An accurate method for direct dual‐energy calibration and decomposition

Cardinal, Héloïse; Fenster, Aaron

doi:10.1118/1.596512

Cited by 123 publications

(89 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The deterministic errors correspond to the bias, but in medical imaging systems, the variance can be significantly larger than the square of the bias; so, both are measured in this paper. Prior noniterative methods such as the polynomial and rational polynomial 3 estimators can be generalized for more than two spectra but, since they were not designed to take into account the noise properties, their output noise variance with multibin data is much larger than the proposed estimator. The proposed estimator has comparable bias to the polynomial and rational polynomial estimators so it has a much smaller MSE.…”

Section: Introductionmentioning

confidence: 99%

“…1 These detectors can analyze the photons into two or more energy bins but most prior research on solving the equations for the energy dependent information 2 assumed only two effective spectra. [3][4][5][6][7] In this paper, I describe an estimator for multibin PHA data and show that its output noise variance is equal to the Cramèr-Rao lower bound (CRLB) (Refs. 8 and 9) over a wide range of operating conditions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Alvarez¹

2011

Med. Phys.

102

View full text Add to dashboard Cite

Purpose: This paper describes a noniterative estimator for the energy dependent information from photon counting detectors with multibin pulse height analysis (PHA). The estimator uses the two function decomposition of the attenuation coefficient [R. E. Alvarez and A. Macovski, Phys. Med. Biol. 21, 733-744 (1976)] and its output is the line integrals of the basis set coefficients. The output noise variance and bias is compared to other noniterative estimators and to the Cramèr-Rao lower bound (CRLB). Methods: The estimator first computes an initial estimate from a linearized maximum likelihood estimator. The errors in the initial estimates are determined at a set of points from measurements on a calibration phantom. The errors at these known points are interpolated to create two-dimensional look up tables of corrections to the initial estimates. During image acquisition, the linearized maximum likelihood estimate for each data point is used as an input to the correction look up tables, and the final output is the sum of the estimate and the correction. The performance of the estimator is compared to generalizations of the polynomial and rational polynomial estimators for multibin data. The estimators are compared by the mean square error (MSE) and its components, the bias, and the variance of the output. The variance is also compared to the CRLB. The performance is simulated with two to five bins PHA data. The CRLB at a fixed object thickness is also computed as a function of the number of bins. Results: For two bin data, all the estimators' variances are equal to the CRLB. With three or more bins, only the proposed estimator achieves the CRLB while the others, which were not optimized for noise performance, have much larger output variance. The bias of the proposed estimator is equal to the polynomial estimator for calibration phantoms with 40 or more steps, that is, 1600 combinations of basis materials, but is larger than the rational polynomial bias. In all cases at the photon counts tested, the MSE is essentially equal to the variance, indicating that the bias errors are negligible compared to the variance. Conclusions: The estimator provides a noniterative method to compute the energy dependent information from multibin PHA data that achieves the CRLB over a wide range of operating conditions and has low output bias. The estimator can be calibrated based on the measurements of a calibration phantom; so, it does not require measurements of the x-ray energy spectrum or the detector response functions.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Alvarez¹

2011

Med. Phys.

102

View full text Add to dashboard Cite

show abstract

“…The small errors indicate that the nonlinear function selected for dual energy calibration was well-matched to the acquired data. This demonstrates a clear advantage of using nonlinear decomposition to construct dual energy images, particularly, the ability of the dual energy calibration to independently account for the effects of beam hardening 33 for each material. It was observed that TABLE IV.…”

Section: Discussionmentioning

confidence: 99%

“…A nonlinear eight-term rational function was selected for dual energy calibration. 33 This function was reported to be capable of high fitting accuracy while requiring relatively few terms:…”

Section: Dual Energy Decompositionmentioning

confidence: 99%

Quantification of breast density with dual energy mammography: An experimental feasibility study

