Efficient joint poisson-gauss restoration using multi-frame L2-relaxed-L0 analysis-based sparsity

Recently we proposed an efficient technique based on analysis-based sparsity in tight frames to restore images affected by shift-invariant blur and additive white Gaussian noise. Here we apply the same alternate marginal optimization idea used in that work, but dealing with combined Poissonian-Gaussian noise, which we approximate as Gaussian, additive and signal-dependent. We operate (1) by adding to the original image and its associated sparse vector another auxiliary variable to be optimized in the loop: the blurred, but not yet noisy, image; and (2) by using a quadratic soft constraint. We also re-formulate the previous prior modelling in order to perform a standard maximum a posteriori estimation, and generalize the approach to allow for a multi-frame prior. The proposed technique is computationally efficient and yields state-of-the-art performance.