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Register a new userHyperspectral Image Restoration via Multi-mode and Double-weighted Tensor Nuclear Norm Minimization
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Added by
Sheng Liu
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Tensor nuclear norm (TNN) induced by tensor singular value decomposition plays an important role in hyperspectral image (HSI) restoration tasks. In this letter, we first consider three inconspicuous but crucial phenomenons in TNN. In the Fourier transform domain of HSIs, different frequency components contain different information; different singular values of each frequency component also represent different information. The two physical phenomenons lie not only in the spectral dimension but also in the spatial dimensions. Then, to improve the capability and flexibility of TNN for HSI restoration, we propose a multi-mode and double-weighted TNN based on the above three crucial phenomenons. It can adaptively shrink the frequency components and singular values according to their physical meanings in all modes of HSIs. In the framework of the alternating direction method of multipliers, we design an effective alternating iterative strategy to optimize our proposed model. Restoration experiments on both synthetic and real HSI datasets demonstrate their superiority against related methods.
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Low-rankness is important in the hyperspectral image (HSI) denoising tasks. The tensor nuclear norm (TNN), defined based on the tensor singular value decomposition, is a state-of-the-art method to describe the low-rankness of HSI. However, TNN ignores some of the physical meanings of HSI in tackling the denoising tasks, leading to suboptimal denoising performance. In this paper, we propose the multi-modal and frequency-weighted tensor nuclear norm (MFWTNN) and the non-convex MFWTNN for HSI denoising tasks. Firstly, we investigate the physical meaning of frequency components and reconsider their weights to improve the low-rank representation ability of TNN. Meanwhile, we also consider the correlation among two spatial dimensions and the spectral dimension of HSI and combine the above improvements to TNN to propose MFWTNN. Secondly, we use non-convex functions to approximate the rank function of the frequency tensor and propose the NonMFWTNN to relax the MFWTNN better. Besides, we adaptively choose bigger weights for slices mainly containing noise information and smaller weights for slices containing profile information. Finally, we develop the efficient alternating direction method of multiplier (ADMM) based algorithm to solve the proposed models, and the effectiveness of our models are substantiated in simulated and real HSI datasets.
Rank minimization methods have attracted considerable interest in various areas, such as computer vision and machine learning. The most representative work is nuclear norm minimization (NNM), which can recover the matrix rank exactly under some restricted and theoretical guarantee conditions. However, for many real applications, NNM is not able to approximate the matrix rank accurately, since it often tends to over-shrink the rank components. To rectify the weakness of NNM, recent advances have shown that weighted nuclear norm minimization (WNNM) can achieve a better matrix rank approximation than NNM, which heuristically set the weight being inverse to the singular values. However, it still lacks a sound mathematical explanation on why WNNM is more feasible than NNM. In this paper, we propose a scheme to analyze WNNM and NNM from the perspective of the group sparse representation. Specifically, we design an adaptive dictionary to bridge the gap between the group sparse representation and the rank minimization models. Based on this scheme, we provide a mathematical derivation to explain why WNNM is more feasible than NNM. Moreover, due to the heuristical set of the weight, WNNM sometimes pops out error in the operation of SVD, and thus we present an adaptive weight setting scheme to avoid this error. We then employ the proposed scheme on two low-level vision tasks including image denoising and image inpainting. Experimental results demonstrate that WNNM is more feasible than NNM and the proposed scheme outperforms many current state-of-the-art methods.
Since the matrix formed by nonlocal similar patches in a natural image is of low rank, the nuclear norm minimization (NNM) has been widely used in various image processing studies. Nonetheless, nuclear norm based convex surrogate of the rank function usually over-shrinks the rank components and makes different components equally, and thus may produce a result far from the optimum. To alleviate the above-mentioned limitations of the nuclear norm, in this paper we propose a new method for image restoration via the non-convex weighted Lp nuclear norm minimization (NCW-NNM), which is able to more accurately enforce the image structural sparsity and self-similarity simultaneously. To make the proposed model tractable and robust, the alternative direction multiplier method (ADMM) is adopted to solve the associated non-convex minimization problem. Experimental results on various types of image restoration problems, including image deblurring, image inpainting and image compressive sensing (CS) recovery, demonstrate that the proposed method outperforms many current state-of-the-art methods in both the objective and the perceptual qualities.
Tensor ring (TR) decomposition has been successfully used to obtain the state-of-the-art performance in the visual data completion problem. However, the existing TR-based completion methods are severely non-convex and computationally demanding. In addition, the determination of the optimal TR rank is a tough work in practice. To overcome these drawbacks, we first introduce a class of new tensor nuclear norms by using tensor circular unfolding. Then we theoretically establish connection between the rank of the circularly-unfolded matrices and the TR ranks. We also develop an efficient tensor completion algorithm by minimizing the proposed tensor nuclear norm. Extensive experimental results demonstrate that our proposed tensor completion method outperforms the conventional tensor completion methods in the image/video in-painting problem with striped missing values.
The process of rank aggregation is intimately intertwined with the structure of skew-symmetric matrices. We apply recent advances in the theory and algorithms of matrix completion to skew-symmetric matrices. This combination of ideas produces a new method for ranking a set of items. The essence of our idea is that a rank aggregation describes a partially filled skew-symmetric matrix. We extend an algorithm for matrix completion to handle skew-symmetric data and use that to extract ranks for each item. Our algorithm applies to both pairwise comparison and rating data. Because it is based on matrix completion, it is robust to both noise and incomplete data. We show a formal recovery result for the noiseless case and present a detailed study of the algorithm on synthetic data and Netflix ratings.
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