| The related tasks of image reconstruction and image restoration often result in ill-posed inverse problems. An effective method of solving such problems is the use of optimization algorithms to minimize an appropriate error function. However, for large or noisy data sets, such techniques may require a prohibitive amount of processing to obtain acceptable results. The inclusion of various constraints in optimization algorithms produces methods which are much more robust, yielding results of excellent quality in a reasonable amount of time. This thesis discusses two new algorithms which use such techniques to solve the problems of Limited View Tomography (LVT) and autofocus of Synthetic Aperture Radar (SAR) images.; Transmission tomography is a method of forming an image corresponding to the density of a two-dimensional slice through and object from measurements of the average absorption of x-rays along various lines through the object. LVT is a special case of this problem in which the angular range and/or number of measurements are limited. Use of a version of the conjugate gradients algorithm with nonnegativity and hyperplane constraints produces reconstructions superior to those obtained with conventional techniques such as backprojection.; SAR is common remote sensing technique which images a strip of ground below an airborne radar antenna. Unknown deviations in the path of the antenna can degrade the quality of the reconstructed image. Phase Adjustment by Contrast Enhancement (PACE) is a novel algorithm which solves for these deviations by maximizing the contrast of the image produced. This is also accomplished with the conjugate gradients algorithm, modified by using a multiresolution constraint procedure. Further modifications increase the speed of PACE without a significant loss in image quality. |
