Improved non-convex robust principal component analysis method

Abstract

The invention discloses an improved non-convex robust principal component analysis method. The method comprises the steps of converting a to-be-processed video into a two-dimensional matrix D with thesize of m rows and n columns; inputting the two-dimensional matrix D into a pre-constructed model of an improved non-convex robust principal component analysis method, wherein the output is a low-rank matrix B corresponding to a video background and a sparse matrix F corresponding to a video foreground, and the model of the improved non-convex robust principal component analysis method adopts a generalized non-convex kernel norm as a rank function of the model and adopts a structured sparse norm as a 10 norm in the model. The method has the advantages that the rank function in the traditionalrobust principal component analysis method can be better approximated, and the effect of the robust principal component analysis method in foreground and background separation of the video is improved. According to the method, a structured sparse norm is introduced, a structured sparse model is established for the foreground of the video, the structured information of the model is greatly enriched, and the effect of separating the foreground and the background of the video influenced by factors such as illumination and fluctuation by a robust principal component analysis method is improved.

Description

technical field [0001] The invention relates to an improved non-convex robust principal component analysis method, which belongs to the technical field of multimedia processing. Background technique [0002] At present, the robust principal component analysis method is widely used in traffic control, social security and signal processing as the main method of video foreground and background separation. main research object. The traditional video foreground and background separation methods are mainly based on pixel-level processing methods, which have many defects and often ignore the structured information between pixels in the video, and the effect is not obvious; with the development of video processing technology, the main The component analysis method came into being. This method mainly uses singular value decomposition to reduce the dimensionality of video-based multidimensional data. , but there are many defects that cannot be ignored, and also seriously hinder the ...

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Problems solved by technology

The traditional video foreground and background separation methods are mainly based on pixel-level processing methods, which have many defects and often ignore the structured information between pixels in the video, and the effect is not obvious; with the development of video processing technology, the main The component analysis method came into being. This method mainly uses singular value decomposition to reduce the dimensionality of video-based multidimensional data. , but there are many defects that cannot be ignored, and also seriously hinder the development of this method. For example, in the process of dimensionality reduction, the principal component analysis method will lose a lot of information, it cannot handle square matrices well, and the obtained principal components are not Optimal and less consideration of defects in information elements such as time and space; in order to better separate the foreground and background of the video, in this context, the robust principal component analysis method is proposed and widely used in the foreground and background separation of the video, The main idea is to divide the video into low-rank background and sparse foreground, but the traditional robust principal component analysis method is an NP-hard problem, which is difficult to solve. In order to solve this problem, various optimization algorithms have been proposed. For example, the principal component tracking method and a series of improved algorithms based on this method. These improved algorithms mainly use substitution functions to approximate the rank function and sparse function in traditional robust principal component analysis. The substitution function used in many optimization algorithms initially Most of them are convex functions, and the approximation degree is not high. With the deepening of people's research, non-convex substitution functions have been widely introduced into low-rank sparse models, but how to find non-convex substitution functions with higher Introducing structured information from videos into compositional analysis remains a sought-after goal in recent years

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