Jan 30

A-space covariance from x-ray detector noise

Tag: Noise,Physics,softwareadmin @ 10:47 am

My last post showed that detection performance is determined by the signal to noise ratio (SNR). I derived a formula for the SNR with multispectral measurements, which depends on the covariance of the A-space data. This post shows how to compute the A-space covariance from the x-ray data noise and the effective attenuation coefficient matrix. In general, this depends on the type of estimator used so instead I will use the Cramèr-Rao lower bound (CRLB), which is the minimum covariance for any unbiased estimator. This gives a general result independent of the specific estimator implementation. I will show that the constant covariance CRLB is sufficiently accurate for our purposes. These results will allow us to compute signal to noise ratios for limited energy resolution measurements that are directly comparable to the Tapiovaara-Wagner[Tapiovaara1985] optimal SNR with complete energy information.

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