Empirical cupping correction for CT scanners with tube voltage modulation (ECCU)

X-ray CT measures the attenuation of polychromatic x-rays through an object of interest. The CT data aquired are the negative logarithm of the relative x- ray intensity behind the patient. These data must undergo water precorrection to linearize the measured data and convert them into line integrals through the patient that can be reconstructed to yield the final CT image. The function to linearize the measured projection data depends on the tube voltage U. In most circumstances, CT scans are carried out with a constant tube voltage. For those cases there are dozens of different techniques to carry out water precor-rection. In our case the tube voltage is rather modulated as a function of the object. We propose an empirical cupping correction (ECCU) algorithm to correct for CT cupping artifacts that are induced by non-linearities in the projection data. The method is rawdata-based, empirical and does neither require knowledge of the x-ray spectrum nor of the attenuation coefficients. It aims at linearizing the attenuation data using a precorrection function of polynomial form in the polychromatic attenuation data q and in the tube voltage U. The coefficients of the polynomial are determined once using a calibration scan of a homogeneous phantom. Computing the coefficients is done in image domain by fitting a series of basis images to a template image. The template image is obtained directly from the uncorrected phantom image and no assumptions on the phantom size or of its positioning are made. Rawdata are precorrected by passing them through the once-determined polynomial. Numerical examples are shown to demonstrate the quality of the precorrection. ECCU achieves to remove the cupping artifacts and to obtain well-calibrated CT-values. A combination of ECCU with analytical techniques yielding a hybrid cupping correction method is possible and allows for channel-dependent correction functions.