Ducote

Molloi

2010

Medical Physics

View full text Add to dashboard Cite

Purpose: Breast density, the percentage of glandular breast tissue, has been shown to be a strong indicator of breast cancer risk. A quantitative method to measure breast density with dual energy mammography was investigated using physical phantoms. Methods: The dual energy mammography system used a tungsten anode x-ray tube with a 50 m rhodium beam filter for low energy images and a 300 m copper beam filter for high energy images. Glandular and adipose equivalent phantoms of uniform thickness were used to calibrate a dual energy basis decomposition algorithm. Four different phantom studies were used to evaluate the technique. The first study consisted of phantoms with thicknesses of 2.5-8.5 cm in 0.5 cm steps with variable densities centered at a mean of 28%. The second study consisted of phantoms at a fixed thickness of 4.0 cm, which ranged in densities from 0% to 100% in increments of 12.5%. The third study consisted of 4.0 cm thick phantoms at densities of 25%, 50% and 75% each imaged at three areal sizes, approximately 62.5, 125, and 250 cm 2 , in order to assess the effect of breast size on density measurement. The fourth study consisted of step phantoms designed to more closely mimic the shape of a female breast with maximal thicknesses from 3.0 to 7.0 cm at a fixed density of 50%. All images were corrected for x-ray scatter. Results: The RMS errors in breast density measurements were 0.44% for the variable thickness phantoms, 0.64% for the variable density phantoms, 2.87% for the phantoms of different areal sizes, and 4.63% for step phantoms designed to closely resemble the shape of a breast. Conclusions:The results of the phantom studies indicate that dual energy mammography can be used to measure breast density with an RMS error of approximately 5%.

show abstract

“…The equation was derived as a simplified version of a function used in dual-energy material decomposition. 54 We chose the current function for three reasons. First, there is a mathematical similarity between Eq.…”

Section: Discussionmentioning

confidence: 99%

Image‐based spectral distortion correction for photon‐counting x‐ray detectors

Ding

Molloi

2012

Medical Physics

View full text Add to dashboard Cite

Purpose: To investigate the feasibility of using an image-based method to correct for distortions induced by various artifacts in the x-ray spectrum recorded with photon-counting detectors for their application in breast computed tomography (CT). Methods: The polyenergetic incident spectrum was simulated with the tungsten anode spectral model using the interpolating polynomials (TASMIP) code and carefully calibrated to match the x-ray tube in this study. Experiments were performed on a Cadmium-Zinc-Telluride (CZT) photoncounting detector with five energy thresholds. Energy bins were adjusted to evenly distribute the recorded counts above the noise floor. BR12 phantoms of various thicknesses were used for calibration. A nonlinear function was selected to fit the count correlation between the simulated and the measured spectra in the calibration process. To evaluate the proposed spectral distortion correction method, an empirical fitting derived from the calibration process was applied on the raw images recorded for polymethyl methacrylate (PMMA) phantoms of 8.7, 48.8, and 100.0 mm. Both the corrected counts and the effective attenuation coefficient were compared to the simulated values for each of the five energy bins. The feasibility of applying the proposed method to quantitative material decomposition was tested using a dual-energy imaging technique with a three-material phantom that consisted of water, lipid, and protein. The performance of the spectral distortion correction method was quantified using the relative root-mean-square (RMS) error with respect to the expected values from simulations or areal analysis of the decomposition phantom. Results: The implementation of the proposed method reduced the relative RMS error of the output counts in the five energy bins with respect to the simulated incident counts from 23.0%, 33.0%, and 54.0% to 1.2%, 1.8%, and 7.7% for 8.7, 48.8, and 100.0 mm PMMA phantoms, respectively. The accuracy of the effective attenuation coefficient of PMMA estimate was also improved with the proposed spectral distortion correction. Finally, the relative RMS error of water, lipid, and protein decompositions in dual-energy imaging was significantly reduced from 53.4% to 6.8% after correction was applied. Conclusions: The study demonstrated that dramatic distortions in the recorded raw image yielded from a photon-counting detector could be expected, which presents great challenges for applying the quantitative material decomposition method in spectral CT. The proposed semi-empirical correction method can effectively reduce these errors caused by various artifacts, including pulse pileup and charge sharing effects. Furthermore, rather than detector-specific simulation packages, the method requires a relatively simple calibration process and knowledge about the incident spectrum. Therefore, it may be used as a generalized procedure for the spectral distortion correction of different photon-counting detectors in clinical breast CT systems. V C 2012 American Association of Physicists in Medi...

show abstract

An accurate method for direct dual‐energy calibration and decomposition

Cited by 123 publications

References 0 publications

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

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

Quantification of breast density with dual energy mammography: An experimental feasibility study

Image‐based spectral distortion correction for photon‐counting x‐ray detectors

Contact Info

Product

Resources

About