Blind Deconvolution for a Curved Motion Based on Cepstral Analysis

When a camera moves during its exposure time, the captured image is degraded by the motion. Despite the several decades of researches, image deconvolution to restore a blurred image still remains an issue, particularly in blind deconvolution cases in which the actual shape of the blur is unknown. The cepstral approaches have been used to estimate a linear motion. In this paper, we propose a Point Spread Function (PSF) estimation method from a single blurred image. We extend the classical cepstral approaches that have been used for Uniform Linear motion PSF estimation. Focusing on Uniform Non-Linear motion (UNLM) that goes one direction and potentially weakly curves, we solve the PSF estimation problem as a camera path estimation problem. To solve the ill-posed problem, we derive a constraint on the behavior of the cepstra of UNLM PSFs. In a first step, we estimate several PSF candidates from the cepstrum of a blurred image. Then, we select the best PSF candidate by evaluating the candidates based on the ringing artifacts on the restored images obtained using the candidates. The performance of the proposed method is verified using both synthetic images and real images.