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We describe a Bayesian PET reconstruction method that incorporates an image prior model with mixed continuity constraints. In this paper we concentrate on imagin the brain which we assume can be partitioned into four tissue classes: gray matter, white matter, cerebral spinal fluid, and partial volume (PV). Each PV image voxel is assumed to be an arbitrary combination of neighboring pure tissues. The PET image is then modeled as a piece-wise smooth function through a Gibbs prior. Assume that the image intensity of each homogeneous tissue region or partial volume region is governed by a thin-plate energy function. We apply first- and second-order edge detection techniques to estimate region boundaries, and then categorize these boundaries based on the tissue types adjacent to each boundary. Rather than use the binary processes representation region boundaries such as weal-plate mode, we adopt a controlled- continuity approach to influence boundary formation. The rationale is that while the first-order edge detection can capture the jumps between two different pure regions, the second-order one can capture the crease connecting a pure region to partial volume region. As we transition from homogeneous to partial volume regions, we enforce zero-th order continuity. Discontinuities in intensity are allowed only a transitions between two different homogeneous regions. We refer to this model as a modified weak-plate model with controlled continuity. We present the result of a computer simulated phantom study in which partial volume effects are explicitly modeled. Results indicate that we obtain superior region of interest quantization using this approach in comparison to a partial volume correction method that has previously been proposed for quantitation using filtered back-projection images.
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