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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.<\/jats:p>","DOI":"10.1155\/2020\/1286909","type":"journal-article","created":{"date-parts":[[2020,11,7]],"date-time":"2020-11-07T03:20:45Z","timestamp":1604719245000},"page":"1-10","source":"Crossref","is-referenced-by-count":8,"title":["New Robust Regularized Shrinkage Regression for High-Dimensional Image Recovery and Alignment via Affine Transformation and Tikhonov Regularization"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9334-8588","authenticated-orcid":true,"given":"Habte Tadesse","family":"Likassa","sequence":"first","affiliation":[{"name":"Department of Statistics, College of Natural and Computational Sciences, Ambo University, Ambo, Ethiopia"}]},{"given":"Wen","family":"Xian","sequence":"additional","affiliation":[{"name":"Chinese Academy of Sciences, Fujian Institute of Research on the Structure of Matter Fuzhou, Fuzhou, China"}]},{"given":"Xuan","family":"Tang","sequence":"additional","affiliation":[{"name":"Chinese Academy of Sciences, Fujian Institute of Research on the Structure of Matter Fuzhou, Fuzhou, China"}]}],"member":"311","reference":[{"first-page":"1","article-title":"Dual recovery network with online compensation for image super-resolution","author":"S. 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