New Robust Principal Component Analysis for Joint Image Alignment and Recovery via Affine Transformations, Frobenius and L2,1 Norms

Abstract

This paper proposes an effective and robust method for image alignment and recovery on a set of linearly correlated data via Frobenius and L2,1 norms. The most popular and successful approach is to model the robust PCA problem as a low-rank matrix recovery problem in the presence of sparse corruption. The existing algorithms still lack in dealing with the potential impact of outliers and heavy sparse noises for image alignment and recovery. Thus, the new algorithm tackles the potential impact of outliers and heavy sparse noises via using novel ideas of affine transformations and Frobenius and L2,1 norms. To attain this, affine transformations and Frobenius and L2,1 norms are incorporated in the decomposition process. As such, the new algorithm is more resilient to errors, outliers, and occlusions. To solve the convex optimization involved, an alternating iterative process is also considered to alleviate the complexity. Conducted simulations on the recovery of face images and handwritten digits demonstrate the effectiveness of the new approach compared with the main state-of-the-art works.

New Robust Regularized Shrinkage Regression for High-Dimensional Image Recovery and Alignment via Affine Transformation and Tikhonov Regularization

“…In these simulations, the effectiveness of the proposed method is compared with the aforementioned methods based on natural face images, video face images, and windows. Secondly, we furthermore evaluated checking the effectiveness of the algorithm through using the mean square error [11][12][13]58].…”

“…To overcome this drawback, a myriad of robust algorithms have been addressed to deal with outliers and heavy sparse noises in high-dimensional images. Likassa et al [11][12][13] considered new robust algorithms via affine transformations and L 2,1 norms for image recovery and alignment which boosted the performance of the algorithms. Moreover, [14][15][16][17] proposed an efficient extension of RPCA using affine transformations.…”

“…erefore, the search of an affine transformation and Tikhonov regularization term is required to improve the performance of algorithms. To circumvent this dilemma, Likassa [11] proposed a low-rank robust regression (LR-RR) algorithm to clean the outliers and sparse errors from highly contaminated data. Although LR-RR can mitigate the impact of sparse errors inside and outside subspaces, its sensitivity to sparse errors and outliers lying in the disjoint subspaces jeopardizes its performance in some severe scenarios.…”

New Robust PCA for Outliers and Heavy Sparse Noises’ Detection via Affine Transformation, the L ∗ , w Liang1, Likassa2, Zhang3 et al. 2021International Journal of Mathematics and Mathematical SciencesSelf Cite5000View full textAdd to dashboardCite

“…In practice, I 0 i are generally not well aligned, entailing the above low-rank sparse decomposition to be imprecise. To take account of this, inspired by [39,43,44], we apply affine transformations τ i to the potentially misaligned input images I 0 i to get a collection of transformed images I i � I 0 i oτ i , where the operator o indicates the transformation. We can then stack these aligned images into a matrix and obtain…”

“…In this work, novel ideas affine transformation, the spatial weight matrix, the weighted nuclear norm, and the L 2,1 norms are taken into consideration to boost the performance of the proposed method. Similar to [39,43], parameters in our experiments are chosen heuristically. Different datasets are taken into account to examine the effectiveness of the proposed method as compared to the baselines' RASL [43] and NQLSD [22].…”