A new approach for beam hardening correction based on the local spectrum distributions

Abstract Energy dependence of material absorption and polychromatic nature of x-ray beams in the Computed Tomography (CT) causes a phenomenon which called “beam hardening”. The purpose of this study is to provide a novel approach for Beam Hardening (BH) correction. This approach is based on the linear attenuation coefficients of Local Spectrum Distributions (LSDs) in the various depths of a phantom. The proposed method includes two steps. Firstly, the hardened spectra in various depths of the phantom (or LSDs) are estimated based on the Expectation Maximization (EM) algorithm for arbitrary thickness interval of known materials in the phantom. The performance of LSD estimation technique is evaluated by applying random Gaussian noise to transmission data. Then, the linear attenuation coefficients with regarding to the mean energy of LSDs are obtained. Secondly, a correction function based on the calculated attenuation coefficients is derived in order to correct polychromatic raw data. Since a correction function has been used for the conversion of the polychromatic data to the monochromatic data, the effect of BH in proposed reconstruction must be reduced in comparison with polychromatic reconstruction. The proposed approach has been assessed in the phantoms which involve less than two materials, but the correction function has been extended for using in the constructed phantoms with more than two materials. The relative mean energy difference in the LSDs estimations based on the noise-free transmission data was less than 1.5%. Also, it shows an acceptable value when a random Gaussian noise is applied to the transmission data. The amount of cupping artifact in the proposed reconstruction method has been effectively reduced and proposed reconstruction profile is uniform more than polychromatic reconstruction profile.