of the proposed NLSTF approach over several state-of-the-art HSI super-resolution approaches. Hyperspectral images (HSIs) are usually contaminated by various kinds of noise, such as stripes, deadlines, impulse noise, Gaussian noise, and so on, which significantly limits their subsequent application. In this paper, we model the stripes, deadlines, and impulse noise as sparse noise, and propose a unified mixed Gaussian noise and sparse noise removal framework named spatial–spectral total variation regularized local low-rank matrix recovery (LLRSSTV). The HSI is first divided into local overlapping patches, and rank-constrained low-rank matrix recovery is adopted to effectively separate the low-rank clean HSI patches from the sparse noise. Differing from the previous low-rank-based HSI denoising approaches, which process all the patches individually, a global spatial–spectral total variation regularized image reconstruction strategy is utilized to ensure the global spatial–spectral smoothness of the reconstructed image from the low-rank patches. In return, the globally reconstructed HSI further promotes the separation of the local low-rank components from the sparse noise. An augmented Lagrange multiplier method is adopted to solve the proposed LLRSSTV model, which simultaneously explores both the local low-rank property and the global spatial–spectral smoothness of the HSI. Both simulated and real HSI experiments were conducted to illustrate the advantage of the proposed method in HSI denoising, from visual quantitative evaluations and time cost.