A wavelet-based quadratic extension method for image deconvolution in the presence of poisson noise

Iterative optimization algorithms such as the forward-backward and Douglas-Rachford algorithms have gained much popularity since they provide efficient solutions to a wide class of non-smooth convex minimization problems arising in signal/image recovery. However, when images are degraded by a convolution operator and a Poisson noise, a particular attention must be paid to the associated minimization problem. To solve it, we propose a new optimization method which consists of two nested iterative steps. The effectiveness of the proposed method is demonstrated via numerical comparisons.