Preservation of functional edges in the application of minimum cross-entropy (MXE) reconstruction with an anatomical prior

Full text: MXE reconstruction involves combination of a maximum likelihood term and a penalty term which regularizes the solution by discouraging excessive variations between neighbouring voxels where anatomical boundaries exist. The result is that smoothing is constrained to within anatomical boundaries. A limitation is that this may reduce edge resolution in areas where variation in functional data does not align with anatomical boundaries. To overcome this problem a modified algorithm is proposed which uses a combination of two gaussian priors: one based on the registered anatomical image, the second based on the probability of a functional edge being defined in the previous iteration. The algorithm was designed to reenforce the penalty term where functional and anatomical edges co-exist; however presence of an isolated functional edge encourages an unconstrained solution. The objective is to utilise complementary information from the anatomical image (MRI or CT) without adversely affecting the reconstruction of the functional data (SPECT or PET). A simplified phantom which incorporates both anatomical and functional edges was used to test and optimise the algorithm. Projection data were simulated for fanbeam acquisition (128 projections) and reconstruction was performed using an ordered subsets version of the algorithm (subset size 16). The edge resolution was measured by estimating the width of a gaussian fitted to the derivative for a profile through the reconstructed image. Noise was estimated for a region of constant activity remote from any defined edge. Preliminary findings confirm that the algorithm can provide a regularized solution in which functional edges are preserved with little loss in the edge enhancement encouraged by the anatomical prior