EPFL
 Biomedical Imaging GroupSTI
EPFL
  Publications
English only   BIG > Publications > Multigrid Reconstruction


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

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

Multigrid Image Reconstruction from Arbitrarily Spaced Samples

M. Arigovindan, M. Sühling, P. Hunziker, M. Unser

Proceedings of the 2002 IEEE International Conference on Image Processing (ICIP'02), Rochester NY, USA, September 22-25, 2002, pp. III.381-III.384.



We propose a novel multiresolution-multigrid based signal reconstruction method from arbitrarily spaced samples. The signal is reconstructed on a uniform grid using B-splines basis functions. The computation of spline weights is formulated as a variational problem. Specifically, we minimize a cost that is a weighted sum of two terms: (i) the sum of squared errors at the specified points; (ii) a quadratic functional that penalizes the lack of smoothness. The problem is equivalent to solving a very large system of linear equations, with the dimension equal to the number of grid points. We develop a computationally efficient multiresolution-multigrid scheme for solving the system. We demonstrate the method with image reconstruction from contour points.

Errata

  • p. III-382, the regularization filter is lacking some first-order difference operators Δ. It should read P(z1, z2) = −(hyhx) B3(z1) Δ2(z2) − (hxhy) Δ2(z1) B3(z2).

  • p. III-382, in the final expression of the regularization filter, a term β should be replaced by B. After introduction of the missing first-order difference operators, it should read P(z1, z2) = (hyhx3) B7(z1) B3(z2) Δ4(z2) + (1 ⁄hx hy) Δ2(z1) B5(z1) Δ2(z2) B5(z2) + (hxhy3) B7(z2) B3(z1) Δ4(z1).


@INPROCEEDINGS(http://bigwww.epfl.ch/publications/arigovindan0201.html,
AUTHOR="Arigovindan, M. and S{\"{u}}hling, M. and Hunziker, P. and
        Unser, M.",
TITLE="Multigrid Image Reconstruction from Arbitrarily Spaced
        Samples",
BOOKTITLE="Proceedings of the 2002 {IEEE} International Conference
        on Image Processing ({ICIP'02})",
YEAR="2002",
editor="",
volume="{III}",
series="",
pages="381--384",
address="Rochester NY, USA",
month="September 22-25,",
organization="",
publisher="",
note="")

© 2002 IEEE. 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 IEEE.
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.