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Beam hardening is a well-known effect in X-ray CT scanning that is caused by the interaction of a broad polychromatic source spectrum with energy-dependent material attenuation. If the scanned object only consists of a single material, the beam hardening effect can be corrected by sinogram precorrection techniques. However, when multiple materials are present, it becomes much more difficult to fully compensate for this distortion; in general, the beam hardening can contribute to reconstruction artifacts such as cupping and streaking. In this paper, we present a novel model-based iterative reconstruction algorithm that incorporates beam hardening correction (MBIR-BHC). Unlike most correction algorithms, which require knowledge of the X-ray spectrum or mass attenuation functions, the MBIR-BHC algorithm works by simultaneously reconstructing the image and estimating the beam-hardening function. The method is based on the assumption that the object is formed by a combination of two distinct materials that can be separated based on their densities. We formulate a poly-energetic X-ray forward model using a polynomial function of two material projections: one for the low-density material and one for the high. We then develop an alternating minimization algorithm for jointly estimating the reconstructed image, the material segmentation, and the coefficients of the two component polynomial that models the beam-hardening function. With this approach, the spectrum and mass attenuation functions are not needed in advance, and the correction is adapted to the dataset being reconstructed. We examine the performance of the proposed algorithm using both simulated and real datasets. Results indicate that the MBIR-BHC algorithm significantly reduces several reconstruction artifacts without advanced knowledge of the X-ray spectrum and material properties.
Jin et al. (Tue,) studied this question.