Dual-noise-dual-problem Approach To The Augmented Lagrange Multiplier Method For Robust Principal Component Analysis

Robust principal component analysis(RPCA) is one of the most useful tools to recover a low-rank data component from the superposition of a sparse component and achieve the dimension reduction. More and more attention has been obtained to the RPCA for the robustness it owns facing with the sparse component and it has been used widely in many fields. Besides, many research studies focus on the methods of resolving the RPCA problem, in which the augmented Lagrange multiplier method(ALM) is almost one of the most accurate methods.However this paper points out that the ALM method still suffers from two problems, in which one is the brutal force initialization phase of the Lagrange multiplier resulting in low convergence speed and the other one is the ignorance of other types of noise resulting in low accuracy. These will make the results be disturbed by the Gaussian noise unavoidably.The work in this paper is mainly about the robust principal component analysis and the augmented Lagrange multiplier method for the RPCA, which is aimed at enhancing the calculation accuracy and the robustness facing with the sparse component and the Gaussian noise at the same time. The works in this paper can be summarize as follows:At first, we investigate the project background and have a discussion on the purpose and significance of this research. And we also give a brief introduction about the RPCA and several algorithms for the RPCA. Furthermore, we introduce the process of resolving the RPCA via these algorithms, especially the process via the ALM method and we point out the shortage existing in the ALM algorithm.Secondly, for the purpose of enhancing the calculation accuracy of this method, we provide an optimal Lagrange multiplier in the initialization phase of the augmented Lagrange multiplier method via solving the dual problem of the RPCA problem. It can reduce the iteration times and enhance the calculation accuracy. We name this advanced method as the dual-problem augmented Lagrange multiplier method.Thirdly, in order to reinforce the robustness of the RPCA when it faces with the sparse component and the Gaussian noise at same time, we propose a dual noise convex optimization model for the RPCA. This model defines that the original da ta is disturbed by the sparse component and Gaussian noise and lie in a low-dimensional subspace. Based on this dual-noise model, we propose an advanced method which is the dual-noise dual-problem augmented Lagrange multiplier method.At last, we do three groups of experiments on the DPALM and the DNDPALM method to observe its performance on calculation accuracy. The experiments are the simulation experiment, removing the shadows on human face image and extracting the dynamic foreground. From the experimental results, we find that, compared with other methods for the RPCA, the DPALM method obtains the higher calculation accuracy and the DNDPALM method owns the better robustness facing with dual noise.