PET image reconstruction incorporating anatomical information using segmented regression

We describe a Bayesian PET reconstruction method that incorporates anatomical information extracted from a partial volume segmentation of a co-registered magnetic resonance (MR) image. For the purposes of this paper we concentrate on imaging the brain which we assume can be partitioned into four tissue classes: gray matter, white matter, cerebral spinal fluid, and partial volume. The PET image is then modeled as a piece-wise smooth function through a Gibbs prior. Within homogeneous tissue regions the image intensity is assumed to be governed by a thin plate energy function. Rather than use the anatomical information to guide the formation of a binary process representing region boundaries, we use the segmented anatomical image as a template to customize the Gibbs energy in such a way that we apply thin-plate smoothing within homogeneous tissue regions while enforcing zeroth order continuity as we transition from homogeneous to partial volume regions. Discontinuities in intensity are allowed only at transitions between two different homogeneous regions. We refer to this model as segmented thin-plate regression with controlled continuities. We present the results of a detailed computer simulated phantom study in which partial volume effects are explicitly modeled. Results indicate that we obtain superior region of interest quantitation using this approach in comparison to a 2D partial volume correction method that has previously been proposed for quantitation using filtered backprojection images.