Multi-observation blind deconvolution with an adaptive sparse prior

This paper describes a robust algorithm for estimating a single latent sharp image given multiple blurry and/or noisy observations. The underlying multi-image blind deconvolution problem is solved by linking all of the observations together via a Bayesian-inspired penalty function, which couples the unknown latent image along with a separate blur kernel and noise variance associated with each observation, all of which are estimated jointly from the data. This coupled penalty function enjoys a number of desirable properties, including a mechanism whereby the relative-concavity or sparsity is adapted as a function of the intrinsic quality of each corrupted observation. In this way, higher quality observations may automatically contribute more to the final estimate than heavily degraded ones, while troublesome local minima can largely be avoided. The resulting algorithm, which requires no essential tuning parameters, can recover a sharp image from a set of observations containing potentially both blurry and noisy examples, without knowing a priori the degradation type of each observation. Experimental results on both synthetic and real-world test images clearly demonstrate the efficacy of the proposed method.