The attenuated spline reconstruction technique for single photon emission computed tomography

Nicholas E Protonotarios; Athanassios S Fokas; Kostas Kostarelos; George A Kastis

doi:10.1098/rsif.2018.0509

The attenuated spline reconstruction technique for single photon emission computed tomography

J R Soc Interface. 2018 Nov 28;15(148):20180509. doi: 10.1098/rsif.2018.0509.

Authors

Nicholas E Protonotarios^{1

2}, Athanassios S Fokas^{3

4

5}, Kostas Kostarelos^{6

7}, George A Kastis³

Affiliations

¹ Research Center of Mathematics, Academy of Athens, Athens 11527, Greece protost@hotmail.com.
² Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens 15780, Greece.
³ Research Center of Mathematics, Academy of Athens, Athens 11527, Greece.
⁴ Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK.
⁵ Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, USA.
⁶ Nanomedicine Laboratory, Faculty of Biology, Medicine and Health, University of Manchester, Manchester M13 9PL, UK.
⁷ National Graphene Institute, University of Manchester, Manchester M13 9PL, UK.

Abstract

We present the attenuated spline reconstruction technique (aSRT) which provides an innovative algorithm for single photon emission computed tomography (SPECT) image reconstruction. aSRT is based on an analytic formula of the inverse attenuated Radon transform. It involves the computation of the Hilbert transforms of the linear attenuation function and of two sinusoidal functions of the so-called attenuated sinogram These computations are achieved by employing the attenuation information provided by computed tomography (CT) scans and by utilizing custom-made cubic spline interpolation. The purpose of this work is: (i) to present the mathematics of aSRT, (ii) to reconstruct simulated and real SPECT/CT data using aSRT and (iii) to evaluate aSRT by comparing it to filtered backprojection (FBP) and to ordered subsets expectation minimization (OSEM) reconstruction algorithms. Simulation studies were performed by using an image quality phantom and an appropriate attenuation map. Reconstructed images were generated for 45, 90 and 180 views over 360 degrees with 20 realizations and involved Poisson noise of three different levels (NL), namely 100% (NL1), 50% (NL2) and 10% (NL3) of the total counts, respectively. Moreover, real attenuated SPECT sinograms were reconstructed from a real study of a Jaszczak phantom, as well as from a real clinical myocardial SPECT/CT study. Comparisons between aSRT, FBP and OSEM reconstructions were performed using contrast, bias and image roughness. The results suggest that aSRT can efficiently produce accurate attenuation-corrected reconstructions for simulated and real phantoms, as well as for clinical data. In particular, in the case of the clinical myocardial study, aSRT produced reconstructions with higher cold contrast than both FBP and OSEM. aSRT, by incorporating the attenuation correction within itself, may provide an improved alternative to FBP. This is particularly promising for 'cold' regions as those occurring in myocardial ischaemia.

Keywords: analytic image reconstruction; attenuated Radon transform; single photon emission computed tomography (SPECT).

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Algorithms*
Humans
Models, Theoretical*
Phantoms, Imaging*
Tomography, Emission-Computed, Single-Photon / instrumentation
Tomography, Emission-Computed, Single-Photon / methods*