Biomedical Imaging GroupSTI
English only   BIG > Publications > Multiresolution B-Splines

 Home Page
 News & Events
 Tutorials and Reviews
 Download Algorithms

 All BibTeX References

Solving Continuous-Domain Problems Exactly with Multiresolution B-Splines

T. Debarre, J. Fageot, H. Gupta, M. Unser

Proceedings of the Forty-Fourth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'19), Brighton, United Kingdom, May 12-17, 2019, pp. 5122-5126.

We propose a discretization method for continuous-domain linear inverse problems with multiple-order total-variation (TV) regularization. It is based on a recent result that proves that such inverse problems have sparse polynomial-spline solutions. Our method consists in restricting the search space to splines with knots on a uniform grid, which results in a standard convex finite-dimensional problem. As basis functions for this search space, we use the B-splines matched to the regularization order, which are optimally localized. This leads to a well-conditioned, computationally feasible optimization task. Our proposed iterative multiresolution algorithm then refines the grid size until a desired level of accuracy is met and converges to sparse solutions of our inverse problem. Finally, we present experimental results that validate our approach.

AUTHOR="Debarre, T. and Fageot, J. and Gupta, H. and Unser, M.",
TITLE="Solving Continuous-Domain Problems Exactly with Multiresolution
BOOKTITLE="Proceedings of the Forty-Fourth IEEE International Conference
        on Acoustics, Speech, and Signal Processing ({ICASSP'19})",
address="Brighton, United Kingdom",
month="May 12-17,",

© 2019 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.