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Jan 30 2015

The constant covariance approximation to the CRLB with pileup

Tag: Math,Noise,Physics — admin @ 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.

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Jan 26 2015

Probability distribution with pileup

Tag: Math,Noise,Physics — admin @ 5:13 pm
The method to compute SNR in my paper, “Signal to noise ratio of energy selective x-ray photon counting systems with pileup”[1], assumes that the noisy data have a multivariate normal distribution. Appendix A of the paper describes a Monte Carlo simulation to study the conditions under which the normal distribution assumption is valid. In this post, I will expand on the discussion in the paper and present Matlab code to reproduce the figures.

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Jan 05 2015

SNR with pileup-3 PHA detector statistics with pileup

Tag: Math,Physics,software — admin @ 11:31 am
This post continues the discussion of my paper “Signal to noise ratio of energy selective x-ray photon counting systems with pileup”[1], which is available for free download here. Following the road map described in my last post, I am deriving and validating formulas for the statistics of photon counting detectors with pileup. In this post, I describe formulas for the expected value and covariance of pulse height analysis data with pileup and present software to verify the formulas with Monte Carlo simulations.

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