Ultrafast Preconditioned Conjugate Gradient MAP reconstruction for fully 3-D microPET

Iterative 3D PET reconstruction represents a very computational challenge due to the large number of lines of response (LOR) collected for each data set. This iterative 3D reconstruction also needs a lot of iterations to achieve an acceptable PET reconstructed image. A preconditioned conjugate gradient (PCG) method was previously shown to have faster convergence rate than expectation maximization (EM) type algorithms. For the microPET, images suffer from crystal penetration blurring due to small scanner radius. An exact 2D blur model is needed to achieve high resolution image. A Preconditioned Conjugate Gradient (PCG) method is described for reconstruction of high-resolution 3D images from the microPET Inveon small-animal scanner from Siemens. The projector pair is used as part of a factored system matrix that takes into account detector-pair response by using shift-variant sinogram blur kernels, attenuation correction, and detector efficiency corrections. The system matrix for geometric projection is based on depth dependent solid angle calculation in combination with a spatially variant detector response model. The mircoPET PCG is combined with OSEM to accelerate convergence. This reconstruction model achieves a high resolution animal image; however, it took an hour to reconstruct a frame. Therefore, we describe an ultrafast forward and back projector pair based on Symmetry and SIMD projector (SSP). The proposed method produces similar quality images when compared to those obtained with the software package from Siemens and requires order of magnitude less computation.