Blind Deconvolution for Poissonian Blurred Image With Total Variation and L0-Norm Gradient Regularizations

This paper proposes a regularized blind deconvolution method for restoring Poissonian blurred image. The problem is formulated by utilizing the ${L}_{0}$ -norm of image gradients and total variation (TV) to regularize the latent image and point spread function (PSF), respectively, and combining them with the negative logarithmic Poisson log-likelihood. To solve the problem, we propose an approach which combines the methods of variable splitting and Lagrange multiplier to convert the original problem into three sub-problems, and then design an alternating minimization algorithm which incorporates the estimation of PSF and latent image as well as the updation of Lagrange multiplier into account. We also design a non-blind deconvolution method based on TV regularization to further improve the quality of the restored image. Experimental results on both synthetic and real-world Poissonian blurred images show that the proposed method can achieve restored images of very high quality, which is competitive with or even better than some state of the art methods.