Method and apparatus for computed tomography (CT) and material decomposition with pile-up correction calibrated using real pulse pileup effect and detector response

An apparatus to process projection measurements, the apparatus comprising:

• processing circuitry configured to
• obtain projection data comprising recorded counts that (i) correspond to energy bins of an X-ray detector, (ii) are affected by pileup of X-rays within a detection time window, and (iii) have a pileup-affected spectrum that is distorted relative to a true spectrum of the detected X-rays, wherein the recorded counts represent X-rays detected at respective photon-counting detector elements comprising the X-ray detector, and the detected X-rays have been transmitted through an object being imaged,
• obtain a forward model of pulse pileup that estimates the pileup-affected spectrum of the recorded counts based on an input of a pileup-corrected spectrum proposed to represent the true spectrum of the detected X-rays, the forward model including parameters specific to the respective photon-counting detector elements, and the forward model representing two or more orders of pulse pileup and including a respective pileup response matrix for each one of the two or more orders of pulse pileup, and
• correct the projection data using the forward model to generate corrected projection data, wherein
• an nth-order of pulse pileup of the two or more orders of pulse pileup represents n+1 X-rays being detected at one of the photon-counting detector elements within a detection time window, and n is a positive integer.