Sequential regularized MLEM reconstruction method for incomplete sinograms

Abstract

In this study, we investigate the capability of the well-known maximum likelihood expectation maximization (MLEM) method in handling the incomplete sinogram reconstruction. MLEM method is known to be able to deal with the missing parts via system matrix modeling. We propose sequentially applied regularized MLEM method for the image reconstruction from the incomplete sinograms. Median filtering (MED), L-filtering (L) and block matching 3D (BM3D) filtering were employed as spatial domain regularizers, separately. The MLEM method was applied sequentially by decreasing gradually the amount of the regularization when the image update between the consecutive iterations was negligible. The sequential application of the MLEM method is used to compensate for the blurring caused by the regularization filters. In order to test the proposed approach thoroughly, we constructed wide test dataset consisting of three sparse sinograms (by using 25%, 10% and 5.5% of the sinogram data), the ECAT HRRT type sinogram (81.2% of the sinogram data), ClearPET type sinogram (88.3% of the sinogram data), AX-PET type sinogram (56% of the sinogram data) and a hypothetical checkerboard type sinogram (50% of the sinogram data) of the Shepp-Logan phantom. The constructed incomplete sinograms were contaminated with the Poisson noise. The incomplete sinograms were reconstructed by using filtered backprojection, MLEM without filtering, MLEM with MED, MLEM with L and MLEM with BM3D filtering. We evaluated the approach visually and with the quantitative normalized mean square error (NMSE). The results showed that MLEM without filtering cannot correct the artifacts related to the missing sinogram bins for some of the generated incomplete sinograms. On the other hand, MLEM method with spatial regularization filter was able to provide successfully reconstructed images for all cases. Quantitative NMSE values were in parallel with the visual impression of the reconstructed images.