A method for point spread function estimation for accurate quantitative imaging

A. A. Attarwala, D. Hardiansyah, C. Romano, M. Roscher, F. Molina-Duran, B. Wangler, G. Glatting

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Aim: A method to determine the point spread function (PSF) of an imaging system based on a set of 3-D Gaussian functions is presented for a robust estimation of the recovery corrections for accurate activity quantification in positron emission tomography (PET) and single-photon emission computed tomography systems. Materials and Methods: The spatial resolution of the ALBIRA II PET subsystem was determined using a 370-kBq 22Na point source. The measured data were reconstructed with a maximum-likelihood expectation-maximization algorithm. The PSF was calculated based on the National Electrical Manufacturing Association (NEMA) NU-4 2008 protocol and on alternative methods based on three 3-D fitting functions for the xyz-directions: 1) a 3-D Gaussian function (3-D 1-Gauss) and convolutions of this function with a pixel size (3-D Gaussp) or source dimension of O 0.25 mm (3-D Gausss); 2) the sum of two Gaussian functions (3-D 2-Gauss); and 3) three Gaussian functions (3-D 3-Gauss). Goodness of fit and the method based on an Akaike information criterion were used for choosing the best function. A MATLAB-based mathematical source simulation study was performed to quantify the relevance of PSFs calculated from the different methods. Results: Based on the PSFs calculated from the NEMA protocol, the full-width at half-maximum (FWHM) in xyz-directions were 1.68, 1.51, and 1.50 mm. The corresponding results using 3-D Gauss and 3-D Gausss functions both were (1.87 ± 0.01), (1.70 ± 0.01), and (1.50 ± 0.01) mm and for 3-DGaussp were (1.84 ± 0.01), (1.67 ± 0.01), and (1.47 ± 0.01) mm. The FWHMs calculated with 3-D 2-Gauss and 3-D 3-Gauss were (1.78 ± 0.01), (1.74 ± 0.01), and (1.83 ± 0.01) mm and (1.76 ± 0.03), (1.72 ± 0.03), and (1.78 ± 0.03) mm, respectively. All coefficients of variations of the fit parameters were ≤29% and the adjusted R2 were ≥0.99. Based on Akaike weights wi, the 3-D 3-Gauss method was best supported by the data ( wi = 100%). The simulation study showed a relative error in quantification of spherical lesions in the range of 15%-45% for lesions of diameters 1-5 mm compared to the PSFs based on the NEMA method. Conclusion: An alternative method to calculate the PSFs of imaging systems to accurately correct for recovery effects is presented. The proposed method includes choosing and fitting of 3-D functions, validation of fitting quality, and choosing the function best supported by the data along with an estimation of the uncertainty.

Original languageEnglish
Pages (from-to)961-969
Number of pages9
JournalIEEE Transactions on Nuclear Science
Issue number3
Publication statusPublished - Mar 2018


  • Akaike information criterion (AIC)
  • Gaussian function
  • National Electrical Manufacturing Association (NEMA)
  • point spread function (PSF)


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