Jan 30

The constant covariance approximation to the CRLB with pileup

Tag: Math,Noise,Physicsadmin @ 12:06 pm
In my last post, I showed that the probability distribution of photon counting detector data with pileup is multivariate normal for the counts typically used in material selective imaging. With the normal distribution and a linear model, the Cramèr-Rao lower bound (CRLB) for the covariance of the A-vector data includes a term that depends on the change in the measurement data covariance with A. Without pileup I show in this post and in the Appendix of my “Dimensionality and noise …” paper[2], available for free download here, that the change in covariance term is negligible for large enough counts. In Appendix B of my “SNR with pileup …” paper[1], I show that the term is also negligible with pileup. In this post, I will present and explain the code to reproduce the figures in that section.