Multispectral image denoising using sparse and graph Laplacian Tucker decomposition
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Multispectral image denoising using sparse and graph Laplacian Tucker decomposition Xiaoce Wu1 , Bingyin Zhou1 (
), Qingyun Ren1 , and Wei Guo1
c The Author(s) 2020.
various kinds of noises which degrade visual quality, and affect the results obtained in those applications. MSI denoising is thus useful as a basic preprocessing step which can improve performance of subsequent processes. In recent years, it has attracted more and more attention in the fields of computer vision and remote sensing. A great many MSI denoising approaches have been proposed to date [4]. The spatial-spectral structure of an MSI corresponds to a 1D signal at each spatial point, and a grayscale image in each spectral band. Hence, straightforward denoising employs conventional methods for 1D signals and grayscale images, such as wavelet domain soft thresholding [5], K-SVD [6], and block-matching and 3D filtering (BM3D) [7]. However, those methods only take into account spectral correlation or spatial correlation, and thus satisfactory results cannot be generally achieved. To overcome this issue, various methods aimed at making full use of spatial-spectral correlation have been proposed. Some examples include the use of principal component analysis [8], multidimensional Wiener filtering [9], and tensor decompositions [10–12]. Because MSI denoising is inherently ill-posed, formulating and exploiting prior knowledge plays a central role in addressing the problem. Nonlocal spatial self-similarity and global correlation in spectrum, which have been shown to be two very reasonable priors [13–15], are commonly used. Nonlocal self-similarity refers to a phenomenon when observing an MSI from a perspective of small fullband patches: each full-band patch is similar to many other, non-local, ones. Global correlation in spectrum means that there is a large amount of spectral redundancy in an MSI: different bands’ images are generally highly correlated.
Abstract Multispectral image denoising is a basic problem whose results affect subsequent processes such as target detection and classification. Numerous approaches have been proposed, but there are still many challenges, particularly in using prior knowledge of multispectral images, which is crucial for solving the illposed problem of noise removal. This paper considers both non-local self-similarity in space and global correlation in spectrum. We propose a novel low-rank Tucker decomposition model for removing the noise, in which sparse and graph Laplacian regularization terms are employed to encode this prior knowledge. It can jointly learn a sparse and low-rank representation while preserving the local geometrical structure between spectral bands, so as to better capture simultaneously the correlation in spatial and spectral directions. We adopt the alternating direction method of multipliers to solve the resulting problem. Experiments demonstrate that the proposed method outperforms the state-of-theart, such as cube-based and tensor-based methods, both quantitatively and qualitatively. Keywords denoisin
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