Completely localized and parallel iterative algorithms for shift-variant image deblurring

Two completely localized algorithms for deblurring shift-variant defocused images are presented. The algorithms exploit limited support domain of 2D shift-variant point spread functions (PSFs) to localize the deblurring process. Focused image at each pixel is modeled by a truncated Taylor-series polynomial and a localized equation is obtained which expresses the blurred image as a function of the focused image and its derivatives. This localized equation forms the basis of the two algorithms. The first algorithm iteratively improves the estimated focused image by directly evaluating the localized equation for a given blurred image. The second algorithm uses the localized equation in a gradient descent method to improve the focused image estimate. The algorithms use spatial derivatives of the estimate and hence exploit smoothness to reduce computation. However, no assumptions about the blurring PSFs such as circular symmetry or separability are required for computational efficiency. Due to complete localization, the algorithms are fully parallel, that is, focused image estimates at each pixel can be computed independently. Performance of the algorithms is compared quantitatively with other shift-variant image restoration techniques, both for computational efficiency and for robustness against noise. The new algorithms are found to be faster and do not produce any blocking artifacts that are present in sectioning methods for image restoration. Further, the algorithms are stable and work satisfactorily even in the presence of large blur. Simulation results of the algorithms are presented for both Cylindrical and Gaussian PSFs. The performance of the algorithms on real data is discussed.