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


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

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

Reconstruction of Biomedical Images and Sparse Stochastic Modeling

E. Bostan, U. Kamilov, M. Unser

Proceedings of the Ninth IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI'12), Barcelona, Kingdom of Spain, May 2-5, 2012, pp. 880-883.



We propose a novel statistical formulation of the image-reconstruction problem from noisy linear measurements. We derive an extended family of MAP estimators based on the theory of continuous-domain sparse stochastic processes. We highlight the crucial roles of the whitening operator and of the Lévy exponent of the innovations which controls the sparsity of the model. While our family of estimators includes the traditional methods of Tikhonov and total-variation (TV) regularization as particular cases, it opens the door to a much broader class of potential functions (associated with infinitely divisible priors) that are inherently sparse and typically nonconvex. We also provide an algorithmic scheme—naturally suggested by our framework—that can handle arbitrary potential functions. Further, we consider the reconstruction of simulated MRI data and illustrate that the designed estimators can bring significant improvement in reconstruction performance.


@INPROCEEDINGS(http://bigwww.epfl.ch/publications/bostan1201.html,
AUTHOR="Bostan, E. and Kamilov, U. and Unser, M.",
TITLE="Reconstruction of Biomedical Images and Sparse Stochastic
        Modeling",
BOOKTITLE="Proceedings of the Ninth {IEEE} International Symposium on
        Biomedical Imaging: {F}rom Nano to Macro ({ISBI'12})",
YEAR="2012",
editor="",
volume="",
series="",
pages="880--883",
address="Barcelona, Kingdom of Spain",
month="May 2-5,",
organization="",
publisher="",
note="")

© 2012 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.