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.
Highlights
High-dimensional images for alignment and recovery [1,2,3,4] arise in different scenarios such as image processing [5] and surveillance [6, 7]
The proposed method is employed on distorted video images as shown in Figures 3 and 4 under column 1. ereby, the proposed method has improved the performance of the developed algorithm by pruning out the potential impact of outliers and heavy sparse noises as shown in Figures 3 and 4. e proposed method is more superior to the others [30, 31, 38, 39]. is entails inclusion of an affine transformation and Tikhonov regularization has boosted the performance of the new method
By including an extra term both an affine transformation and Tikhonov regularization, the new approach has obtained a minimum mean square error [30, 31, 38, 39], entailing more better image alignment and recovery having a potential to prune out the errors and outliers in high-dimensional video face images (Table 1). e new incorporation of the affine transformation and Tikhonov regularization has boosted the performance of the new approach as compared with the state-of-the-art methods
Summary
High-dimensional images for alignment and recovery [1,2,3,4] arise in different scenarios such as image processing [5] and surveillance [6, 7]. Since the inception of the pioneering work of robust principal component analysis (RPCA) by Candes et al [8], a myriad of algorithms have been addressed for robust sparse low-rank image recovery, e.g., [9, 10]. These methods do not work well when the outliers and heavy sparse noises are heavily skewed. E authors of [18,19,20] developed robust algorithms to decompose the original corrupted data as clean and sparse errors These algorithms are not scalable and robust when the number of observations becomes large. Podosinnikova et al [21] developed robust PCA to minimize the reconstruction
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
