Image Denoising with Patch Estimation and Low Patch-rank Regularization

In this paper, we propose an image denoising algorithm for data contaminated by Poisson noise using patch estimation and low patch-rank regularization. In order to form the data fidelity term, we take the patch-based poisson likelihood, which will effectively remove the ´blurring´ effect. For the sparse prior, we use the low patch-rank as the regularization, avoiding the choosing of dictionary. Putting together the data fidelity and the prior terms, the denoising problem is formulated as the minimization of a maximum a posteriori (MAP) objective functional involving three terms: the data fidelity term, a sparsity prior term, in the form of a low patch-rank regularization, and a non-negativity constraint (as Poisson data are positive by definition). Experimental results show that this algorithm achieved better results via giving specific constraints on different component and get faster convergence rate.