Jan 24
Detection theory with A-space data
In my last posts I discussed the background for applying statistical detection theory to x-ray imaging. In this post, I will show how to incorporate the A-space description into the model. This will lead me to discuss the effect of the basis set functions on the approximation or representation error of the attenuation coefficients of body materials. I will show that there are optimal functions that minimize the error but that other basis functions, such as the attenuation coefficient functions of different materials, do not lead to substantially larger errors. Once the A-space description is in the model, we can derive a signal to noise ratio that is directly comparable to the Tapiovaara-Wagner SNR[Tapiovaara1985] and we can compare the SNR with limited energy resolution to the ideal with complete spectral information.
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