Sparse estimation for pulse pile-up correction in photon-counting detectors

Photon counting computed tomography (PCCT) is a next-generation imaging technology with high spatial resolution and energy discrimination. However, its performance is limited by pulse pile-up, where multiple photons arrive within a short time, their signals overlapping and reducing counting accuracy. This study formulates the estimation of carrier generation time and quantity from pile-up current waveforms as an inverse problem. Based on a drift-diffusion model for carrier transport in semiconductors, the problem is ill-conditioned and noise-sensitive due to diffusion-induced signal blurring. To address this, we apply two approaches: truncated singular value decomposition (TSVD) for stabilization, and L1 regularization with sparse estimation using prior knowledge. Simulations show TSVD suppresses noise, while sparse estimation achieves better resolution and separates overlapping events effectively.