End-to-End Differentiable Photon Counting CT

Quantitative imaging is an important feature of spectral X-ray and CT systems, especially photon-counting CT (PCCT) imaging systems, which is achieved through material decomposition (MD) using spectral measurements. In this work, we present a novel framework that makes the PCCT imaging chain end-to-end differentiable (differentiable PCCT), with which we can leverage quantitative information in the image domain to enable cross-domain learning and optimization for upstream models. Specifically, the material decomposition from maximum-likelihood estimation (MLE) was made differentiable based on the Implicit Function Theorem and inserted as a layer into the imaging chain for end-to-end optimization. This framework allows for an automatic and adaptive solution of a wide range of imaging tasks, ultimately achieving quantitative imaging through computation rather than manual intervention. The end-to-end training mechanism effectively avoids the need for direct-domain training or supervision from intermediate references as models are trained using quantitative images. We demonstrate its applicability in two representative tasks: correcting detector energy bin drift and training an object scatter correction network using cross-domain reference from quantitative material images.