All ETDs from UAB

Advisory Committee Chair

Carmeliza Navasca

Advisory Committee Members

Chengcui Zhang

Wei Zhu

Ian Knowles

Ravindran Sivaguru

Document Type

Dissertation

Date of Award

2021

Degree Name by School

Doctor of Philosophy (PhD) College of Arts and Sciences

Abstract

Tensor completion is a higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from a partially observed tensor. Here we work on a numerical method to reconstructs a tensor (matrix) with missing entries by finding the optimal factors through linear least squares and the singular vector through a proximal algorithm of soft thresholding. The performance of our algorithm is tested on color images and surveillance videos.In addition, we continued working on those algorithm to get an optimal way of finding the regularization parameter to improve the quality of our output. For this purpose we used Flexible Hybrid Methods for L1 regularization. In this work, we focus on the flexible methods based on Golub-Kahan process to solve the L1 regularized problem and CP decomposition to recover our tensor. To test the performance of our algorithm we tested it on colored images and compared to the original CP decomposition algorithm. Furthermore, working with colored images might sometimes give an output image with noise which led us to work on how to denoise and deblur a colored image. Our algorithm uses Total Variation (TV) which was first introduced by Rudin, Osher and Fatemi in 1992. We use a dual approach proposed by Chambolle called gradient projection which we extends to the tensor. This algorithm was tested on videos and RGB images.

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