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

We present three-dimensional (3-D) reconstruction algorithms that address fully 3-D tomographic reconstruction for a septa-less, stationary, and rectangular camera. 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 response between the measured interaction points. We use fixed-width, evenly spaced radial bins in order to use the fast Fourier transform but use irregular angular sampling to minimize the number of unnormalizable zero efficiency sinogram bins. To address persisting low-efficiency bins, we perform two-dimensional (2-D) 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 2-D image in the 3DRP algorithm. We present artifact-free, essentially spatially isotropic images of Monte Carlo data with full-width at half-maximum resolutions of 1.5, 2.3, and 3.1 mm at the center, in the bulk, and in the corners of the FOV, respectively.