CT scanner x‐ray spectrum estimation from transmission measurements

Abstract

Purpose:In diagnostic CT imaging, multiple important applications depend on the knowledge of the x-ray spectrum, including Monte Carlo dose calculations and dual-energy material decomposition analysis. Due to the high photon flux involved, it is difficult to directly measure spectra from the x-ray tube of a CT scanner. One potential method for indirect measurement involves estimating the spectrum from transmission measurements. The expectation maximization ͑EM͒ method is an accurate and robust method to solve this problem. In this article, this method was evaluated in a commercial CT scanner. Methods: Two step-wedges ͑polycarbonate and aluminum͒ were used to produce different attenuation levels. Transmission measurements were performed on the scanner and the measured data from the scanner were exported to an external computer to calculate the spectra. The EM method was applied to solve the equations that represent the attenuation processes of polychromatic x-ray photons. Estimated spectra were compared to the spectra simulated using a software provided by the manufacturer of the scanner. To test the accuracy of the spectra, a verification experiment was performed using a phantom containing different depths of water. The measured transmission data were compared to the transmission values calculated using the estimated spectra. Results: Spectra of 80, 100, 120, and 140 kVp from a dual-source CT scanner were estimated. The estimated and simulated spectra were well matched. The differences of mean energies were less than 1 keV. In the verification experiment, the measured and calculated transmission values were in excellent agreement. Conclusions: Spectrum estimation using transmission data and the EM method is a quantitatively accurate and robust technique to estimate the spectrum of a CT system. This method could benefit studies relying on accurate knowledge of the x-ray spectra from CT scanner.

An Extended Algebraic Reconstruction Technique (E-ART) for Dual Spectral CT

“…To our knowledge, there are several methods to estimate the X-ray spectrum of an X-ray tube [24], [25], [32]. We estimate the X-ray spectra from transmission measurements simply by first solving a linear system and then setting negative values to zeros.…”

A Single Scatter Model for X-ray CT Energy Spectrum Estimation and Polychromatic Reconstruction

“…An X-ray tube produces photons of high flux rate and as a result energy-resolved X-ray detection is difficult when an energy-counting detector is used [7], [10]. Newly developed X-ray photon counting detectors that use CdTe and CdZnTe are able to achieve high energy-resolution [11].…”

“…However the sensitivity of a CT detector at each energy still cannot be determined by the model-based method. The final method is to estimate the X-ray energy spectra of a CT from the X-ray projection image [10], [19]. After acquiring the projection image of a step-wedge phantom, the X-ray energy spectra can be estimated by solving the linear integral equations that represent the attenuation processes of X-ray photons as they pass through different thicknesses of materials in the phantom.…”

Application of an expectation maximization method to the reconstruction of X-ray-tube spectra from transmission data

“…Information about this distribution is recovered by using a series of attenuation measurements in which the spectrum is progressively modified by varying the filtration. A number of different approaches have been proposed for the solution of this problem, including the use of the Laplace transform, least squares methods, singular value decomposition and iterative approaches [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. In this work we focus on the application to experimental data of the expectation-maximization method [14,17] to iteratively solve the ill-conditioned linear system that relates the spectral distribution of the X-ray beam to its transmission.…”