Ill-conditioned problems arise frequently in computer vision because the image information contains noise and ambiguities such that the true identity of the scene is not uniquely specified. It is nonetheless possible for humans to infer the structure of objects from incomplete data, presumably through the use of assumptions and computations consistent with natural images. This project focuses on a method in numerical analysis for solving "inverse problems" when the degraded scene has undergone a sequence of steps modeled by a known equation. Reconstruction can then be attempted by finding a solution that minimizes the deviation from that equation. The method is exemplified by its application to the deblurring problem. In this problem, deblurring is achieved by computing a succession of images, each slightly deblurred from the previous, such that the complete set satisfies the equations specifying the diffusion process of blurring. Deblurring and more general problems are studied in this project, using the method of minimization of equation error to inject the necessary assumptions to uniquely infer information in visual data.
