Abstract
A new system—Monoscale Dual Ridgelet Frame (MDRF) is constructed in this paper, which can be viewed as a generalized version of Monoscale Ridgelet introduced by Candes. The MDRT takes the Dual Ridgelet Frame as its basic component. We show that localizing the Dual Ridgelet Frame into small squares, dyadic partition of [0, 1]2, constitutes a dual frame in L 2[0,1]2 again. As an example, the high performance of the MDRF for image denoising is demonstrated experimentally.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Candès, E.J.: Harmonic Analysis of Neural Netwoks. Appl. Comput. Harmon. Anal. 6, 197–218 (1999)
Candès, E.J.: On the Representation of Mutilated Sobolev Functions. SIAM J. Math. Anal. 1, 2495–2509 (1999)
Donoho, L.: Orthonormal Ridgelet and Straight Singularities. SIAM J. Math Anal. 31, 1062–1099 (2000)
Flesia, G., Hel-Or, H., Averbuch, A., Candès, E.J., Coifman, R.R., Donoho, D.L.: Digital Implementation of Ridgelet Packets. In: Stoeckler, J., Welland, G.V. (eds.) Beyond Wavelets, pp. 31–60. Academic Press, London (2003)
Shan, T., Jiao, L.C., Feng, X.C.: Ridgelet Frame. In: Proceedings of. Int. Conf. Image Analysis and Recognition. In: Campilho, A., Kamel, M. (eds.) ICIAR 2004. LNCS, vol. 3211, pp. 479–486. Springer, Heidelberg (2004)
Shan, T., Zhang, X.R., Jiao, L.C.: Dual Ridgelet Frame Constructed Using Biorthonormal Wavelet Basis. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal, Philadelphia, PA, USA (March 2005) (To appear)
Candès, E.J.: Monoscale Ridgelet for the Representation of Images with Edges. Dept. Statist., Stanford Univ., Stanford, CA, Tech. Rep. (1999)
Deans, S.R.: The Radon Transform and Some of Its Applications. Wiley, New York (1983)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Shan, T., Jiao, L. (2005). Monoscale Dual Ridgelet Frame. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2005. Lecture Notes in Computer Science, vol 3656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11559573_33
Download citation
DOI: https://doi.org/10.1007/11559573_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29069-8
Online ISBN: 978-3-540-31938-2
eBook Packages: Computer ScienceComputer Science (R0)