Oct 30
Rationale for the new estimator
The past two posts have discussed estimators for A-vector data. I showed that with the same number of measurement spectra as the A-vector dimension, any estimator that solves the deterministic equations is the maximum likelihood estimator (MLE) and it will achieve the Cramèr-Rao lower bound (CRLB). If there are more measurement spectra than the dimension, then the polynomial estimator, which works well for the equal case, has very poor performance giving a variance that can be several hundred times larger than the CRLB. I showed by simulations that with more measurements than dimension the iterative MLE does give a variance close to the CRLB but it has substantial problems. Common to all iterative algorithms, the computation time is long and random. It may fail to converge at all if the initial estimate is too far from the actual value. As it was implemented by Schlomka et al.[2], it also requires measurements of the x-ray source spectrum and the detector spectral response. These are difficult, time consuming and require laboratory equipment that is not usually available in medical institutions.
In this post, I will give an intuitive explanation for the operation of a new estimator that I introduced in my paper[1] “Estimator for photon counting energy selective x-ray imaging with multi-bin pulse height analysis,” which is available for free download here. The estimator is efficient and can be implemented with data that can be measured at medical institutions. The details of the estimator are described in the paper. Here, I will discuss the background and give a rationale on how it works.
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