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Image representation by blob and its application in CT reconstruction from few projections

Han Wang, Laurent Desbat, Samuel Legoupil
Thales TED-XRIS, Moirans, France
arXiv:1107.5087v1 [cs.NA] (25 Jul 2011)

@article{2011arXiv1107.5087W,

   author={Wang}, H. and {Desbat}, L. and {Legoupil}, S.},

   title={"{Image representation by blob and its application in CT reconstruction from few projections}"},

   journal={ArXiv e-prints},

   archivePrefix={"arXiv"},

   eprint={1107.5087},

   primaryClass={"cs.NA"},

   keywords={Computer Science – Numerical Analysis, 65T60, 65F10, 94A20},

   year={2011},

   month={jul},

   adsurl={http://adsabs.harvard.edu/abs/2011arXiv1107.5087W},

   adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

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The localized radial symmetric function, or blob, is an ideal alternative to the pixel basis for X-ray computed tomography (CT) image reconstruction. In this paper we develop image representation models using blob, and propose reconstruction methods for few projections data. The image is represented in a shift invariant space generated by a Gaussian blob or a multiscale blob system of different frequency selectivity, and the reconstruction is done through minimizing the Total Variation or the 1 norm of blob coefficients. Some 2D numerical results are presented, where we use GPU platform for accelerating the X-ray projection and back-projection, the interpolation and the gradient computations.
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