Oct 18

Why is polynomial estimator variance so large?

Tag: Math,Noiseadmin @ 9:11 am
Anyone with experience in energy selective imaging is struck by the terrible performance of polynomial estimators discussed in my last post. This is most likely due to the fact that in the past the number of spectra was almost always equal to the dimension of the A-vector. In this case, as I showed in the last post, any estimator that solves the deterministic, noise free equations is the maximum likelihood estimator (MLE). With equal number of spectra and dimension, the polynomial estimator is accurate for low-noise data so it provides an ’efficient’ estimator. That is its covariance is equal to the Cramèr-Rao lower bound (CRLB). In this post, I examine the reason for the poor performance with more measurements than the A-vector dimension.

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