Exact inversion of the exponential x-ray transform for rotating slant-hole (RSH) SPECT.

The RSH SPECT scanner provides parallel-beam attenuated projections for a fully 3D acquisition geometry. The geometry can be represented by circles on the unit sphere of projection directions, one circle for each position of the detector head. Unlike most other fully 3D geometries this one is particularly challenging because there are no 2D subsets in the data. When no attenuation is present, it is well known that an unmeasured projection can be synthesized if it lies inside one of the measured circles. The main result of this work is that under some assumptions on the attenuation distribution, attenuated projections within a circle can be synthesized from available attenuated projections. One consequence is that RSH SPECT projections can be rebinned into a conventional SPECT geometry for which analytic attenuation correction techniques are available.

[1]  Donald C. Solmon,et al.  Inversion of the exponential X‐ray transform. I: Analysis , 1988 .

[2]  Håkan Elmqvist,et al.  Three-dimensional total variation norm for SPECT reconstruction , 2001 .

[3]  Rolf Clackdoyle,et al.  Attenuation correction for rotating slant-hole (RSH) SPECT using exact rebinning , 2001 .

[4]  Xiaochuan Pan,et al.  A unified analysis of exact methods of inverting the 2-D exponential radon transform, with implications for noise control in SPECT , 1995, IEEE Trans. Medical Imaging.

[5]  R Clackdoyle,et al.  Attenuation correction in SPECT using consistency conditions for the exponential ray transform. , 1999, Physics in medicine and biology.

[6]  C. Metz,et al.  The exponential Radon transform , 1980 .

[7]  D. E. Wessell.  Rotating slant‐hole single‐photon emission‐computed tomography , 2000 .

[8]  K F Koral,et al.  Simulated ECT of the left ventricle using rotating slant-hole collimator and two camera positions. , 1984, Journal of nuclear medicine : official publication, Society of Nuclear Medicine.

[9]  F. Noo,et al.  Three-dimensional image reconstruction from exponential parallel-beam projections , 2001 .

[10]  Rolf Clackdoyle,et al.  Inversion of the 3D exponential x-ray transform for a half equatorial band and other semi-circular geometries. , 2002, Physics in medicine and biology.

[11]  S. Dale,et al.  Effects of non-optimal acquisition geometry in myocardial perfusion imaging using Ectomography , 1997 .

[12]  Andrew Markoe,et al.  Fourier Inversion of the Attenuated X-Ray Transform , 1984 .

[13]  Frédéric Noo,et al.  Image reconstruction in 2D SPECT with 180° acquisition , 2001 .

[14]  T. Ribbe,et al.  Bedside tomographic scintigraphy: a diagnostic tool in intensive care and the emergency room , 2001 .

[15]  Losiph Shneiberg.  Some inversion formulas in the single photon emission computed tomography , 1994 .

[16]  Xiaochuan Pan,et al.  A family of π-scheme exponential Radon transforms and the uniqueness of their inverses , 2002 .

[17]  Matilda Larsson,et al.  A mobile tomographic gamma camera system for acute studies , 1997 .