New Robust PCA for Outliers and Heavy Sparse Noises’ Detection via Affine Transformation, the L ∗ , w and L 2,1 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, $L_{\ast ,w}$ , and the $L_{\mathrm{2,1}}$ norms. The new method considers the spatial weight matrix to account the correlated samples in the data, the $L_{\mathrm{2,1}}$ norm to tackle the dilemma of extreme values in the high-dimensional images, and the $L_{\ast ,w}$ 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.