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

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 inco...

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Main Authors: Habte Tadesse Likassa, Wen Xian, Xuan Tang
Format: Article
Language:English
Published: Wiley 2020-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2020/1286909
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author Habte Tadesse Likassa
Wen Xian
Xuan Tang
author_facet Habte Tadesse Likassa
Wen Xian
Xuan Tang
author_sort Habte Tadesse Likassa
collection DOAJ
description 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.
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spelling doaj-art-b60f6c57594741f4bd68267c98e702b02025-08-20T03:20:55ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252020-01-01202010.1155/2020/12869091286909New Robust Regularized Shrinkage Regression for High-Dimensional Image Recovery and Alignment via Affine Transformation and Tikhonov RegularizationHabte Tadesse Likassa0Wen Xian1Xuan Tang2Department of Statistics, College of Natural and Computational Sciences, Ambo University, Ambo, EthiopiaChinese Academy of Sciences, Fujian Institute of Research on the Structure of Matter Fuzhou, Fuzhou, ChinaChinese Academy of Sciences, Fujian Institute of Research on the Structure of Matter Fuzhou, Fuzhou, ChinaIn 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.http://dx.doi.org/10.1155/2020/1286909
spellingShingle Habte Tadesse Likassa
Wen Xian
Xuan Tang
New Robust Regularized Shrinkage Regression for High-Dimensional Image Recovery and Alignment via Affine Transformation and Tikhonov Regularization
International Journal of Mathematics and Mathematical Sciences
title New Robust Regularized Shrinkage Regression for High-Dimensional Image Recovery and Alignment via Affine Transformation and Tikhonov Regularization
title_full New Robust Regularized Shrinkage Regression for High-Dimensional Image Recovery and Alignment via Affine Transformation and Tikhonov Regularization
title_fullStr New Robust Regularized Shrinkage Regression for High-Dimensional Image Recovery and Alignment via Affine Transformation and Tikhonov Regularization
title_full_unstemmed New Robust Regularized Shrinkage Regression for High-Dimensional Image Recovery and Alignment via Affine Transformation and Tikhonov Regularization
title_short New Robust Regularized Shrinkage Regression for High-Dimensional Image Recovery and Alignment via Affine Transformation and Tikhonov Regularization
title_sort new robust regularized shrinkage regression for high dimensional image recovery and alignment via affine transformation and tikhonov regularization
url http://dx.doi.org/10.1155/2020/1286909
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AT wenxian newrobustregularizedshrinkageregressionforhighdimensionalimagerecoveryandalignmentviaaffinetransformationandtikhonovregularization
AT xuantang newrobustregularizedshrinkageregressionforhighdimensionalimagerecoveryandalignmentviaaffinetransformationandtikhonovregularization