Sketch describing the projection of an object f(x, y) containing a circular metal insert by a single ray at a projection angle θ. The lengths intersected by the ray with the object and the metal insert are L(t,θ) and l(t,θ), respectively.

Illustration of the metal artifact reduction algorithm based on the thickness and background normalizations. 1) Generation of a sinogram from the CT scan. 2) Image reconstruction using the sinogram 1). Generation of sinograms 3) and 3') by forward-projecting the uncorrected image after replacing its internal components by air and redefining the internal components, except the metal insert, by the segmentation procedure, respectively. 4) Extraction of metal traces from the original sinogram. Generation of normalized sinograms 5) and 5') dividing 1) by 3) and 3'), respectively. Interpolated sinograms 6) and 6') by applying the linear interpolation to 5) and 5'), respectively, with the known metal traces. Generation of corrected sinograms 7) and 7') by multiplying 6) and 6') by 3) and 3'), respectively (the denormalization procedure). Generation of corrected images 8) and 8').

(a) Simple circular numerical phantom consisting of water (μ_water), bone (μ_bone) and gold (μ_Au). Radii of each material r_j, where j=water, bone, and Au, are 200, 100 and 20 mm, respectively. The center of gold material is located at t₀=120 mm. (b) Comparison of normalized sinograms obtained at θ=0^o. Symbols describe the simulation results, whereas solid lines describe theoretical calculations.

(a) Interpolated sinograms with various functions which include simple linear function, 2nd-, 3rd-, and 4th-order Lagrange functions, and cubic spline. For comparison, the thickness- and background-normalized sinograms with linear interpolation are also plotted. (b) Sinograms denormalized from the thickness and background normalizations. For comparison, the original sinogram with linear interpolation is also plotted. All the profiles are extracted from sinograms obtained at θ=263^o at which the effect of interpolation can be well addressed.

Restored images by using various interpolation methods for (a) an original image: (b) linear interpolation, (c) 2nd-order Lagrange interpolation, (d) 3rd-order Lagrange interpolation, (e) 4th-order Lagrange interpolation, (f) cubic spline interpolation, (g) linear interpolation in the thickness-normalized sinogram, and (h) linear interpolation in the background-normalized sinogram.

Column (a) shows the reconstructed images with metal objects having various sizes. Column (b) and (c) shows the restored images using the thickness and background normalization methods, respectively. Column (d) shows the restored images using the background normalization method without the segmentation procedure. The insets are the profiles extracted from sinograms obtained at θ=30^o.

Column (a) shows the reconstructed images with various numbers of metal objects. Column (b) and (c) shows the restored images using the thickness and background normalization methods, respectively. Column (d) shows the restored images using the background normalization method without the segmentation procedure. The insets are the profiles extracted from sinograms obtained at θ=30^o.