Localized and computationally efficient approach to shift-variant image deblurring

A new localized and computationally efficient approach is presented for shift/space-variant image restoration. Unlike conventional approaches, it models shift-variant blurring in a completely local form based on the recently proposed Rao transform (RT). RT facilitates almost exact inversion of the blurring process locally and permits very fine-grain parallel implementation. The new approach naturally exploits the spatial locality of blurring kernels and smoothness of underlying focused images. It formulates the deblurring problem in terms of local parameters that are less correlated than raw image data. It is a fundamental advance that is general and not limited to any specific form of the blurring kernel such as a Gaussian. It has significant theoretical and computational advantages in comparison with conventional approaches such as those based on singular value decomposition of blurring kernel matrices. Experimental results are presented for both synthetic and real image data. This approach is also relevant to solving integral equations.