The use of MAP estimation techniques in the tomographic reconstruction of Poisson noise corrupted images

Nelson Delfino d'Ávila MascarenhasSaulo Savio Leite SantosPaulo Estevão Cruvinel

This work presents new methods for the tomographic reconstruction of images with Poisson noise corrupted projections. The reconstruction method is performed by first filtering the noisy projections under the Maximum a Posteriori criterion and subsequently reconstructing the images through conventional filtering-backprojection methods using the ramp filter. The "a priori" knowledge is incorporated by using several densities, including the Gaussian and densities defined on the non-negative real line. These densities were used to denote the fact that the rates of counting on the projections are non-negative quantities. Experimental results, both simulated and real, indicate that, by using the MAP criterion, it is possible to obtain better performance, as compared to conventional methods of reconstruction, with a very small increase in computational effort.

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