| The purpose of this dissertation is to introduce some novel image restoration algorithms for digital photography, which has one of the fastest growing consumer electronics market in recent years. As such, a lot of attempts have been made to improve the quality of the digital pictures in comparison with photographs taken with silver halide films. Many of these methods have their roots in discrete signal and image processing that are developed in the last two to three decades, but the ever-increasing computational power of personal computers has made possible new designs and advanced techniques.;The algorithms we are presenting here are divided into two main categories. The first set of methods can be implemented inside the digital cameras, taking advantage of the programmability of the pixels and the availability of a compression codec that is commonly found inside any design of the cameras. The second set of methods are for off-camera restoration, where we make use of the computational power available in the computer host to solve a harder problem called blind image deconvolution. In addition to practical algorithms, we also have a more theoretical contribution to the study of the transform coefficient distributions, which affects the design of many image enhancement and restoration techniques.;Because the methods presented in this dissertation touch on many different technical areas, including optics, digital signal and image processing, algebraic geometry, functional analysis, as well as statistical estimation, we do not expect any reader to have mastered all of these disciplines. Instead, to accommodate a wide range of backgrounds and to make the dissertation somewhat self-sufficient, we include the mathematical and physical preliminaries whenever necessary to our discussion. |
