A detector-response compensation simulation study with 3D MLEM in SPECT compares distance-dependent and distance-nondependent resolution methods

Background Correcting spatial resolution in single photon emission computed tomography (SPECT) using iterative methods has proven effective in many studies. This correction involves using a projection matrix (projector) to simulate the acquisition of projections by a gamma camera, along with a back-projection matrix (back-projector), which is generally the transpose of the projector without any attenuation modeling. This study examined the contribution of distance-dependent detector-response compensation (DRC) and compared it to the accelerated version and the distance-nondependent method. Two projecttors (P1 and P2) and their corresponding back-projectors (B1 and B2) were implemented. P1 represented the distance-dependent response model, while P2 represented a nondependent average response model. Three reconstruction pairs were used: P1/B1 and P1/B2 for distance-dependent DRC, and P2/B2 for distance-nondependent DRC. The reconstruction method was the full 3D maximum-likelihood expectation maximization (MLEM), using simulated digital phantom projections that included attenuation, distance-dependent resolution, and Poisson noise without considering scatter. Results The assessment used transaxial slices. For full-width spatial resolution at half maximum (FWHM), P1 outperformed P2. P1/B2 outperformed P1/B1, with closer approximation after each iteration. Regarding Poisson noise, P1/B1 was more efficient than P1/B2 and P2/B2. Edge artifacts and overshoots were less intense with P2/B2 than the other pairs. P1/B2 and P2/B2 achieved the best relative contrast performance. The root mean squared error (RMSE) or normalized mean error (NME) showed that P1/B1 was best for low projection counts and large iteration numbers, while P1/B2 was best for high projection counts and low iteration numbers. On RMSE, the reconstruction pair performance depended on projection noise level, phantom insert size and type, and iteration. Conclusions No pair was consistently more efficient than the others across all parameters. Using P1/B1, which is far from convergence iteration, could yield results similar to other methods. Considering scatter would likely result in worse and more similar results across the three pairs. Although P2/B2 generally performed worse than P1/B2, they were similar and had more straightforward implementation. The number of iterations should be chosen according to the reconstruction pair, projection count, and desired spatial resolution.