Abstract
A new image-denoising algorithm is proposed, which uses the Generalized Cross Validation technique in the ridgelet frame domain. The proposed algorithm has two advantages: first, it can select the optimal threshold automatically without the knowledge of the noise level; second, it has the ability to well recover the ‘line-type’ structures contained in noisy images. Experimentally, the high performance of the proposed algorithm is demonstrated.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Portilla, J., Strela, V., Wainwright, M.J., Simoncelli, E.P.: Image Denoising Using Scale Mixtures of Gaussians in the Wavelet Domain. IEEE Trans. Image Processing. 12, 1338–1351 (2003)
Donoho, D.L., Johnstone, I.M.: Ideal Spatial Adaptation Via Wavelet Shrinkage. Biometrika 81, 425–455 (1994)
Donoho, D.L., Johnstone, I.M.: Wavelet Shrinkage: Asymptotic Journal of Royal Statistical Society. Series B 57, 301–369 (1995)
Jansen, M., Malfait, M., Bultheel, A.: Generalized Cross Validation for Wavelet Thresholding. Signal Processing. 56, 33–44 (1997)
Norman, W., Gregory, T.W.: Wavelet Shrinkage and Generalized Cross Validation for Image Denoising. IEEE Trans. Image Processing 7, 82–90 (1998)
Weyrich, N., Warhola, G.T.: De-noising Using Wavelets and Cross Validation. In: Singh, S.P. (ed.) Approximation Theory, Wavelets and Applications. NATO ASI Series C: Mathematics and Physical Sciences, vol. 454, pp. 523–532. Kluwer, Dordrecht (1995)
Weyrich, N., Warhola, G.T.: De-noising by Wavelet Shrinkage and Generalized Cross Validation with Applications to Speech. In: Chui, C.K., Schumaker, L.L. (eds.) Wavelets and Multilevel Approximation, Approximation Theory VIII, Singapore, pp. 407–414 (1995)
Candès, E.J.: Harmonic Analysis of Neural Networks. Appl. Comput. Harmon. Anal. 6, 197–218 (1999)
Donoho, D.L.: Orthonormal Ridgelet and Linear Singularities. SIAM J. Math Anal. 31, 1062–1099 (2000)
Tan, S., Jiao, L.C., Feng, X.C.: Ridgelet Frame. In: Campilho, A., Kamel, M. (eds.) ICIAR 2004. LNCS, vol. 3211, pp. 479–486. Springer, Heidelberg (2004)
Tan, S., Jiao, L.C.: Ridgelet Bi-Frame. Appl. Comput. Harmon. Anal. 20, 391–402 (2006)
Jansen, M., Bultheel, A.: Multiple Wavelet Threshold Estimation by Generalized Cross Validation for Data with Correlated Noise. TW Report 250, Leuven, K.U. Department of Computer Science, Leuven, Belgium (1997)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tan, X., He, H. (2007). Image Denoising Based on the Ridgelet Frame Using the Generalized Cross Validation Technique. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2007. Lecture Notes in Computer Science, vol 4633. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74260-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-74260-9_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74258-6
Online ISBN: 978-3-540-74260-9
eBook Packages: Computer ScienceComputer Science (R0)