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

Abstract

In this work, a new robust regularized shrinkage regression method is proposed to recover and align high-dimensional images via affine transformation and Tikhonov regularization. To be more resilient with occlusions and illuminations, outliers, and heavy sparse noises, the new proposed approach incorporates novel ideas affine transformations and Tikhonov regularization into high-dimensional images. The highly corrupted, distorted, or misaligned images can be adjusted through the use of affine transformations and Tikhonov regularization term to ensure a trustful image decomposition. These novel ideas are very essential, especially in pruning out the potential impacts of annoying effects in high-dimensional images. Then, finding optimal variables through a set of affine transformations and Tikhonov regularization term is first casted as mathematical and statistical convex optimization programming techniques. Afterward, a fast alternating direction method for multipliers (ADMM) algorithm is applied, and the new equations are established to update the parameters involved and the affine transformations iteratively in the form of the round-robin manner. Moreover, the convergence of these new updating equations is scrutinized as well, and the proposed method has less time computation as compared to the state-of-the-art works. Conducted simulations have shown that the new robust method surpasses to the baselines for image alignment and recovery relying on some public datasets.

An Efficient New Robust PCA Method for Joint Image Alignment and Reconstruction via the L 2,1 Norms and Affine Transformation

“…Objective function Constraints [40] min 23,33,35,[41][42][43] min 35,[45][46][47][48] min 34,[49][50][51] min…”

“…(4) e L 2,1 norm of G is taken to estimate the Gaussian noise in real applications so as to minimize the potential impact of outliers, occlusions and illuminations, and heavy sparse errors. Unlike to the others work [2,[33][34][35][36][37][38][39], the new method tries to decompose the aggregated errors as the Gaussian noise and sparse error, which make the new method more novel. (5) e new set of equations, which are derived in more detailed including affine transformation using an ADMM method, is used to improve the robustness and solve the set of new optimization problems.…”

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…”

New Robust Regression Method for Outliers and Heavy Sparse Noise Detection via Affine Transformation for Head Pose Estimation and Image Reconstruction in Highly Complex and Correlated Data: Applications in Signal Processing

“…Images, processing particularly for the head pose estimation and image recovery, have been important research potential topics and can have applications in a variety of areas such as surveillance systems [1,2], signal processing [3,4], image denoising [5][6][7][8][9] and recovery [10,11], communications [12], computational imaging [13,14], and computer vision [15][16][17][18][19]. However, analyzing visual data is a difficult task due to miscellaneous adverse effects such as illuminations, outliers, and sparse noises.…”