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Frequency-dependent signal and noise in spectroscopic x-ray imaging.

ABSTRACT: PURPOSE:We present a new framework for theoretical analysis of the noise power spectrum (NPS) of photon-counting x-ray detectors, including simple photon-counting detectors (SPCDs) and spectroscopic x-ray detectors (SXDs), the latter of which use multiple energy thresholds to discriminate photon energies. METHODS:We show that the NPS of SPCDs and SXDs, including spatio-energetic noise correlations, is determined by the joint probability density function (PDF) of deposited photon energies, which describes the probability of recording two photons of two different energies in two different elements following a single-photon interaction. We present an analytic expression for this joint PDF and calculate the presampling and digital NPS of CdTe SPCDs and SXDs. We calibrate our charge sharing model using the energy response of a cadmium zinc telluride (CZT) spectroscopic x-ray detector and compare theoretical results with Monte Carlo simulations. RESULTS:Our analysis shows that charge sharing increases pixel signal-to-noise ratio (SNR), but degrades the zero-frequency signal-to-noise performance of SPCDs and SXDs. In all cases considered, this degradation was greater than 10%. Comparing the presampling NPS with the sampled NPS showed that degradation in zero-frequency performance is due to zero-frequency noise aliasing induced by charge sharing. CONCLUSIONS:Noise performance, including spatial and energy correlations between elements and energy bins, are described by the joint PDF of deposited energies which provides a method of determining the photon-counting NPS, including noise-aliasing effects and spatio-energetic effects in spectral imaging. Our approach enables separating noise due to x-ray interactions from that associated with sampling, consistent with cascaded systems analysis of energy-integrating systems. Our methods can be incorporated into task-based assessment of image quality for the design and optimization of spectroscopic x-ray detectors.

SUBMITTER: Tanguay J

PROVIDER: S-EPMC7496729 | biostudies-literature | 2020 Jul

REPOSITORIES: biostudies-literature

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Frequency-dependent signal and noise in spectroscopic x-ray imaging.

Tanguay Jesse J Kim Jinwoo J Kim Ho Kyung HK Iniewski Kris K Cunningham Ian A IA

Medical physics 20200422 7

<h4>Purpose</h4>We present a new framework for theoretical analysis of the noise power spectrum (NPS) of photon-counting x-ray detectors, including simple photon-counting detectors (SPCDs) and spectroscopic x-ray detectors (SXDs), the latter of which use multiple energy thresholds to discriminate photon energies.<h4>Methods</h4>We show that the NPS of SPCDs and SXDs, including spatio-energetic noise correlations, is determined by the joint probability density function (PDF) of deposited photon e ...[more]

PMID: 32239517

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Project description:To develop and test a method to quantify the effect of dimensionality on the noise in energy selective x-ray imaging.The Cramèr-Rao lower bound (CRLB), a universal lower limit of the covariance of any unbiased estimator, is used to quantify the noise. It is shown that increasing dimensionality always increases, or at best leaves the same, the variance. An analytic formula for the increase in variance in an energy selective x-ray system is derived. The formula is used to gain insight into the dependence of the increase in variance on the properties of the additional basis functions, the measurement noise covariance, and the source spectrum. The formula is also used with computer simulations to quantify the dependence of the additional variance on these factors. Simulated images of an object with three materials are used to demonstrate the trade-off of increased information with dimensionality and noise. The images are computed from energy selective data with a maximum likelihood estimator.The increase in variance depends most importantly on the dimension and on the properties of the additional basis functions. With the attenuation coefficients of cortical bone, soft tissue, and adipose tissue as the basis functions, the increase in variance of the bone component from two to three dimensions is 1.4 × 10(3). With the soft tissue component, it is 2.7 × 10(4). If the attenuation coefficient of a high atomic number contrast agent is used as the third basis function, there is only a slight increase in the variance from two to three basis functions, 1.03 and 7.4 for the bone and soft tissue components, respectively. The changes in spectrum shape with beam hardening also have a substantial effect. They increase the variance by a factor of approximately 200 for the bone component and 220 for the soft tissue component as the soft tissue object thickness increases from 1 to 30 cm. Decreasing the energy resolution of the detectors increases the variance of the bone component markedly with three dimension processing, approximately a factor of 25 as the resolution decreases from 100 to 3 bins. The increase with two dimension processing for adipose tissue is a factor of two and with the contrast agent as the third material for two or three dimensions is also a factor of two for both components. The simulated images show that a maximum likelihood estimator can be used to process energy selective x-ray data to produce images with noise close to the CRLB.The method presented can be used to compute the effects of the object attenuation coefficients and the x-ray system properties on the relationship of dimensionality and noise in energy selective x-ray imaging systems.

Project description:BackgroundIn MRI, the signal-to-noise ratio (SNR) theoretically increases with B0 field strength. However, because of attenuation of the radiofrequency (RF) fields at 7T, it is not certain if this SNR gain can be realized for prostate imaging.Purpose/hypothesisTo investigate the SNR gain in prostate imaging at 7T as compared with 3T. It is expected that SNR will improve for prostate imaging at 7T compared with 3T.Study typeProspective.SubjectsFour healthy volunteers and one prostate cancer patient.Field strength/sequenceAll subjects were scanned at 3T and at 7T using optimal coil setups for both field strengths. For all volunteers, proton density-weighted images were acquired for SNR analysis and actual flip angle imaging (AFI) B 1 + | maps were acquired for correction of measured SNR values. In the patient, a T2 -weighted (T2 w) image was acquired at 3T and at 7T.AssessmentSNR was calculated in the prostate region for all volunteers. SNR was normalized for flip angle, receiver bandwidth, and voxel volume. SNR was also calculated for different sensitivity encoding (SENSE) acceleration factors.Statistical testingSNR values are represented as the arithmetic mean of SNR values in the prostate. Estimated SNR in the T2 w image is calculated as the arithmetic mean of the signal intensity (SI) divided by the standard deviation of the SI in a specified zone. Tumor-to-tissue contrast is calculated as (SItumor +SIzone )/( SItumor -SIzone ).ResultsAn increase in SNR ranging from 1.7-fold to 2.8-fold was measured in the prostate at 7T in comparison to 3T for four volunteers. At 7T, it is possible to achieve a 4-fold SENSE acceleration in the left-right direction with similar SNR to a nonaccelerated 3T image. T2 w imaging was done at 3T and 7T in one patient, where improved tumor-to-tissue contrast was demonstrated at 7T.Data conclusionSNR improves for prostate imaging at 7T as compared with 3T.Level of evidence2 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2019;49:1446-1455.

Dataset Information

Frequency-dependent signal and noise in spectroscopic x-ray imaging.

Publications

Frequency-dependent signal and noise in spectroscopic x-ray imaging.

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