An efficient reconstruction method for nonuniform attenuation compensation in nonparallel beam geometries based on Novikov's explicit inversion formula

Abstract

This paper investigates an accurate reconstruction method to invert the attenuated Radon transform in nonparallel beam (NPB) geometries. The reconstruction method contains three major steps: 1) performing one-dimensional phase-shift rebinning; 2) implementing nonuniform Hilbert transform; and 3) applying Novikov's explicit inversion formula. The method seems to be adaptive to different settings of fan-beam geometry from very long to very short focal lengths without sacrificing reconstruction accuracy. Compared to the conventional bilinear rebinning technique, the presented method showed a better spatial resolution, as measured by modulation transfer function. Numerical experiments demonstrated its computational efficiency and stability to different levels of Poisson noise. Even with complicated geometries such as varying focal-length and asymmetrical fan-beam collimation, the presented method achieved nearly the same reconstruction quality of parallel-beam geometry. This effort can facilitate quantitative reconstruction of single photon emission computed tomography for cardiac imaging, which may need NPB collimation geometries and require high computational efficiency.

The meaning of interior tomography

“…While the CT reconstruction algorithms are advanced rapidly, SPECT techniques are improved as well (Rullgard 2004a, Li et al 2005, Tang et al 2005a, 2005b, Noo et al 2007. As a unique tomographic imaging modality, SPECT is to reconstruct a radioactive source distribution within a patient from data collected with a gamma camera at multiple orientations.…”

Image reconstruction from truncated data in single-photon emission computed tomography with uniform attenuation

“…Numerical testing using a SPECT version of the Shepp-Logan phantom [29] was performed under various conditions. This phantom is displayed in figure 7, while table 1 gives a Reconstructions from the simulated data were performed with and without added Poisson noise and also with and without introduced truncation.…”

“…Numerical testing using a SPECT version of the Shepp-Logan phantom [29] was performed under various conditions. This phantom is displayed in figure 7, while table 1 gives a description of the ellipses that form this phantom by addition.…”

“…The insertion of this expansion into(29) givesk µ (t, τ ) = ∞ n=0 (−µ) n+1 π(n + 1)! r n+1 (µτ )a n+1 (t) (B.4)…”

High-order total variation minimization for interior SPECT

“…Inspired by the development of reconstruction algorithms for computed tomography (CT), the single-photon emission computed tomography (SPECT) techniques are being rapidly improved [1][2][3][4][5][6][7][8]. As a unique biomedical tomographic imaging technique, SPECT is to reconstruct a radioactive source distribution from externally measured data.…”