Comparison of SPECT lesion detectability between preconditioned alternating projection algorithm (PAPA) and expectation-maximization algorithm with total variation regularizer (EM-TV)

Objectives Comparison of lesions detectability between PAPA and conventional EM-TV algorithm in the maximum a posteriori (MAP) SPECT reconstruction.

Methods We introduced PAPA algorithm. MAP ECT reconstruction is formulated as a constrained convex optimization problem with TV. Its solution satisfies a system of fixed point equations defined as two proximity operators deduced from convex functions that express TV-norm and constraint. To reduce staircasing artifact, we introduced second order TV gradient (gPAPA). TV is defined as a composition of a convex function and first-order difference matrix. This is in contrast to conventional TV implementation, where a positive small ad hoc parameter ϵ is used to avoid non-differentiability. SPECT data from a uniform cylinder and a cylinder with hot and cold spheres were simulated using Monte Carlo method. Different noise realizations were reconstructed. Channelized Hotelling observer (CHO) analysis was performed. Normalized noise power spectra were obtained.

Results PAPA demonstrates significantly higher CHO detectability indices, as compared to EM-TV. Adding second order TV term to PAPA algorithm further improves detectability. Image noise is significantly lower for PAPA.

Conclusions PAPA might allow low-dose SPECT exams, as compared to EM-TV due to significant noise reduction