Evaluation of the spline reconstruction technique for PET
Authors: Kastis George A. , Kyriakopoulou Dimitra , Gaitanis Anastasios , Fernández Yolanda , Hutton Brian F. , Fokas Athanasios S. 
Published: March 2014

Purpose:

The spline reconstruction technique (SRT), based on the analytic formula for the inverse Radon transform, has been presented earlier in the literature. In this study, the authors present an improved formulation and numerical implementation of this algorithm and evaluate it in comparison to filtered backprojection (FBP).

Methods:

The SRT is based on the numerical evaluation of the Hilbert transform of the sinogram via an approximation in terms of “custom made” cubic splines. By restricting reconstruction only within object pixels and by utilizing certain mathematical symmetries, the authors achieve a reconstruction time comparable to that of FBP. The authors have implemented SRT in STIR and have evaluated this technique using simulated data from a clinical positron emission tomography (PET) system, as well as real data obtained from clinical and preclinical PET scanners. For the simulation studies, the authors have simulated sinograms of a point‐source and three digital phantoms. Using these sinograms, the authors have created realizations of Poisson noise at five noise levels. In addition to visual comparisons of the reconstructed images, the authors have determined contrast and bias for different regions of the phantoms as a function of noise level. For the real‐data studies, sinograms of an18F‐FDG injected mouse, a NEMA NU 4‐2008 image quality phantom, and a Derenzo phantom have been acquired from a commercial PET system. The authors have determined: (a) coefficient of variations (COV) and contrast from the NEMA phantom, (b) contrast for the various sections of the Derenzo phantom, and (c) line profiles for the Derenzo phantom. Furthermore, the authors have acquired sinograms from a whole‐body PET scan of an 18F‐FDG injected cancer patient, using the GE Discovery ST PET/CT system. SRT and FBP reconstructions of the thorax have been visually evaluated.

Results:

The results indicate an improvement in FWHM and FWTM in both simulated and real point‐source studies. In all simulated phantoms, the SRT exhibits higher contrast and lower bias than FBP at all noise levels, by increasing the COV in the reconstructed images. Finally, in real studies, whereas the contrast of the cold chambers are similar for both algorithms, the SRT reconstructed images of the NEMA phantom exhibit slightly higher COV values than those of FBP. In the Derenzo phantom, SRT resolves the 2‐mm separated holes slightly better than FBP. The small‐animal and human reconstructions via SRT exhibit slightly higher resolution and contrast than the FBP reconstructions.

Conclusions:

The SRT provides images of higher resolution, higher contrast, and lower bias than FBP, by increasing slightly the noise in the reconstructed images. Furthermore, it eliminates streak artifacts outside the object boundary. Unlike other analytic algorithms, the reconstruction time of SRT is comparable with that of FBP. The source code for SRT will become available in a future release of STIR.