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

We present 3D reconstruction algorithms that address fully 3D tomographic reconstruction using septaless, stationary, and rectangular cameras. The field of view (FOV) encompasses the entire volume enclosed by detector modules capable of measuring depth of interaction (DOI). The Filtered Backprojection based algorithms incorporate DOI, accommodate irregular sampling, and minimize interpolation in the data by defining lines of responses between the measured interaction points. We use fixed-width, evenly spaced radial bins in order to use the FFT, but use irregular angular sampling to minimize the number of unnormalizable zero efficiency sinogram bins (ZEB). To address persisting ZEBs, we perform 2D nearest neighbor radial smoothing, employ a semi-iterative procedure to estimate the unsampled data, and mash the "in plane" and the first oblique projections to reconstruct the 2D image in the 3DRP algorithm. We present artifact free, essentially spatially isotropic images of Monte Carlo data with FWHM resolutions of 1.50 mm, 2.25 mm, and 3.00 mm at the center, in the bulk, and at the edges and comers of the FOV respectively.