Deconvolving Poissonian images by a novel hybrid variational model

In this paper, we propose a novel hybrid variational model for deconvolving Poissonian images by describing the original image as two parts – a cartoon part characterized by total variation, and a detailed part which has sparse representation over the wavelet basis. Fast and efficient iterative algorithms based on the split Bregman method are then employed. Under some conditions we prove the convergence properties of the iterative algorithms. Experiments demonstrate that the proposed hybrid model efficiently removes the noise and avoids the staircase effect simultaneously, which leads to a visually pleasant deconvolution result.

► This study has identified a hybrid model for deconvolving Poissonian images. ► Comparison of different wavelets for Poissonian image deconvolution. ► New iterative algorithms for the proposed hybrid model. ► The study of convergence of proposed iterative algorithms.