Exact dual energy material decomposition from inconsistent rays (MDIR)
Authors: Maaß Clemens , Meyer Esther , Kachelrieß Marc 
Published: February 2011

Purpose: Dual energy CT (DECT) allows calculating images that show the spatial distribution of the electron density and the atomic number or, more common, images of two basis material densities. In contrast, the Hounsfield unit that is shown in standard CT images is a measure of the x‐ray attenuation, which is a function of the atomic number and electron density. To acquire additional information, DECT measures the object of interest using two different detected x‐ray spectra. Most clinical CT scanners realize dual energy CT by fast tube voltage switching or by dual source dual detector arrangements and therefore do not allow measuring geometrically identical lines with each spectrum. Then, it is not possible to preprocess the raw data and calculate dual energy‐specific raw data sets. The combination of the information of both spectra rather needs to be carried out in image domain after image reconstruction. Compared to the ideal raw data‐based dual energy approaches, those image‐based DECT methods are inferior because they are not able to correctly deal with the polychromatic nature of the x‐rays. This article proposes a dedicated dual energy reconstruction algorithm for inconsistent rays that correctly accounts for all spectral effects.Methods: Material decomposition from inconsistent rays (MDIR) is an iterative method to indirectly perform raw data‐based DECT even though different lines were measured for both spectra. Its iterative nature allows treating the x‐ray polychromaticity correctly. The iterative process is initialized by density images that were obtained from an image‐based material decomposition. Those images suffer from errors that originate from the polychromatic nature of the spectra. These errors are calculated by polychromatic forward projection of each measured line. After correction of the initial material density images, the polychromatic forward projection is repeated with more accurate material density images, yielding a more accurate error calculation. To demonstrate the proposed method, simulations and measurements were performed using clinical and preclinical dual source dual energy CT scanners.Results: Two iterations of MDIR are sufficient to greatly improve the qualitative and quantitative information in material density images. It is shown that banding artifacts, cupping artifacts, and mean density errors can be completely eliminated. Simulations with high geometrical inconsistency between the rays of different spectra indicate that nearly exact material decomposition is possible with MDIR. Furthermore, simulations show that the method works well in the presence of materials with K‐edges within the detected spectrum. Phantom measurements using a clinical dual source CT scanner show the elimination of artifacts, which cause up to 4% mean density error.Conclusions: At moderate computational burden, the proposed MDIR algorithm yields images of the same high quality as direct raw data‐based DECT methods. In contrast to those, MDIR is applicable to the case of inconsistent rays, as it often occurs in clinical or preclinical CT. Compared to image‐based methods MDIR reduces artifacts and improves mean density errors in material density images. All dual energy postprocessing methods that are in use today, such as bone removal, virtual noncontrast images, etc., can be applied to the images provided by MDIR.