title: Empirical beam hardening correction (EBHC) for CT.
abstract: OBJECTIVE
  Due to x-ray beam polychromaticity and scattered radiation, attenuation measurements tend to be underestimated. Cupping and beam hardening artifacts become apparent in the reconstructed CT images. If only one material such as water, for example, is present, these artifacts can be reduced by precorrecting the rawdata. Higher order beam hardening artifacts, as they result when a mixture of materials such as water and bone, or water and bone and iodine is present, require an iterative beam hardening correction where the image is segmented into different materials and those are forward projected to obtain new rawdata. Typically, the forward projection must correctly model the beam polychromaticity and account for all physical effects, including the energy dependence of the assumed materials in the patient, the detector response, and others. We propose a new algorithm that does not require any knowledge about spectra or attenuation coefficients and that does not need to be calibrated. The proposed method corrects beam hardening in single energy CT data.
  
  
  METHODS
  The only a priori knowledge entering EBHC is the segmentation of the object into different materials. Materials other than water are segmented from the original image, e.g., by using simple thresholding. Then, a (monochromatic) forward projection of these other materials is performed. The measured rawdata and the forward projected material-specific rawdata are monomially combined (e.g., multiplied or squared) and reconstructed to yield a set of correction volumes. These are then linearly combined and added to the original volume. The combination weights are determined to maximize the flatness of the new and corrected volume. EBHC is evaluated using data acquired with a modern cone-beam dual-source spiral CT scanner (Somatom Definition Flash, Siemens Healthcare, Forchheim, Germany), with a modern dual-source micro-CT scanner (Tomo-Scope Synergy Twin, CT Imaging GmbH, Erlangen, Germany), and with a modern C-arm CT scanner (Axiom Artis dTA, Siemens Healthcare, Forchheim, Germany). A large variety of phantom, small animal, and patient data were used to demonstrate the data and system independence of EBHC.
  
  
  RESULTS
  Although no physics apart from the initial segmentation procedure enter the correction process, beam hardening artifacts were significantly reduced by EBHC. The image quality for clinical CT, micro-CT, and C-arm CT was highly improved. Only in the case of C-arm CT, where high scatter levels and calibration errors occur, the relative improvement was smaller.
  
  
  CONCLUSIONS
  The empirical beam hardening correction is an interesting alternative to conventional iterative higher order beam hardening correction algorithms. It does not tend to over- or undercorrect the data. Apart from the segmentation step, EBHC does not require assumptions on the spectra or on the type of material involved. Potentially, it can therefore be applied to any CT image.
authors.affiliation: Institute of Medical Physics, University of Erlangen-Nürnberg, 91052 Erlangen, Germany.
authors.forename: Yiannis
authors.initials: Y
authors.lastname: Kyriakou
authors.forename: Esther
authors.initials: E
authors.lastname: Meyer
authors.forename: Daniel
authors.initials: D
authors.lastname: Prell
authors.forename: Marc
authors.initials: M
authors.lastname: Kachelriess
mesh_terms: D000465:Algorithms; D000818:Animals; D016477:Artifacts; D055592:Biophysical Phenomena; D006801:Humans; D019047:Phantoms, Imaging; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods; D051381:Rats; D012542:Scattering, Radiation; D014057:Tomography, X-Ray Computed / Q000706:statistics & numerical data*; D014965:X-Rays