Fast Deconvolution Using a Combination of Richardson-Lucy Iterations and Diffusion Regularisation

This paper presents a novel hybrid approach to address the non-blind deconvolution inverse problem, from the viewpoint of a future application to medical imaging. Motivated by the efficiency of diffusion models applied to inverse problems, we propose to integrate Diffusion Posterior Sampling (DPS) with variational methods through Richardson-Lucy iterations. The benefit of our method is to reduce by a factor of 10 the number of sampling steps currently required by DPS. Several numerical experiments demonstrate that our framework achieves comparable performance to existing deconvolution strategies, while seemingly reducing the computing time and the hallucination effect, both particularly important for medical applications.