Application of Inverse Problems in Imaging

In this project, we studied how to enhance image quality by denoising and deblurring a given image mathematically. We compared some existing state-of-the-art methods for image denoising and deblurring. We implemented the algorithms numerically using Matlab. We studied the possibility of combining statistical analysis with the traditional image restoration methods including using wavelets and framelets and we derived some encouraging preliminary results. My research student Alleta Maier gave a sequence of talks on the project including the Pacific Northwest Mathematical Association of America conference at Oregon State University in April, 2016; Linfield College Taylor Series in March, 2016, and Linfield College Student Symposium in May, 2016. The results derived from this project successfully built the ground work for our further study of the problem and were used directly in the REU project on image deblurring in the summer of 2016 at Willamette University under my supervision