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The effect of intrinsic attenuation correction methods on the stationarity of the 3‐D modulation transfer function of SPECT
Author(s) -
Glick S. J.,
Hawkins W. G.,
King M. A.,
Penney B. C.,
Soares E. J.,
Byrne C. L.
Publication year - 1992
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 - 10.1118/1.596773
Subject(s) - attenuation , optical transfer function , attenuator (electronics) , fourier transform , iterative reconstruction , optics , exponential function , physics , point spread function , correction for attenuation , mathematics , mathematical analysis , computer science , artificial intelligence
The application of stationary restoration techniques to SPECT images assumes that the modulation transfer function (MTF) of the imaging system is shift invariant. It was hypothesized that using intrinsic attenuation correction (i.e., methods which explicitly invert the exponential radon transform) would yield a three‐dimensional (3‐D) MTF which varies less with position within the transverse slices than the combined conjugate view two‐dimensional (2‐D) MTF varies with depth. Thus the assumption of shift invariance would become less of an approximation for 3‐D post‐ than for 2‐D pre‐reconstruction restoration filtering. SPECT acquisitions were obtained from point sources located at various positions in three differently shaped, water‐filled phantoms. The data were reconstructed with intrinsic attenuation correction, and 3‐D MTFs were calculated. Four different intrinsic attenuation correction methods were compared: (1) exponentially weighted backprojection, (2) a modified exponentially weighted backprojection as described by Tanaka et al . [Phys. Med. Biol. 29 , 1489–1500 (1984)], (3) a Fourier domain technique as described by Bellini et al . [IEEE Trans. ASSP 27 , 213–218 (1979)], and (4) the circular harmonic transform (CHT) method as described by Hawkins et al . [IEEE Trans. Med. Imag. 7 , 135–148 (1988)]. The dependence of the 3‐D MTF obtained with these methods, on point source location within an attenuator, and on shape of the attenuator, was studied. These 3‐D MTFs were compared to: (1) those MTFs obtained with no attenuation correction, and (2) the depth dependence of the arithmetic mean combined conjugate view 2‐D MTFs. It was determined that using either the Bellini or CHT method yielded 3‐D MTFs which were the least nonstationary of the methods tested, and 3‐D point spread functions (PSFs) which exhibited minimal noise amplification. Hence, both the Bellini and CHT attenuation correction methods appear to be good choices to use in preparation for stationary post‐reconstruction filtering of studies where a uniform attenuation medium can be assumed.