Anisotropic total variation regularization for the maximum a posteriori ordered subsets expectation maximization reconstruction in fan-beam SPECT

Objectives To minimize the partial volume effect while preserving the optimal tradeoff between noise and bias in the reconstructed fan-beam SPECT images.

Methods We created elliptical cylinder digital phantom containing hot and cold spheres with diameters ranging from 0.9 cm to 2.2 cm on the warm background and simulated SPECT data via Monte Carlo technique with 10% and 20% noise levels (100 noise samples, each). We modified conventional TV (L1) norm and replaced it with two independent TV (L1u) norms in fan-beam plane (TVx, TVy) and in the axial direction (TVz). The SPECT data were reconstructed using maximum a posteriori (MAP) ordered subset expectation maximization (OSEM) algorithm with total variation (TV) regularization (MAP-OSEM-TV). We compared performance of the modified anisotropic TV norm that requires tuning of two hyperparameters to conventional isotropic TV regularization with one hyperparameter.

Results We found that the modified TV regularization only slightly decreased the partial volume effect at the cost of somewhat increased noise and bias, as compared to conventional TV norm.

Conclusions A small improvement in terms of minimization of the partial volume effect can be achieved using the modified TV norm, at the expense of slight increased bias and noise, and higher computational cost of reconstruction