Learning Approach for Computing Tikhonov Regularization Parameters

Modern imaging technologies have been at the forefront of scientific research and medical diagnosis. Typically, the cost of producing these images is quite high, while device defects, environmental variations, as well as movements generated by the objects being imaged, may result in noisy, poor-quality images. As a method to improve the cost-benefit of imaging technologies, image deblurring has become a large class of problems central to the field of image processing. Because these problems are often ill-posed, standard inversion methods, e.g. by inverting a matrix, result in unstable, low-quality solutions. Instead, researchers have been using Tikhonov regularization as a general framework to solve image deblurring problems. This thesis investigates various forms of Tikhonov regularization as well as an extension that uses multiple regularization terms, and proposes a learning approach for computing regularization parameters when training data are available.