What are good apertures for defocus deblurring?

In recent years, with camera pixels shrinking in size, images are more likely to include defocused regions. In order to recover scene details from defocused regions, deblurring techniques must be applied. It is well known that the quality of a deblurred image is closely related to the defocus kernel, which is determined by the pattern of the aperture. The design of aperture patterns has been studied for decades in several fields, including optics, astronomy, computer vision, and computer graphics. However, previous attempts at designing apertures have been based on intuitive criteria related to the shape of the power spectrum of the aperture pattern. In this paper, we present a comprehensive framework for evaluating an aperture pattern based on the quality of deblurring. Our criterion explicitly accounts for the effects of image noise and the statistics of natural images. Based on our criterion, we have developed a genetic algorithm that converges very quickly to near-optimal aperture patterns. We have conducted extensive simulations and experiments to compare our apertures with previously proposed ones.