Regularized Richardson-Lucy algorithm for reconstruction of Poissonian medical images

The physical limitations of medical imaging devices together with the adverse effect of measurement noises tend to reduce the resolution and contrast of resulting diagnostic images. As a result, there is a need to preprocess the images before their interpretation by a medical practitioner. The present study is concerned with the case in which the images of interest are degraded by convolutional blur and Poisson noises. Such a situation is prevalent in many imaging modalities including PET, SPECT and confocal microscopy. To alleviate the image degradation, there exist a range of solution methods which are based on the principles originating from the fixed-point algorithm of Richardson and Lucy (RL). In this paper, we extend the RL algorithm to incorporate a constraint that requires the image of interest to be sparsely represented in the domain of a suitable linear transform. In this case, the positivity of the reconstructed image and its representation coefficients is ensured by using a positive valued dictionary of “representation atoms”. The superiority of the proposed algorithm over some alternative reconstruction methods has been established through a series of numerical experiments.