EPFL
 Biomedical Imaging GroupSTI
EPFL
  Publications
English only   BIG > Publications > Interior Tomography


 CONTENTS
 Home Page
 News & Events
 People
 Publications
 Tutorials and Reviews
 Research
 Demos
 Download Algorithms

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

Multiscale Interior Tomography Using 1D Generalized Total Variation

M. Lee, J.P. Ward, M. Unser, J.C. Ye

Proceedings of The Third International Conference on Image Formation in x-Ray Computed Tomography, Salt Lake City UT, USA, June 22-25, 2014, pp. 347-350.



We propose a method for accurate and fast reconstruction of the interior of a 2D or 3D tomographic image from its incomplete local Radon transform. Unlike the existing interior tomography work with 2D total variation, the proposed algorithm guarantees exact recovery using a 1D generalized total variation semi-norm for regularization. The restrictions placed on an image by our 1D regularizer are much more relaxed than those imposed by the 2D regularizer in previous works. Furthermore, to further accelerate the algorithm up to a level of clinical use, we propose a multi-resolution reconstruction method by exploiting the Bedrosian theorem for the Hilbert transform. More specifically, as the high frequency part of the image can be quickly recovered using Hilbert transform thanks to the Bedrosian equality, we show that computationally expensive iterative reconstruction can be applied only for the low resolution images in downsampled domain, which significantly reduces the computational burden. We demonstrate the efficacy of the algorithm using circular fan-beam and helical cone-beam data.


@INPROCEEDINGS(http://bigwww.epfl.ch/publications/lee1401.html,
AUTHOR="Lee, M. and Ward, J.P. and Unser, M. and Ye, J.C.",
TITLE="Multiscale Interior Tomography Using {1D} Generalized Total
        Variation",
BOOKTITLE="Proceedings of The Third International Conference on Image
        Formation in {x}-Ray Computed Tomography ({ICIFXRCT'14})",
YEAR="2014",
editor="",
volume="",
series="",
pages="347--350",
address="Salt Lake City UT, USA",
month="June 22-25,",
organization="",
publisher="",
note="")

© 2014 The University of Utah. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from The University of Utah.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.