Infimal convolution-based regularization for SPECT reconstruction

Total variation (TV) regularization is efficient in suppressing noise, but is known to suffer from staircase artifacts. The goal of this work was to develop a regularization method using the infimal convolution of the first- and the second-order derivatives to reduce or even prevent staircase artifacts in the reconstructed images, and to investigate if the advantage in noise suppression by this TV-type regularization can be translated into dose reduction.

In the present work, we introduce the infimal convolution of the first- and the second-order total variation (ICTV) as the regularization term in penalized maximum likelihood reconstruction. The preconditioned alternating projection algorithm (PAPA), previously developed by the authors of this article, was employed to produce the reconstruction. Using Monte Carlo-simulated data, we evaluate noise properties and lesion detectability in the reconstructed images and compare the results with conventional total variation (TV) and clinical EM-based methods with Gaussian post filter (GPF-EM). We also evaluate the quality of ICTV regularized images obtained for lower photon number data, compared with clinically used photon number, to verify the feasibility of radiation-dose reduction to patients by use of the ICTV reconstruction method.

By comparison with GPF-EM reconstructed images, we have found that the ICTV-PAPA method can achieve a lower background variability level while maintaining the same level of contrast. Images reconstructed by the ICTV-PAPA method with 80,000 counts per view exhibit even higher channelized Hotelling observer (CHO) signal-to-noise ratio (SNR), as compared to images reconstructed by the GPF-EM method with 120,000 counts per view.

In contrast to the TV-PAPA method, the ICTV-PAPA reconstruction method avoids substantial staircase artifacts, while producing reconstructed images with higher CHO SNR and comparable local spatial resolution. Simulation studies indicate that a 33% dose reduction is feasible by switching to the ICTV-PAPA method, compared with the GPF-EM clinical standard.