Computationally efficient deblurring of shift-variant highly defocused images

A localized and efficient iterative approach is presented for deblurring images that are highly defocused with arbitrary shift-variant point spread functions (PSF). This approach extends a recently proposed local technique, the RT technique, which works only for medium levels of blur to work for significantly higher levels of blur. The RT technique is used to localize the blurring kernel at each pixel, and a region around the pixel with size comparable to the size of the blurring kernel is divided into several smaller regions (intervals). The blurred image in each interval is modeled separately by truncated Taylor-series polynomials. This step improves the accuracy of the image model for low order truncated Taylor-series expansions. The blurred image value at each pixel is expressed as the sum of multiple partial blur integrals with each integral term corresponding to one interval. Then an expression is derived for the focused image value at a pixel in terms of the derivatives of the blurred image in the central image region and solutions in the surrounding regions. This expression is solved iteratively at each pixel in parallel to obtain a focused image. The starting solution is assumed to be either zero or the blurred image itself. It is found that this new technique can effectively invert large blurs for which the original RT method failed. In our experiments the truncated Taylor series expansion was limited to third order. Theory and algorithms as well as experimental results on both simulation and real data are presented.