In this thesis, two robust affine transformation-assisted methods with both real-world applications and methodology development are developed to deal with out-liers and heavy sparse noise. Firstly, we present a new robust regression approachfor head pose estimation and face reconstruction via affine transformations. To berobust against miscellaneous adverse effects such as occlusions, outliers and heavysparse noise, the new algorithm incorporates affine transformations with robustregression for more faithful low-rank plus sparse image representation, where thelow-rank component lies in a union of disjoint subspaces. Consequently, the dis-torted or misaligned images can be rectified by the affine transformations to rendermore accurate regression outcomes. The search of the optimal variables and affinetransformations is cast as a convex optimization problem. To alleviate the com-putational complexity, the Alternating Direction Method of Multipliers (ADMM)approach is employed and a new set of equations are established to update theoptimization variables and affine transformations iteratively in a round-robin man-ner. Moreover, the convergence of these new updating equations is scrutinized aswell.Secondly, we propose a new robust algorithm for image recovery via affine transfor-mations and theL2,1norm. To be robust against various annoying effects, the newalgorithm integrates affine transformations to yield a more accurate low-rank plussparse decomposition. In addition, theL2,1norm is employed to remove the cor-related samples across the images, enabling the new approach to be more resilient
iito outliers and large variations in the images. The problem is first formulated asa convex optimization problem. Afterward, ADMM is utilized again to derive anew set of updating equations to recursively find the optimization variables andaffine transformations.Simulations show that the two proposed algorithms are superior to the state-of-the-art works in terms of some common metrics for head pose estimation, facereconstruction, and image recovery on some public databases

In this thesis, two robust affine transformation-assisted methods with both real-world applications and methodology development are developed to deal with out-liers and heavy sparse noise. Firstly, we present a new robust regression approachfor head pose estimation and face reconstruction via affine transformations. To berobust against miscellaneous adverse effects such as occlusions, outliers and heavysparse noise, the new algorithm incorporates affine transformations with robustregression for more faithful low-rank plus sparse image representation, where thelow-rank component lies in a union of disjoint subspaces. Consequently, the dis-torted or misaligned images can be rectified by the affine transformations to rendermore accurate regression outcomes. The search of the optimal variables and affinetransformations is cast as a convex optimization problem. To alleviate the com-putational complexity, the Alternating Direction Method of Multipliers (ADMM)approach is employed and a new set of equations are established to update theoptimization variables and affine transformations iteratively in a round-robin man-ner. Moreover, the convergence of these new updating equations is scrutinized aswell.Secondly, we propose a new robust algorithm for image recovery via affine transfor-mations and theL2,1norm. To be robust against various annoying effects, the newalgorithm integrates affine transformations to yield a more accurate low-rank plussparse decomposition. In addition, theL2,1norm is employed to remove the cor-related samples across the images, enabling the new approach to be more resilient
iito outliers and large variations in the images. The problem is first formulated asa convex optimization problem. Afterward, ADMM is utilized again to derive anew set of updating equations to recursively find the optimization variables andaffine transformations.Simulations show that the two proposed algorithms are superior to the state-of-the-art works in terms of some common metrics for head pose estimation, facereconstruction, and image recovery on some public databases

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