3-D reconstruction in PET cameras with irregular sampling and depth of interaction

We present three-dimensional (3-D) reconstruction algorithms that address f ully 3-D tomographic reconstruction for a septa-less, stationary, and recta ngular camera. The field of view (FOV) encompasses the entire volume enclos ed by detector modules capable of measuring depth of interaction (DOI). The filtered backprojection-based algorithms incorporate DOI, accommodate irre gular sampling, and minimize interpolation in the data by defining lines of response between the measured interaction points. We use fixed-width, even ly spaced radial bins in order to use the fast Fourier transform but use ir regular angular sampling to minimize the number of unnormalizable zero effi ciency sinogram bins. To address persisting low-efficiency bins, we perform two-dimensional (2-D) nearest neighbor radial smoothing, employ a semi-ite rative procedure to estimate the unsampled data, and mash the "in plane" an d the first oblique projections to reconstruct the 2-D image in the 3DRP al gorithm. We present artifact-free, essentially spatially isotropic images o f Monte Carlo data with full-width at half-maximum resolutions of 1.5, 2.3, and 3.1 turn at the center, in the bulk, and in the corners of the FOV, re spectively.