Estimation of basis line-integrals in a spectral distortion-modeled photon counting detector using low-rank approximation-based x-ray transmittance modeling: K-edge imaging application

Okkyun Lee, Steffen Kappler, Christoph Polster, Katsuyuki Taguchi

Research output: Contribution to journalArticle

Abstract

Photon counting detectors (PCD) provide multiple energy-dependent measurements for estimating basis lineintegrals. However, the measured spectrum is distorted from the spectral response effect (SRE) via charge sharing, K-fluorescence emission, etc. Thus, in order to avoid bias and artifacts in images, the SRE needs to be compensated. For this purpose, we recently developed a computationally efficient three-step algorithm for PCD-CT without contrast agents by approximating smooth x-ray transmittance using low-order polynomial bases. It compensated the SRE by incorporating the SRE model in a linearized estimation process and achieved nearly the minimum variance and unbiased (MVU) estimator. In this paper, we extend the three-step algorithm to K-edge imaging applications by designing optimal bases using a low-rank approximation to model x-ray transmittances with arbitrary shapes (i.e., smooth without the K-edge or discontinuous with the K-edge). The bases can be used to approximate the x-ray transmittance and to linearize the PCD measurement modeling and then the three-step estimator can be derived as in the previous approach: Estimating the xray transmittance in the first step, estimating basis line-integrals including that of the contrast agent in the second step, and correcting for a bias in the third step. We demonstrate that the proposed method is more accurate and stable than the low-order polynomial-based approaches with extensive simulation studies using gadolinium for the K-edge imaging application. We also demonstrate that the proposed method achieves nearly MVU estimator, and is more stable than the conventional maximum likelihood estimator in high attenuation cases with fewer photon counts.

Original languageEnglish (US)
JournalIEEE Transactions on Medical Imaging
DOIs
StateAccepted/In press - Aug 27 2017

Fingerprint

Photons
X-Rays
Detectors
Imaging techniques
X rays
Contrast Media
Polynomials
Gadolinium
Artifacts
Maximum likelihood
Fluorescence

Keywords

  • Approximation algorithms
  • Attenuation
  • Energy measurement
  • Imaging
  • K-edge imaging
  • low-rank approximation
  • maximum likelihood
  • Maximum likelihood estimation
  • photon counting detector
  • Photonics
  • spectral response effect
  • X-ray imaging
  • x-ray transmittance

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering

Cite this

@article{d32aaf90e45a42648ccd6b6c45b0a8dd,
title = "Estimation of basis line-integrals in a spectral distortion-modeled photon counting detector using low-rank approximation-based x-ray transmittance modeling: K-edge imaging application",
abstract = "Photon counting detectors (PCD) provide multiple energy-dependent measurements for estimating basis lineintegrals. However, the measured spectrum is distorted from the spectral response effect (SRE) via charge sharing, K-fluorescence emission, etc. Thus, in order to avoid bias and artifacts in images, the SRE needs to be compensated. For this purpose, we recently developed a computationally efficient three-step algorithm for PCD-CT without contrast agents by approximating smooth x-ray transmittance using low-order polynomial bases. It compensated the SRE by incorporating the SRE model in a linearized estimation process and achieved nearly the minimum variance and unbiased (MVU) estimator. In this paper, we extend the three-step algorithm to K-edge imaging applications by designing optimal bases using a low-rank approximation to model x-ray transmittances with arbitrary shapes (i.e., smooth without the K-edge or discontinuous with the K-edge). The bases can be used to approximate the x-ray transmittance and to linearize the PCD measurement modeling and then the three-step estimator can be derived as in the previous approach: Estimating the xray transmittance in the first step, estimating basis line-integrals including that of the contrast agent in the second step, and correcting for a bias in the third step. We demonstrate that the proposed method is more accurate and stable than the low-order polynomial-based approaches with extensive simulation studies using gadolinium for the K-edge imaging application. We also demonstrate that the proposed method achieves nearly MVU estimator, and is more stable than the conventional maximum likelihood estimator in high attenuation cases with fewer photon counts.",
keywords = "Approximation algorithms, Attenuation, Energy measurement, Imaging, K-edge imaging, low-rank approximation, maximum likelihood, Maximum likelihood estimation, photon counting detector, Photonics, spectral response effect, X-ray imaging, x-ray transmittance",
author = "Okkyun Lee and Steffen Kappler and Christoph Polster and Katsuyuki Taguchi",
year = "2017",
month = "8",
day = "27",
doi = "10.1109/TMI.2017.2746269",
language = "English (US)",
journal = "IEEE Transactions on Medical Imaging",
issn = "0278-0062",
publisher = "Institute of Electrical and Electronics Engineers Inc.",

