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An inversion formula for the exponential Radon transform in spatial domain with variable focal‐length fan‐beam collimation geometry
Author(s) -
Wen Junhai,
Liang Zhengrong
Publication year - 2006
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.2170596
Subject(s) - collimator , imaging phantom , collimated light , radon transform , geometry , exponential function , mathematics , computation , inversion (geology) , optics , mathematical analysis , physics , algorithm , laser , paleontology , structural basin , biology
Inverting the exponential Radon transform has a potential use for SPECT (single photon emission computed tomography) imaging in cases where a uniform attenuation can be approximated, such as in brain and abdominal imaging. Tretiak and Metz derived in the frequency domain an explicit inversion formula for the exponential Radon transform in two dimensions for parallel‐beam collimator geometry. Progress has been made to extend the inversion formula for fan‐beam and varying focal‐length fan‐beam (VFF) collimator geometries. These previous fan‐beam and VFF inversion formulas require a spatially variant filtering operation, which complicates the implementation and imposes a heavy computing burden. In this paper, we present an explicit inversion formula, in which a spatially invariant filter is involved. The formula is derived and implemented in the spatial domain for VFF geometry (where parallel‐beam and fan‐beam geometries are two special cases). Phantom simulations mimicking SPECT studies demonstrate its accuracy in reconstructing the phantom images and efficiency in computation for the considered collimator geometries.