Cluster-based priors for MAP PET image reconstruction

We propose two forms of cluster-based priors for the maximum a Posterior (MAP) algorithm to improve PET image reconstruction quantitatively. Conventionally, most priors in MAP reconstruction use weighted differences between voxel intensities within a small localized spatial neighborhood, exploiting intensity similarities amongst adjacent voxels. It was hypothesized that by incorporating a larger collection of voxels with similar properties, the MAP approach has a greater ability to impose smoothness while preserving edges. We propose to use clustering techniques as applied to pre-reconstructed images to define clustered neighborhoods of voxels with similar intensities. Two forms of cluster-based priors were proposed. The unweighted cluster-based prior (CP-U) applies a uniform weight regardless of position within a cluster to voxel value differences. The distance weighted cluster-based prior (CP-W) applies different weights based on the distance between voxels within a cluster. The two forms of cluster-based priors, CP-U and CP-W, are implemented within MAP reconstruction. The fuzzy C-means (FCM) method is used to cluster the filtered backprojection (FBP) reconstructed image before MAP reconstruction. To evaluate the proposed priors, a mathematical brain phantom was used in analytic simulations to generate the projection data. We compare reconstructed images from the proposed cluster-based priors MAP algorithms with those from conventional MLEM and quadratic prior (QP) MAP algorithms, using the regional bias (normalized mean squared error, NMSE) vs noise (normalized standard deviation tradeoff, NSD) tradeoff curves. MAP reconstruction using cluster-based priors (CP-U-MAP and CP-W-MAP) dramatically improved the noise vs. bias tradeoff when the number of clusters selected is equal to or larger than the true number of clusters within the image. However, the CP-U-MAP may introduce some bias in a region that may be wrongly clustered, e.g. when the number of selected clus- ers is smaller than the true number of clusters, a problem that is largely avoided by CP-W-MAP reconstruction which exhibits very robust quantitative performance.