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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 &#x201C;representation atoms&#x201D;. The superiority of the proposed algorithm over some alternative reconstruction methods has been established through a series of numerical experiments.

Regularized Richardson-Lucy algorithm for reconstruction of Poissonian medical images