Empirical projection-based basis-component decomposition method

Abstract

Advances in the development of semiconductor based, photon-counting x-ray detectors stimulate research in the domain of energy-resolving pre-clinical and clinical computed tomography (CT). For counting detectors acquiring x-ray attenuation in at least three different energy windows, an extended basis component decomposition can be performed in which in addition to the conventional approach of Alvarez and Macovski a third basis component is introduced, e.g., a gadolinium based CT contrast material. After the decomposition of the measured projection data into the basis component projections, conventional filtered-backprojection reconstruction is performed to obtain the basis-component images. In recent work, this basis component decomposition was obtained by maximizing the likelihood-function of the measurements. This procedure is time consuming and often unstable for excessively noisy data or low intrinsic energy resolution of the detector. Therefore, alternative procedures are of interest. Here, we introduce a generalization of the idea of empirical dual-energy processing published by Stenner et al. to multi-energy, photon-counting CT raw data. Instead of working in the image-domain, we use prior spectral knowledge about the acquisition system (tube spectra, bin sensitivities) to parameterize the line-integrals of the basis component decomposition directly in the projection domain. We compare this empirical approach with the maximum-likelihood (ML) approach considering image noise and image bias (artifacts) and see that only moderate noise increase is to be expected for small bias in the empirical approach. Given the drastic reduction of pre-processing time, the empirical approach is considered a viable alternative to the ML approach.

Photon counting spectral CT component analysis of coronary artery atherosclerotic plaque samples

“…These calculations are based on a generalization of an empirical dual energy CT calibration method. 16,17 In short, in dual energy X-ray imaging, a soft-tissue image and a bone image can be easily calculated from a linear combination of a high-energy and a low-energy image. This approach was extended in two ways in order to get material images: first, nonlinear effects were also taken into account by including quadratic terms in the linear combinations and second, the number of energy channels was six instead of two.…”

Quantitative Spectral K-Edge Imaging in Preclinical Photon-Counting X-Ray Computed Tomography

“…The details of the system have been described in a recent publication. Spectral CT data were processed using an empirical material decomposition method first introduced for dual-energy CT, 28 which was recently extended to energysensitive photon counting CT 29 and provided voxel-based iodine concentrations in molar (M) for each vial. A KEVEX PXS10-65 W microfocus x-ray tube with a nominal x-ray focal spot size of approximately 10 μm and a planar, singlerow, 1024-pixel, 3-mm-thick CdTe detector (Gamma Medica-Ideas, Fornebu, Norway) were mounted on a rotating gantry in fan beam geometry.…”

Model-Based Iterative Reconstruction for Dual-Energy X-Ray CT Using a Joint Quadratic Likelihood Model

“…Assuming is conditionally Gaussian with mean and covariance given by (8) and (9), the distribution of is given by (10) where is a normalizing constant, and is the inverse covariance of (11) where (12) (13) With the assumption of measurements at distinct projections being conditionally independent, the distribution of the data given the object information is given by (14) However, this function is still a nonlinear function of because the conditional expectation, , is in general a nonlinear function of the argument . In Section II-C, we will use this result to construct a fully quadratic approximation to the loglikelihood in (14).…”

“…The coefficients of the polynomial approximations can be determined empirically by system calibration. Possible calibration methods include a projection-domain calibration [11], [46], or an imagedomain approach [12]. One may also compute the decomposition through an iterative estimation process [4], [13]- [15].…”