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

Peidong Liang,Chentao Zhang,Habte Tadesse Likassa,Jielong Guo,Niansheng Tang

doi:10.1155/2021/3047712

Abstract

In this paper, we propose a novel robust algorithm for image recovery via affine transformations, the weighted nuclear, L ∗ , w , and the L 2,1 norms. The new method considers the spatial weight matrix to account the correlated samples in the data, the L 2,1 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.

Highlights

Robust methods have been successfully applied to numerous computer vision tasks, including face recognition [1], signal processing, scene categorization [2], point cloud segmentation using image processing [3, 4], and object detection [5]
Analyzing visual data is a difficult task due to miscellaneous adverse effects such as illuminations, outliers, and sparse noises. It is of importance developing a new approach for image alignment and recovery via a convex optimization, which are resilient to various annoying effects
(3) e newly developed method take the potential effects of outliers and heavy sparse noises into account to further propose via the iteratively reweighted alternating iteratively reweighted direction method of multipliers (ADMM) approach to solve the convex optimization problem, and a new set of updating equations is developed to iteratively update the optimization parameters and affine transformations

Summary

Introduction

Robust methods have been successfully applied to numerous computer vision tasks, including face recognition [1], signal processing, scene categorization [2], point cloud segmentation using image processing [3, 4], and object detection [5]. Is paper proposes a new robust algorithm via affine transformation, the L∗,w and L2,1 norms, and spatial weight matrix to reduce the potential impacts of outliers and noises in image and signal processing. To be more resilient to various adverse annoying effects such as occlusions and outliers, the new approach takes the advantages of the novel ideas’ affine transformations, L∗,w and L2,1 norms, for more faithful low-rank sparse image representation. (3) e newly developed method take the potential effects of outliers and heavy sparse noises into account to further propose via the iteratively reweighted ADMM approach to solve the convex optimization problem, and a new set of updating equations is developed to iteratively update the optimization parameters and affine transformations.

Problem Formulation

Methods

Proposed Algorithm

Experimental Simulations

Findings

Conclusion