Robust principal component analysis method based on improved truncation nuclear norm

Abstract

The invention discloses a robust principal component analysis method based on an improved truncated nuclear norm, and the method comprises the steps: obtaining video information, converting the videoinformation into a two-dimensional matrix M with the size of m rows and n columns, inputting the two-dimensional matrix M into a pre-constructed robust principal component analysis model of the improved truncated nuclear norm, and outputting the foreground and background of the video information; according to the improved robust principal component analysis model of the truncation nuclear norm, anon-convex gamma norm is adopted to replace a nuclear norm in a traditional truncation nuclear norm model. The method has the advantages that the gamma norm is adopted to replace a nuclear norm in a traditional truncation nuclear norm model, the approximation degree of a traditional robust principal component analysis model is enhanced, and the video foreground and background separation effect isimproved.

Description

technical field [0001] The invention relates to a robust principal component analysis method based on an improved truncated kernel norm, and belongs to the technical field of video processing. Background technique [0002] Robust Principal Component Analysis (RPCA), as a research hotspot in the field of multimedia information processing, is widely used in video foreground and background separation, video denoising, and face shadow removal. Traditional RPCA is a method of decomposing the observation matrix into low-rank elements and sparse elements, so it is also called sparse low-rank decomposition (Sparse and low-rank decomposition, SLRD) method. However, due to the non-convex and discontinuous characteristics of this problem, it is difficult to solve it directly, and it is an NP-hard problem. In order to solve this problem, the principal component pursuit (Principal Component Pursuit, PCP) algorithm was proposed, but the PCP algorithm also has many defects, such as the hi...

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Problems solved by technology

However, due to the non-convex and discontinuous characteristics of the problem, it is difficult to solve it directly, and it is an NP-hard problem

In order to solve this problem, the principal component pursuit (Principal Component Pursuit, PCP) algorithm was proposed, but the PCP algorithm also has many defects, such as the high time complexity of the algorithm, the nuclear norm all treat singular values ​​equally, and the traditional RPCA method rank function and l 0 The low degree of norm approximation, weak anti-noise ability, and lack of consideration of video structure and motion information seriously affect the wide application of PCP algorithm in practice.

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