Proposes a Bayesian method whereby maximum a posteriori (MAP) estimates of functional (PET and SPECT) images may be reconstructed with the aid of prior information derived from registered anatomical MR images of the same slice. The prior information consists of significant anatomical boundaries that are likely to correspond to discontinuities in an otherwise spatially smooth radionuclide distribution. The authors' algorithm, like others proposed recently, seeks smooth solutions with occasional discontinuities; the contribution here is the inclusion of a coupling term that influences the creation of discontinuities in the vicinity of the significant anatomical boundaries. Simulations on anatomically derived mathematical phantoms are presented. Although computationally intense in its current implication, the reconstructions are improved (ROI-RMS error) relative to filtered backprojection and EM-ML reconstructions. The simulations show that the inclusion of position-dependent anatomical prior Information leads to further improvement relative to Bayesian reconstructions without the anatomical prior. The algorithm exhibits a certain degree of robustness with respect to errors in the location of anatomical boundaries.

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One approach to improved reconstructions in emission tomography has been the incorporation of additional source information via Gibbs priors that assume a source f that is piecewise smooth. A natural Gibbs prior for expressing such constraints is an energy function E ( f , f ) defined on binary valued line processes I as well as f . MAP estimation leads to the difficult problem of minimizing a mixed (continuous and binary) variable objective function. Previous approaches have used Gibbs "potential" functions, + ( f , > and + ( f h ) , defined solely on spatial derivatives, f, and fh, of the source. These + functions implicitly incorporate line processes, but only in an approximate manner. The "correct" + function, +*, consistent with the use of line processes, leads to difficult minimization problems. In this work, we present a method wherein the correct +* function is approached through a sequence of smooth functions. This is the essence of a continuation method in which the minimum of the energy function corresponding to one member of the + function sequence is used as an initial condition for the minimization of the next, less approximate, stage. Our continuation method is implemented using a GEM-ICM procedure. Simulation results show improvement using our continuation method relative to using +* alone, and to conventional EM reconstructions.

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