Empirical dual energy calibration (EDEC) for cone-beam computed tomography

Material-selective imaging using dual energy CT (DECT) relies heavily on well-calibrated material decomposition functions. These require the precise knowledge of the detected x-ray spectra, and even if they are exactly known the reliability of DECT will suffer from scattered radiation. We propose an empirical method to determine the proper decomposition function. In contrast to other decomposition algorithms our empirical dual energy calibration (EDEC) technique requires neither knowledge of the spectra nor of the attenuation coefficients. The desired material-selective raw data p1 and p2 are obtained as functions of the measured attenuation data q1 and q2 (one DECT scan = two raw data sets) by passing them through a polynomial function. The polynomial's coefficients are determined using a general least squares fit based on thresholded images of a calibration phantom. The calibration phantom's dimension should be of the same order of magnitude as the test object, but other than that no assumptions on its exact size or positioning are made. Once the decomposition coefficients are determined DECT raw data can be decomposed by simply passing them through the polynomial. To demonstrate EDEC simulations of an oval CTDI phantom, a lung phantom, a thorax phantom and a mouse phantom were carried out. The method was further verified by measuring a physical mouse phantom, a half-and-half-cylinder phantom and a Yin-Yang phantom with a dedicated in vivo dual source micro-CT scanner. The raw data were decomposed into their components, reconstructed, and the pixel values obtained were compared to the theoretical values. The determination of the calibration coefficients with EDEC is very robust and depends only slightly on the type of calibration phantom used. The images of the test phantoms (simulations and measurements) show a nearly perfect agreement with the theoretical micro values and density values. Since EDEC is an empirical technique it inherently compensates for scatter components. The empirical dual energy calibration technique is a pragmatic, simple, and reliable calibration approach that produces highly quantitative DECT images.