Fast 3D iterative image reconstruction for SPECT with rotating slat collimators

As an alternative to the use of traditional parallel hole collimators, SPECT imaging can be performed using rotating slat collimators. While maintaining the spatial resolution, a gain in image quality could be expected from the higher photon collection efficiency of this type of collimator. However, the use of iterative methods to do fully three-dimensional (3D) reconstruction is computationally much more expensive and furthermore involves slow convergence compared to a classical SPECT reconstruction. It has been proposed to do 3D reconstruction by splitting the system matrix into two separate matrices, forcing the reconstruction to first estimate the sinograms from the rotating slat SPECT data before estimating the image. While alleviating the computational load by one order of magnitude, this split matrix approach would result in fast computation of the projections in an iterative algorithm, but does not solve the problem of slow convergence. There is thus a need for an algorithm which speeds up convergence while maintaining image quality for rotating slat collimated SPECT cameras. Therefore, we developed a reconstruction algorithm based on the split matrix approach which allows both a fast calculation of the forward and backward projection and a fast convergence. In this work, an algorithm of the maximum likelihood expectation maximization (MLEM) type, obtained from a split system matrix MLEM reconstruction, is proposed as a reconstruction method for rotating slat collimated SPECT data. Here, we compare this new algorithm to the conventional split system matrix MLEM method and to a gold standard fully 3D MLEM reconstruction algorithm on the basis of computational load, convergence and contrast-to-noise. Furthermore, ordered subsets expectation maximization (OSEM) implementations of these three algorithms are compared. Calculation of computational load and convergence for the different algorithms shows a speedup for the new method of 38 and 426 compared to the split matrix MLEM approach and the fully 3D MLEM respectively and a speedup of 16 and 21 compared to the split matrix OSEM and the fully 3D OSEM respectively. A contrast-to-noise study based on simulated data shows that our new approach has comparable accuracy as the fully 3D reconstruction method. The algorithm developed in this study allows iterative image reconstruction of rotating slat collimated SPECT data with equal image quality in a comparable amount of computation time as a classical SPECT reconstruction.