BACKGROUND: The beam hardening artifact is one of most important modalities
of metal artifact for polychromatic X-ray computed tomography (CT), which can impair the
image quality seriously.
OBJECTIVE: An iterative approach is proposed to reduce beam hardening
artifact caused by metallic components in polychromatic X-ray CT.
METHODS: According to Lambert-Beer law, the (detected) projections can be
expressed as monotonic nonlinear functions of element geometry projections, which are the
theoretical projections produced only by the pixel intensities (image grayscale) of
certain element (component). With help of a prior knowledge on spectrum distribution of
X-ray beam source and energy-dependent attenuation coefficients, the functions have
explicit expressions. Newton-Raphson algorithm is employed to solve the functions. The
solutions are named as the synthetical geometry projections, which are the nearly linear
weighted sum of element geometry projections with respect to mean of each attenuation
coefficient. In this process, the attenuation coefficients are modified to make
Newton-Raphson iterative functions satisfy the convergence conditions of fixed pointed
iteration(FPI) so that the solutions will approach the true synthetical geometry
projections stably. The underlying images are obtained using the projections by general
reconstruction algorithms such as the filtered back projection (FBP). The image gray
values are adjusted according to the attenuation coefficient means to obtain proper CT
numbers.
RESULTS: Several examples demonstrate the proposed approach is efficient in
reducing beam hardening artifacts and has satisfactory performance in the term of some
general criteria. In a simulation example, the normalized root mean square difference
(NRMSD) can be reduced 17.52% compared to a newest algorithm.
CONCLUSIONS: Since the element geometry projections are free from the effect
of beam hardening, the nearly linear weighted sum of them, the synthetical geometry
projections, are almost free from the effect of beam hardening. By working out the
synthetical geometry projections, the proposed approach becomes quite efficient in
reducing beam hardening artifacts.
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