Estimator for photon counting energy selective x-ray imaging with multibin pulse height analysis

Area of Science:

• Medical Physics
• Image Reconstruction
• Photon Counting Detectors

Background:

• Photon counting detectors with multibin pulse height analysis (PHA) are crucial for energy-dependent imaging.
• Accurate estimation of energy-dependent information is essential for quantitative imaging.
• Existing noniterative estimators often struggle with noise and bias.

Purpose of the Study:

• To develop a novel noniterative estimator for energy-dependent information from multibin PHA data.
• To evaluate the noise variance and bias of the proposed estimator against existing methods and the Cramèr-Rao lower bound (CRLB).

Main Methods:

• Utilizes a two-function decomposition of the attenuation coefficient.
• Employs a linearized maximum likelihood estimator for initial estimates.
• Generates 2D look-up tables for corrections based on calibration phantom measurements.
• Simulates performance using 2-5 bin PHA data and compares Mean Square Error (MSE), bias, and variance.

Main Results:

• The proposed estimator achieves the CRLB for three or more PHA bins, outperforming other estimators with significantly lower output variance.
• Bias is comparable to polynomial estimators for extensive calibration phantoms but higher than rational polynomial estimators.
• MSE is dominated by variance, indicating negligible bias errors at tested photon counts.

Conclusions:

• The developed noniterative estimator accurately computes energy-dependent information from multibin PHA data.
• It achieves the CRLB across various conditions with low output bias.
• Calibration via phantom measurements eliminates the need for x-ray spectrum or detector response function data.