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TY - JOUR

T1 - Estimation of basis line-integrals in a spectral distortion-modeled photon counting detector using low-rank approximation-based x-ray transmittance modeling

T2 - K-edge imaging application

AU - Lee, Okkyun

AU - Kappler, Steffen

AU - Polster, Christoph

AU - Taguchi, Katsuyuki

PY - 2017/8/27

Y1 - 2017/8/27

N2 - Photon counting detectors (PCD) provide multiple energy-dependent measurements for estimating basis lineintegrals. However, the measured spectrum is distorted from the spectral response effect (SRE) via charge sharing, K-fluorescence emission, etc. Thus, in order to avoid bias and artifacts in images, the SRE needs to be compensated. For this purpose, we recently developed a computationally efficient three-step algorithm for PCD-CT without contrast agents by approximating smooth x-ray transmittance using low-order polynomial bases. It compensated the SRE by incorporating the SRE model in a linearized estimation process and achieved nearly the minimum variance and unbiased (MVU) estimator. In this paper, we extend the three-step algorithm to K-edge imaging applications by designing optimal bases using a low-rank approximation to model x-ray transmittances with arbitrary shapes (i.e., smooth without the K-edge or discontinuous with the K-edge). The bases can be used to approximate the x-ray transmittance and to linearize the PCD measurement modeling and then the three-step estimator can be derived as in the previous approach: Estimating the xray transmittance in the first step, estimating basis line-integrals including that of the contrast agent in the second step, and correcting for a bias in the third step. We demonstrate that the proposed method is more accurate and stable than the low-order polynomial-based approaches with extensive simulation studies using gadolinium for the K-edge imaging application. We also demonstrate that the proposed method achieves nearly MVU estimator, and is more stable than the conventional maximum likelihood estimator in high attenuation cases with fewer photon counts.

AB - Photon counting detectors (PCD) provide multiple energy-dependent measurements for estimating basis lineintegrals. However, the measured spectrum is distorted from the spectral response effect (SRE) via charge sharing, K-fluorescence emission, etc. Thus, in order to avoid bias and artifacts in images, the SRE needs to be compensated. For this purpose, we recently developed a computationally efficient three-step algorithm for PCD-CT without contrast agents by approximating smooth x-ray transmittance using low-order polynomial bases. It compensated the SRE by incorporating the SRE model in a linearized estimation process and achieved nearly the minimum variance and unbiased (MVU) estimator. In this paper, we extend the three-step algorithm to K-edge imaging applications by designing optimal bases using a low-rank approximation to model x-ray transmittances with arbitrary shapes (i.e., smooth without the K-edge or discontinuous with the K-edge). The bases can be used to approximate the x-ray transmittance and to linearize the PCD measurement modeling and then the three-step estimator can be derived as in the previous approach: Estimating the xray transmittance in the first step, estimating basis line-integrals including that of the contrast agent in the second step, and correcting for a bias in the third step. We demonstrate that the proposed method is more accurate and stable than the low-order polynomial-based approaches with extensive simulation studies using gadolinium for the K-edge imaging application. We also demonstrate that the proposed method achieves nearly MVU estimator, and is more stable than the conventional maximum likelihood estimator in high attenuation cases with fewer photon counts.

KW - Approximation algorithms

KW - Attenuation

KW - Energy measurement

KW - Imaging

KW - K-edge imaging

KW - low-rank approximation

KW - maximum likelihood

KW - Maximum likelihood estimation

KW - photon counting detector

KW - Photonics

KW - spectral response effect

KW - X-ray imaging

KW - x-ray transmittance

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JO - IEEE Transactions on Medical Imaging

JF - IEEE Transactions on Medical Imaging

SN - 0278-0062

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