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.
Tensor-based methods in HSI super-resolution is not entirely new. Very recently, @cite_80 proposed a non-local sparse Tucker tensor factorization (NLSTF) model for HSI super-resolution. While both NLSTF and our technique tackle this problem from the tensor perspective, NLSTF fails to make use of an auxiliary HR RGB image. Similar to @cite_94 , its realization is relatively heuristic, and hard to be incorporate additional information. Our unified WLRTR method by-passes the tensor dictionary learning process by using high order singular value decomposition (HOSVD) @cite_92 , benefiting us enough flexibility, such as the auxiliary HR RGB image. Besides, NLSTF does not apply any sparsity prior for the underlying HR HSI. In contrast, we introduce the weighted low-rank tensor prior to further refine the solution.
@cite_80 @cite_92 @cite_94
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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. Hyperspectral super-resolution refers to the problem of fusing a hyperspectral image (HSI) and a multispectral image (MSI) to produce a super-resolution image (SRI) that admits fine spatial and spectral resolutions. State-of-the-art methods approach the problem via low-rank matrix approximations to the matricized HSI and MSI. These methods are effective to some extent, but a number of challenges remain. First, HSIs and MSIs are naturally third-order tensors (data “cubes”) and thus matricization is prone to a loss of structural information, which could degrade performance. Second, it is unclear whether these low-rank matrix-based fusion strategies can guarantee the identifiability of the SRI under realistic assumptions. However, identifiability plays a pivotal role in estimation problems and usually has a significant impact on practical performance. Third, a majority of the existing methods assume known (or easily estimated) degradation operators from the SRI to the corresponding HSI and MSI, which is hardly the case in practice. In this paper, we propose to tackle the super-resolution problem from a tensor perspective. Specifically, we utilize the multidimensional structure of the HSI and MSI to propose a coupled tensor factorization framework that can effectively overcome the aforementioned issues. The proposed approach guarantees the identifiability of the SRI under mild and realistic conditions. Furthermore, it works with little knowledge about the degradation operators, which is clearly a favorable feature in practice. Semi-real scenarios are simulated to showcase the effectiveness of the proposed approach. A super-resolution (SR) method based on compressive sensing (CS), structural self-similarity (SSSIM), and dictionary learning is proposed for reconstructing remote sensing images. This method aims to identify a dictionary that represents high resolution (HR) image patches in a sparse manner. Extra information from similar structures which often exist in remote sensing images can be introduced into the dictionary, thereby enabling an HR image to be reconstructed using the dictionary in the CS framework. We use the K-Singular Value Decomposition method to obtain the dictionary and the orthogonal matching pursuit method to derive sparse representation coefficients. To evaluate the effectiveness of the proposed method, we also define a new SSSIM index, which reflects the extent of SSSIM in an image. The most significant difference between the proposed method and traditional sample-based SR methods is that the proposed method uses only a low-resolution image and its own interpolated image instead of other HR images in a database. We simulate the degradation mechanism of a uniform 2 × 2 blur kernel plus a downsampling by a factor of 2 in our experiments. Comparative experimental results with several image-quality-assessment indexes show that the proposed method performs better in terms of the SR effectivity and time efficiency. In addition, the SSSIM index is strongly positively correlated with the SR quality.