Applying linear algebra to image deblurring

Abstract

This thesis expands on the concepts taught in Applied Linear Algebra (MAT-350), using singular value decomposition (SVD) and discrete cosine transform (DCT), with a focus on image deblurring. The principles discussed throughout this thesis were guided by the readings of Deblurring Images Matrices, Spectra, and Filtering by Christian Hansen, James Nagy, and Dianne O’Leary. The thesis will focus on various techniques that were used to deblur an image, how the SVD and DCT were applied, and the results applied to a blurred photo. The mathematics are made easier using MATLAB’s built-in tools including: The Signal Processing Toolbox (SPT) and the Image Processing Toolbox (IPT) as well as tools created by the authors of Deblurring Images Matrices, Spectra, and Filtering. The goal of this project is to not only learn the theoretical side of the mathematics behind image deblurring, but also to write code to implement various techniques used to deblur an image. (Author abstract)