Calibration free beam hardening correction using grangeat-based consistency measure

Due to polychromatic nature of the X-ray spectrum, beam hardening artifacts are introduced in cone beam computed tomography reconstructed images. To reduce these artifacts, projection images can be linearized with higher order polynomials. Polynomial coefficients are usually computed with calibration scans of homogeneous phantoms. This can be a challenging task when the objects with different material composition and geometry are scanned with different tube voltages. Here, we present a beam hardening correction method based on a consistency condition derived from Grangeat's formula for cone beam projections. First, an objective function is designed to quantify the inconsistency between two arbitrary projections. It is observed that inconsistency due to beam hardening is significantly high. Thus, by minimizing the objective function, polynomial parameters can be computed without prior knowledge about material composition, material thickness, x-ray spectrum or detector response. Since the consistency conditions based on Grangeat's formula can be applied to two arbitrary cone beam projections, the modeling of polynomials is very robust. Our preliminary results show that proposed correction significantly reduces beam hardening artifacts like cupping. For the first time, we show that projection linearization optimized by a consistency measure can be applied to real data from a flat panel detector scanner to reduce the beam hardening artifacts. The proposed method can also be extended for multi-material beam hardening correction by using two or more polynomials or by estimating an effective projection linearization for each view.