Photon-limited blind image deconvolution with heavy-tailed priors on kernel and noise
Linghai Kong, Suhua Wei · Inverse Problems and Imaging · 2025
A new blind image deconvolution method is proposed for flash X-ray radiography, with aims to surmount deficiencies of traditional approaches that do not account for complicated physics of image deterioration. Mixture distributions with heavy-tailed very impulsive component are assumed to characterize the noise and blur in radiographs. Under these assumptions, an optimization model is derived by integrating an infimal convolution likelihood into a joint maximum a posteriori estimation, where a Kullback-Leibler divergence based probability density function is proposed to formulate the prior knowledge of the kernel. Moreover, local estimation to the blurry image and expectation maximization for estimating the parameters of the kernel are utilized to gain multi-convexity and computability. To solve the optimization problem numerically, a block coordinate descent based algorithm is proposed, in which majorization-minimization algorithm and Barzilai-Borwein estimate are incorporated with alternating direction method of multipliers to achieve computational efficiency. A series of experiments with synthesized and real noisy blurry images validate the performance of the proposed method, especially in quality and adaptivity.