Forward model for charge sharing and pulse pileup
In plain words
When a photon lands between pixels, its charge splits and is counted twice at the wrong energies; when photons arrive too fast they are counted as one. Both corrupt the measured spectrum.
Precise statement
Construct a detector response model giving the recorded energy spectrum from the incident one, including charge sharing between pixels of 200 to 500 micron pitch, K-escape of the sensor material, and pulse pileup at count rates of $10^{8}$ to $10^{9}$ counts per second per $\mathrm{mm}^2$, accurate enough that material decomposition bias stays below 1 percent. An answer is a validated response matrix with its calibration procedure.
What would settle it
Measurement of the detector response to monoenergetic beams across rate and position, reproduced by the model to within the stated bias.
Status in the literature
Clinical photon-counting CT systems since 2021 apply empirical corrections; a first-principles response model with sub-percent bias was not established.
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