A backprojection filtering algorithm for a spatially varying focal length collimator

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Abstract
Fan-beam collimators are used in single photon emission computed tomography to improve the sensitivity for imaging of small organs. The disadvantage of fan-beam collimation is the truncation of projection data surrounding the organ of interest or, in those cases of imaging large patients, of the organ itself producing reconstruction artifacts. A spatially varying focal length fan-beam collimator has been proposed to eliminate the truncation problem and to maintain good sensitivity for the organ of interest. The collimator is constricted so that the focal lengths of the holes vary across the face of the collimator with the shortest focal lengths at the center and the longer focal lengths at the periphery of the collimator. The variation of the focal length can have various functional forms but in the authors' work it is assumed to increase monotonically toward the edge of the collimator. A backprojection filtering reconstruction algorithm is derived for this type of collimation. The algorithm first backprojects the projections, then performs a two-dimensional filtering. The algorithm is efficient and has been tested via computer simulations.