aSRT: A new analytic reconstruction algorithm for SPECT

We present aSRT, the attenuated Spline Reconstruction Technique for single photon emission computerized tomography (SPECT): an innovative image reconstruction algorithm based on an analytic formulation of the Inverse Attenuated Radon Transform (IART). aSRT involves the calculation of the Hilbert transform of the linear attenuation coefficient and the Hilbert transform of two sinusoidal functions of the so-called attenuated sinogram. This is accomplished by utilizing the attenuation information provided by computerized tomography (CT) scans and by employing custom-made cubic splines 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 back-projection (FBP) and to ordered subsets expectation minimization (OSEM). Simulation studies were performed by using an image quality (IQ) phantom and an appropriate attenuation map. Reconstructed images were generated for 45, 90 and 180 views over 360 degrees and twenty realizations of Poisson noise were created at three different noise levels, namely 100% (NL1), 50% (NL2) and 10% (NL3) of the total counts, respectively. Moreover, real attenuated SPECT sinograms were reconstructed taking into account the corresponding attenuation map provided by a clinical SPECT/CT system. Comparisons between aSRT, FBP and OSEM reconstructions were evaluated using contrast, bias and image roughness. Plots are presented as a function of image roughness. These results suggest that aSRT can efficiently produce accurate attenuation-corrected reconstructions for simulated phantoms, as well as clinical data. The algorithm provides good quality images with significant improvement over FBP and comparable to OSEM. aSRT, by incorporating the attenuation correction within itself, may provide an improved alternative to FBP.