Image deconvolution using a characterization of sharp images in wavelet domain

Image deconvolution is a challenging ill-posed problem when only partial information of the blur kernel is available. Certain regularization on sharp images has to be imposed to constrain the estimation of true images during the blind deconvolution process. Based on the observation that an image of sharp edges tends to minimize the ratio between the `1 norm and the `2 norm of its wavelet frame coefficients, we propose a new characterization of sharp images for image deconvolution. A two-stage method is then developed to solve semi-blind image deconvolution problems. The proposed method is fast, easy to implement and does not require rigorous parameter tune-up. Such a regularization can also be applied to solve non-blind image deconvolution problems and the resulting algorithm achieves good performance without rigorous parameter tune-up.