Particle Filtering for Online Space-Varying Blur Identification

The identification of parameters of spatially variant blurs given a clean image and its blurry noisy version is a challenging inverse problem of interest in many application fields, such as biological microscopy and astronomical imaging. In this paper, we consider a parametric form for the blur and introduce a state-space model that describes the statistical dependence among the neighboring kernels. Our Bayesian approach aims at estimating the posterior distributions of the kernel parameters given the available data. Since those posteriors are not tractable due to the nonlinearities of the model, we propose a sequential Monte Carlo approach to approximate the distributions by processing the data in an online manner. This allows to consider numerous overlapped patches and large scale images at reasonable computational and memory costs. Moreover, it provides a measure of uncertainty due to the Bayesian framework. Practical experimental results illustrate the good performance of our novel approach, emphasizing the benefit to exploit the spatial structure for an improved estimation quality.