On methods for maximum a posteriori image reconstruction with a normal prior

  • Authors:

  • Gabor T. Herman;Alvaro R. De Pierro;Neville Gai

  • Affiliations:

  • Medical Image Processing Group, Department of Radiology, University of Pennsylvania, Philadelphia, Pennsylvania, 19104, USA;Instituto de Matemática, Estatistica e Ciencia de Computa cao, Universidade Estadual de Campinas, CP 6065, Campinas, 13081, Sao Paulo, Brazil;Medical Image Processing Group, Department of Radiology, University of Pennsylvania, Philadelphia, Pennsylvania, 19104, USA

  • Venue:
  • Journal of Visual Communication and Image Representation
  • Year:
  • 1992

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Abstract

In previous publications we proposed, in the area of Positron Emission Tomography (PET), the use of a Maximum A posteriori Probability (MAP) optimization criterion with a particular normal prior which enforces smoothness on the resulting reconstructions. Two iterative algorithms were previously proposed to optimize this functional: one was known to converge to the desired reconstruction but was slow, while for the other it was found experimentally that, although it always appeared to converge an order of magnitude faster than the first one on examples realistic for PET, it could be made to diverge on artificial examples. In this paper we present an algorithm which is as fast as the second of these previously proposed algorithms, but it shares with the first the desirable property that it is guaranteed to converge to the reconstruction which is optimal according to our MAP criterion. We demonstrate the behavior of the algorithm on a variety of examples.