3D OSEM using planograms coordinates

We present a method of performing fully 3D OSEM reconstruction using projectors based on data acquired by planar detector arrays. By using a special choice of parameters to index a line of response (LOR) for a pair of planar detectors, rather than the conventional parameters used for a circular tomograph, all the LORs passing through a point in the field of view (FOV) lie on a 2D plane in the 4D data space. This approach, the ´planogram method´ is a 3D extension of the 2D-linogram technique of Edholm. The key point is where the integration along a sinusoid in the standard approach becomes integration along a line in the planogram data sets resulting in fast and accurate reconstruction operators. We used matched back-projection and forward-projection operators based on a voxel-driven approach to implement fully 3D OSEM. Analytical simulations of noiseless and noisy data sets were used to validate the 3D algorithm. The test object is a 320 mm diameter sphere filled with 40 mm diameter hot and cold lesions. The contrast between the hot lesion and the surrounding background was 2:1. The reconstructed image of noiseless data presents no significant artifacts. We show that the convergence of the algorithm for hot lesions is faster than for the cold lesions and reach a plateau after 30 equivalent EM-ML iterations. The computing time for each iteration on a 1Gh PC based platform is less than 15 minutes.