Modified total variation norm for the maximum a posteriori ordered subsets expectation maximization reconstruction in fan-beam SPECT brain perfusion imaging

The anisotropic geometry of Fan-Beam Collimator (FBC) Single Photon Emission Tomography (SPECT) is used in brain perfusion imaging with clinical goals to quantify regional cerebral blood flow and to accurately determine the location and extent of the brain perfusion defects. One of the difficult issues that need to be addressed is partial volume effect. The purpose of this study was to minimize the partial volume effect while preserving the optimal tradeoff between noise and bias, and maintaining spatial resolution in the reconstructed images acquired in FBC geometry. We modified conventional isotropic TV (L1) norm, which has only one hyperparameter, and replaced it with two independent TV (L1u) norms (TVxy and TVz) along two orthogonal basis vectors (XY, Z) in 3D reconstruction space. We investigated if the anisotropic norm with two hyperparameters (beta xy and beta z, where z is parallel to the axis-of-rotation) performed better in FBC-SPECT reconstruction, as compared to the conventional isotropic norm with one hyperparameter (beta) only. We found that MAP-OSEM reconstruction with modified TV norm produced images with smaller partial volume effect, as compared to the conventional TV norm at a cost of slight increase in the bias and noise.