Effect of noise in the probability matrix used for statistical reconstruction of PET data

Iterative reconstruction algorithms require prior computation of the system probability matrix P. This matrix is usually estimated from approximated calculations. The approach employed to determine P in this work, however, was based on Monte Carlo simulations. While this technique allows P to be described more accurately, the number of simulated events may limit the statistical quality of P, thus affecting the reconstructed image. The goal of this study was to quantify this effect for OSEM and PWLS applied to the small animal PET system MADPET (φ=86 mm). System matrices with different statistical quality were obtained by using subsets of the simulated data, and these were then used to reconstruct two simulated phantoms. The results showed that simulations with more than ≈20 000 detected coincidences per pixel barely improved the accuracy of P, but when less than 4 000 detected coincidences per pixel were used, the statistical quality of P deteriorated strongly. PWLS was more sensitive to the inaccurate description of P than OSEM. For PWLS and 1 mm² pixels, any slight increase of the mean relative error for P in the range 23%-30% strongly affected the image properties, while OSEM in combination with any matrix characterized by a mean relative error below ≈40% (obtained from simulations with more than a mean of ≈680 detected counts per pixel) resulted in reasonable images. Good SNR and contrast was assured when using OSEM and a matrix characterized by a mean relative error below 25% (at least 7 000 detected coincidences per pixel). Discarding elements of P that had very small magnitudes reduced the size of the matrix (storage of nonzero elements) and improved the relative error of P and signal-to-noise ratio, especially if OSEM was employed.