Radial Deblurring with FFTs

Abstract

Radial blurring (sometimes called zoom blurring) of an image occurs when a camera acquires an image while traveling at a high rate of speed towards an object. Removing this blur 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. This shift-variant characteristic precludes the use of traditional FFT-based deblurring techniques. We propose a way around this problem by transforming the coordinate system of the blurred image into a coordinate system in which the blur is linear shift-invariant (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. In a similar fashion, rotational blur about the center point of an image can also be modeled in this way. We define the overall method as exponentially-sampled radial-space deblurring (ESRSD).

Specific focus is given to identifying the blur percentage of a given image because this value is required to perform the proposed ESRSD method. The blur identification is conducted on the image after the coordinate system has been transformed and nonuniform sampling has occurred. Using the characteristics of a motion blur in the frequency domain, a minimization problem is then set up to acquire the blur percentage based on the given data. Results demonstrate that the method yields high-quality restored images in a computationally efficient manner.