Technical Note: The nearest neighborhood-based approach for estimating basis line-integrals using photon-counting detector

Purpose: This study aims to develop a calibration-based estimator for the photon-counting detector (PCD)-based x-ray computed tomography. Methods: We propose the nearest neighborhood (NN)-based estimator, which searches for the nearest calibration data for a given PCD output and sets the associated basis line-integrals as the estimate. Searching for the nearest neighbors can be accelerated using the pre-calculated k-d tree for the data. Results: The proposed method is compared to the model-based maximum likelihood (ML) estimator. For slab phantom study, both ML and NN-based methods achieve the Cramér-Rao lower bound and are unbiased for various combinations of three basis materials (water, bone, and gold). The proposed method is also validated for K-edge imaging and presents almost unbiased Au concentrations in the region of interest. Conclusions: The proposed NN-based method is demonstrated to be as accurate as the model-based ML estimator, but it is computationally efficient and requires only calibration measurements.