Modeling of polychromatic attenuation using computed tomography reconstructed images

Abstract

This paper presents a procedure for estimating an accurate model of the CT imaging process including spectral effects. As raw projection data are typically unavailable to the end-user, we adopt a post-processing approach that utilizes the reconstructed images themselves. This approach includes errors from x-ray scatter and the nonidealities of the built-in soft tissue correction into the beam characteristics, which is crucial to beam hardening correction algorithms that are designed to be applied directly to CT reconstructed images. We formulate this approach as a quadratic programming problem and propose two different methods, dimension reduction and regularization, to overcome ill conditioning in the model. For the regularization method we use a statistical procedure, Cross Validation, to select the regularization parameter. We have constructed step-wedge phantoms to estimate the effective beam spectrum of a GE CT-I scanner. Using the derived spectrum, we computed the attenuation ratios for the wedge phantoms and found that the worst case modeling error is less than 3% of the corresponding attenuation ratio. We have also built two test (hybrid) phantoms to evaluate the effective spectrum. Based on these test phantoms, we have shown that the effective beam spectrum provides an accurate model for the CT imaging process. Last, we used a simple beam hardening correction experiment to demonstrate the effectiveness of the estimated beam profile for removing beam hardening artifacts. We hope that this estimation procedure will encourage more independent research on beam hardening corrections and will lead to the development of application-specific beam hardening correction algorithms.

Specimen size and porosity can introduce error into μCT-based tissue mineral density measurements

“…The BHC dependence of the size-related measurement error highlights the critical importance of BHC choice prior to any analysis of ρ m . Moreover, CT image reconstruction and algorithm-based beam hardening correction is an active area of research and a variety of studies have reported methodological variations [70, 77–89]. Given our results, it is recommended that performance of various mathematical beam-hardening corrections in the use of μCT be further investigated.…”

Heterogeneous meshing and biomechanical modeling of human spine

“…It is known that boneapparent density is closely related to the bone mechanical properties [33]. For this work, we intend to develop a clinical system based on the algorithms developed by Yan et al [34,35]. This will allow us to extract precise bone density measurement from CT slices, which can then be translated to bone mechanical properties.…”

A robust method of x-ray source spectrum estimation from transmission measurements: Demonstrated on computer simulated, scatter-free transmission data

“…The stability improves slightly, but does not approach the eigenvalue curve for the ͕water, iron͖ set, which has the same number of data points M. Interestingly, including more materials does actually improve the system matrix stability. As pointed out by Yan et al, 9 the stability of the spectrum determination problem should not improve much for more than two materials because there are only two main mechanisms, having their own characteristic energy dependence, for x-ray attenuation in the 100-keV energy range. Indeed, we found that stability did not improve when we used more than two materials, when we employed an idealized model for x-ray attenuation where the attenuation splits cleanly into photoelectric and Compton components with similar energy dependence for all materials.…”

“…[4][5][6][7][8][9] The same strategy has also been applied to x-ray spectrum estimation for medical linear accelerators for therapeutic beams. 8,[10][11][12][13][14][15] The problem of reconstructing x-ray spectra from transmission data can be formulated as a linear integral equation.…”