Regularized supervised Bayesian approach for image deconvolution with regularization parameter estimation

Abstract

Abstract Image deconvolution consists in restoring a blurred and noisy image knowing its point spread function (PSF). This inverse problem is ill-posed and needs prior information to obtain a satisfactory solution. Bayesian inference approach with appropriate prior on the image, in particular with a Gaussian prior, has been used successfully. Supervised Bayesian approach with maximum a posteriori (MAP) estimation, a method that has been considered recently, is unstable and suffers from serious ringing artifacts in many applications. To overcome these drawbacks, we propose a regularized version where we minimize an energy functional combined by the mean square error with H 1 regularization term, and we consider the generalized cross validation (GCV) method, a widely used and very successful predictive approach, for choosing the smoothing parameter. Theoretically, we study the convergence behavior of the method and we give numerical tests to show its effectiveness.

Keywords

• Image deconvolution
• Supervised Bayesian approach
• MAP estimation
• Regularization
• GCV method