Weighted Low-Rank Tensor Recovery for Hyperspectral Image Restoration

Abstract

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 vi-

Nonlocal Coupled Tensor CP Decomposition for Hyperspectral and Multispectral Image Fusion

“…11. Spectral curves of the reconstructed HR-HSIs using the real dataset, (a) Pixel [40,180] in compared results and Pixel [10,45] in LR-HSI, (b) Pixel [120,120] in compared results and Pixel [30,30] in LR-HSI, (c) Pixel [168,60] in compared results and Pixel [42,15] in LR-HSI.…”

“…It regards the HSI as a three-order tensor, and decomposes the tensor into a core tensor multiplication by factor matrices representing the three dimensions. Yi et al [42] proposed a weighted low-rank tensor recovery (WLRTR) model that treated the singular values differently. Similar to the nonlocal self-similarity across space (NSS) method [43], the nonlocal similarity between spectral-spatial cubic and spectral correlation can be characterized in tensors.…”

Non-Local Low-Rank Cube-Based Tensor Factorization for Spectral CT Reconstruction

“…To explore nonlocal similarity inside an image, the patch length in spatial domain is usually very small (for examples, 4 × 4 and 6 × 6). This makes it difficult to accurately extract the intrinsic subspace bases of the spatial information for the HOSVD [42]. Meanwhile, we cannot afford the computational cost and memory load of larger patch length in the spatial horizontal and vertical model.…”

Non-Local Meets Global: An Integrated Paradigm for Hyperspectral Denoising

“…After the non-local low-rank modeling was first introduced to HSI denoising in [31], the flowchart of the non-local based methods become fixed: FBPs grouping and low-rank tensor approximation. Almost all the researchers focused on the low-rank tensor modeling of NLFBPGs, such as tucker decomposition [31], sparsity regularized tucker decomposition [39], Laplacian scale mixture low-rank modeling [14], and weighted low-rank tensor recovery [9] to exploit the spatial non-local similarity and spectral low-rank property simultaneously. However, with the increase of spectral number, the computational burden also increases significantly, impeding the application of these methods to the real high-spectrum HSIs.…”

“…The following methods are used for the comparison: spectral low-rank methods, i.e. LRTA [33] 9 ; and finally NGmeet 10 (Algorithm 1), which combines the best of above two fields. Hyper-parameters of all compared methods are set based on authors' codes or suggestions in the paper.…”