Radial Deblurring with FFTs

Radial blurring (sometimes called zoom blurring) of an image is a challenging problem because it is a shift-variant blur. As one travels outward from the center of an image, the blur length increases linearly with distance from the center. This shift-variant characteristic precludes the use of other traditional FFT-based deblurring techniques. We propose a way around this problem by transforming the coordinate system of the blurred image into one in which the blur is LSI. Equivalently, the blurred image is sampled in a particular nonuniform fashion so that the blur becomes LSI in the new discrete-space coordinates. As a result, the blur can be modeled by convolution so that FFT-based deblurring can be used.