New Robust PCA for Outliers and Heavy Sparse Noises’ Detection via Affine Transformation, the L∗,w and L2,1 Norms, and Spatial Weight Matrix in High-Dimensional Images: From the Perspective of Signal Processing

Abstract

In this paper, we propose a novel robust algorithm for image recovery via affine transformations, the weighted nuclear, L∗,w, and the L2,1 norms. The new method considers the spatial weight matrix to account the correlated samples in the data, the L2,1 norm to tackle the dilemma of extreme values in the high-dimensional images, and the L∗,w norm newly added to alleviate the potential effects of outliers and heavy sparse noises, enabling the new approach to be more resilient to outliers and large variations in the high-dimensional images in signal processing. The determination of the parameters is involved, and the affine transformations are cast as a convex optimization problem. To mitigate the computational complexity, alternating iteratively reweighted direction method of multipliers (ADMM) method is utilized to derive a new set of recursive equations to update the optimization variables and the affine transformations iteratively in a round-robin manner. The new algorithm is superior to the state-of-the-art works in terms of accuracy on various public databases.