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Abstract
Low-rank matrix recovery is a large-scale data analysis and processing technology; its related theory has been widely used in image restoration, image denoising, video background modeling, signal recovery and other fields. This paper proposes an improved inexact augmented Lagrange multiplier (IALM) method to solve the harmonic recovery (HR) problem. After that, the performance of the original IALM and the improved IALM are compared when the sparse matrix is a diagonal sparse matrix satisfying certain conditions, and the results show that the improved IALM algorithm is more stable than the original algorithm. Then the improved strategy of the algorithm is extended to two kinds of occasions in which the positions of non-zero elements in sparse matrix are fixed or random, which provides a way to improve the algorithm in different application scenarios. Finally, the original IALM algorithm and the improved IALM algorithm are used to solve the HR problem, and the experimental results show that the improved IALM algorithm has better solution performance.
Highlights
With the rapid development of information technology, the effective use of large-scale data or high-dimensional data has become more and more important for real life and scientific research
The performance of algorithm (n = 20). It can be seen from table 1 that the number of iterations n of inexact augmented Lagrange multiplier (IALM)-matrix low-rank decomposition (MLRD) and IALM-harmonic recovery (HR) are 47 and 18 respectively; table 2 shows that the errors e of the matrix recovered by IALM-MLRD and IALM-HR are 3.63e-04 and 1.29e-08 respectively
In some specific applications, the classical algorithms of MLRD often ignore some prior information in the specific scene, which results in a large deviation of the solution accuracy or convergence speed with the actual demand
Summary
With the rapid development of information technology, the effective use of large-scale data or high-dimensional data has become more and more important for real life and scientific research. Since MC model contains the location information of non-zero elements in the sparse noise matrix, it can be predicted that the solution accuracy and convergence speed of MC theory will be better than those of classical MLRD algorithms in the scenario that the positions of non-zero elements in the sparse matrix are determined. According to the above analysis, the correlation matrix Rx of observation signal x (t) is equal to the sum of a lowrank matrix Rs and a sparse matrix Rn. we can use the MLRD to decompose Rx to get the estimation R∧s of the correlation matrix of the harmonic signal s (t), and get the estimation rs∧ (0) , rs∧ (1) , · · · rs∧ (m − 1) of the correlation functions, and use the equation (11) to get ω1, ω2, · · · , ωp and A1, A2, · · · , Ap. For the solution of the equation (11), we use the least square method to construct the optimization problem (11), and use the global search algorithm to get ω1, ω2, · · · , ωp and A1, A2, · · · , Ap. B.
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