Beam Hardening Correction Using Cone Beam Consistency Conditions

Abstract

The polychromatic X-ray spectrum and the energy-dependent attenuation coefficient of materials cause beam hardening artifacts in CT reconstructed volumes. These artifacts appear as cupping and streak artifacts depending on the material composition and the geometry of the imaged object. CT scanners employ projection linearization to transform polychromatic attenuation to monochromatic attenuation using a polynomial model. Polynomial coefficients are computed during calibration or using prior information such as X-ray spectrum and attenuation properties of the materials. In this paper, we are presenting a novel method to correct beam hardening artifacts by enforcing cone beam consistency conditions on the projection data. We used consistency conditions derived from Grangeat's fundamental relation between cone beam projection data and 3-D Radon transform. The optimal polynomial coefficients for artifact reduction are iteratively estimated by minimizing the inconsistency of a set of projection pairs. The results from simulated and real datasets show the visible reduction of artifacts. Our studies also demonstrate the robustness of the algorithm when the projections are perturbed with other physical measurement and geometrical errors. The proposed method requires neither calibration nor prior information like X-ray spectrum, attenuation properties of the materials and detector response. The algorithm can be used for beam hardening correction in clinical, pre-clinical, and industrial CT systems.

Calibration‐free beam hardening reduction in x‐ray CBCT using the epipolar consistency condition and physical constraints

“…Future work should incorporate those effects into the model. As we could only compare our algorithm to one other calibration-free method, another important future work is a comparison to other methods such as the ones by Krumm et al 7 , Van Gompel et al 8 , Abdurahman et al 20 or Tang et al 13…”

“…From a physical point of view the choice of such a scale can be interpreted as choosing the effective energy of the monochromatic image. In reference 20 Abdurahman et al proposed to solve this by adding an additional constraint fixing the area under the estimated polynomials:…”

“…Alternatively the data can be rebinned into a virtual plane to evaluate a fan-beam consistency condition (FBCC). 17 Recently both approaches have been shown to be related by Lesaint et al 18 and an efficient implementation of the FBCC was presented by Aichert et al 19 The GCC was used by Abdurahman et al 20 to optimize parameters of a multimaterial model consisting of coupled univariate polynomials with a gradient descent algorithm.…”

Calibration‐free beam hardening correction for myocardial perfusion imaging using CT

“…While detailed knowledge of the CT system leads to suitable BH correction, this requires scanner‐specific knowledge and raw data. One can correct for BH artifact using knowledge of the x‐ray spectrum or, in the absence of a known spectrum, using Poisson noise to estimate material attenuation properties or using projection consistency . However, when raw data are unavailable, as in many cases, image‐based approaches are needed.…”

Maximum Likelihood Estimation of Head Motion Using Epipolar Consistency

“…Beam hardening can be corrected by projection linearization using a polynomial model. The parameters for the model are found by optimizing for Grangeat's consistency [5,6]. Hoffmann et al used Grangeat's consistency to estimate parameters of an additive scatter model [7].…”