Color video recovery method and system based on high-order tensor singular value decomposition

Abstract

The invention belongs to the technical field of color video recovery, and discloses a color video recovery method and system based on high-order tensor singular value decomposition, and the method comprises the steps that a low-rank part and a sparse part are extracted from a p-order tensor based on a high-dimensional robust principal component analysis (HTRPCA) problem; according to the p-order tensor, conjugate properties of a block diagonal matrix are generated, and an improved algorithm of a tensor product and tensor SVD is proposed; T-SVD is implemented on the tensor, and a new tensor dimension rank is defined; a tensor nuclear norm based on a tensor forward rank is utilized, and a near-end operator and an ADMM algorithm are utilized to solve an HTRPCA problem, so that accurate recovery guarantee of the HTRPCA is realized. Experimental results show that on the premise of theoretical optimal parameters, for generating data and color videos, HTRPCA has superiority in the aspect of processing corresponding problems, and theoretical guarantee is provided for accurate tensor recovery.

Description

technical field [0001] The invention belongs to the technical field of color video restoration, and in particular relates to a color video restoration method and system based on high-order tensor singular value decomposition. Background technique [0002] At present, with the development of data science and computer hardware capabilities, it is possible for people to process high-dimensional tensors with large amounts of data. Tensors are powerful tools for modeling multidimensional data, such as color images, videos, hyperspectral images, etc. For the processing of high-dimensional data, traditional sparse recovery methods represented by compressed sensing and low-rank matrices expand high-dimensional data into vectors or matrices, and then perform data modeling. However, this approach destroys the multidimensional features of the original data, thereby irreversibly losing the corresponding structural information. The tensor principal component analysis problem is a basic...

AI Technical Summary

Problems solved by technology

[0010] (1) The traditional robust principal component analysis method can only deal with matrix data and has limitations on the dimensionality of the data

[0011] (2) The existing TRPCA method does not perform well when applied to high-dimensional data (p≥4)

[0012] (3) The algebraic framework of high-dimensional tensors is currently in the preliminary research stage, and some key elements such as tensor representation, general operations, and decomposition lack unified or optimal definitions

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