29 October 1993 Poisson MAP superresolution estimator with smoothness constraint
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Abstract
A well known problem associated with super-resolution of imagery is the introduction of oscillatory artifacts into the super-resolved object estimate. In this paper, we derive a Maximum A-Posteriori (MAP) object estimator subject to a constraint on the norm of the first differences of adjacent object pixels. The posterior density is derived from a Poisson observation model and a Poisson prior for the object. It is shown that this optimization problem is identical to a MAP estimator with a Markov Random Field (MRF) prior using zero- and first-order neighborhood cliques. While most MRF priors used for image restoration neglect the singleton clique, our model incorporates this additional a-priori object knowledge into the estimator. An iterative solution to the optimization problem is developed using the Picard iteration technique. Results are presented which demonstrate substantial artifact reduction while achieving the bandwidth extension necessary to accomplish super-resolution. Test cases include extended objects and natural scenes.
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Philip J. Sementilli, Philip J. Sementilli, Mariappan S. Nadar, Mariappan S. Nadar, Bobby R. Hunt, Bobby R. Hunt, } "Poisson MAP superresolution estimator with smoothness constraint", Proc. SPIE 2032, Neural and Stochastic Methods in Image and Signal Processing II, (29 October 1993); doi: 10.1117/12.162024; https://doi.org/10.1117/12.162024
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