Abstract
Noise exhibits low rank or no sparsity in the low-rank matrix recovery, and the nuclear norm is not an accurate rank approximation of low-rank matrix. In the present study, to solve the mentioned problem, a novel nonconvex approximation function of the low-rank matrix was proposed. Subsequently, based on the nonconvex rank approximation function, a novel model of robust principal component analysis was proposed. Such model was solved with the alternating direction method, and its convergence was verified theoretically. Subsequently, the background separation experiments were performed on the Wallflower and SBMnet datasets. Furthermore, the effectiveness of the novel model was verified by numerical experiments.
Highlights
As fuelled by the advancement of big data and artificial intelligence industry, the data in the image processing, semantic analysis, and other application fields exhibit extremely large scale and dimension, leading to a significant difficulty of data processing and analysis
In the present study, using Wallflower and SBMnet, the novel model was adopted to solve background separation problem; subsequently, it was compared with existing GoDec [38], ALM, RegL1-ALM [24], NCRPCA, Grassmannian Online Subspace Updates with Structured-Sparsity (GOSUS) [19], and SLM [22] methods
Since the premise of the low-rank matrix recovery model adopted for image reconstruction is that the matrix corresponded by the background part is low rank, the rank of matrix Y recovered by the algorithm should be maximally small, and the most ideal result is that the rank is 1
Summary
As fuelled by the advancement of big data and artificial intelligence industry, the data in the image processing, semantic analysis, and other application fields exhibit extremely large scale and dimension, leading to a significant difficulty of data processing and analysis. To recover the low-rank structure from the data containing sparse large noises, Chandrasekaran et al [7] and Wright et al [8] built a robust principal component analysis model, which is expressed below:. E difference between algorithms of Gao and Liu was that the section of first-pass RPCA introduced structure sparse norm considering the foreground structural continuity It utilized the adaptive regularization parameter based on the significant adjustment of motion detection method to do group-sparsity operation, and thereby better results were obtained. Based on the mentioned inspirations, starting from the construction of nonconvex rank approximation function of low-rank matrix, the present study built a low-rank matrix recovery model suitable for nonconvex approximation in different image processing problems and designed the corresponding algorithm to obtain more accurate low-rank matrix part from the original data, as an attempt to solve the specific problems (e.g., image reconstruction and image denoising). A previously selected small positive number ε (generally, ε 10− 7, 10− 8) can be taken in the following form [24]: ‖X − PY − E‖∞ ≤ ε, ‖Y − J‖∞ ≤ ε
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