Interpolation
For
Lei Zhu, Angel
Pineda, Rebecca Fahrig
Interpolation methods are
commonly used in x-ray CT systems. Within the framework of filtered-backprojection based cone beam CT reconstruction, both
heuristic mathematical derivation and practical experiments reveal that 1D
horizontal (the direction of ramp-filtering) interpolation performs much better
than 1D vertical interpolation for CT scans on human torsos. This fact stems
from the Fourier domain asymmetry of the projection data and the high-freqency error amplification due to ramp-filtering. To
minimize the error in the final reconstructed image, more estimation weight
should be put in the interpolation direction which generates less error. A 2D
interpolation method with an anisotropic kernel is proposed thereby. For the
ease of implementation, an equivalent conventional isotropic 2D interpolation
with pre and post processing is applied instead. It stretches the data in the
vertical direction by a factor of alpha before the conventional 2D
interpolation to reduce its contribution in the missing data estimation, and
squeezes it back thereafter. This algorithm is evaluated by two practical
applications: bad detector region estimation and metallic artifact reduction.
The results show that the modified 2D interpolation method reduces the mean
square error of the reconstructed image by ~30% as compared to the conventional
2D interpolation method, and the residual artifacts by this method are less
evident also because sharp edges are suppressed effectively. In the case that
the original signal characteristics is unknown and the optimal alpha is hard to
estimate, 1D horizontal interpolation can be used as an effective alternative
with only a little loss of image quality.