Multiple Norms and Boundary Constraint Enforced Image Deblurring via Efficient MCMC Algorithm

Abstract

Image non-blind deblurring is still an ill-posed problem. Uncertainty in solutions occurs when singular vectors of forward model matrix spanning the noise subspace have rather small singular values. This letter proposes a new image deblurring algorithm, called MNBC-Gibbs (multiple norms and boundary constraint enforced Gibbs sampling). To be more specific, the quadratic and sparseness-inducing norms are combined to construct regularization term, and the objective function is gradually minimized without requirement of regularization parameter choice. In particular, we propose an efficient Markov chain Monte Carlo (MCMC) method equipped with closed-form solution, artifacts processing and non-negative constraint to approximate the posterior distribution and estimate uncertainty for the unknown. Satisfactory deblurring results with sharp edges can be generated while maintaining smoothness without raising extra noise. The quantitative evaluations on different blur kernels and comparison with state-of-the-art image deblurring methods demonstrate the superiority of the proposed method. In addition, we show that our method can effectively deal with real blurry images.