Iterative Regularization and Nonlinear Inverse Scale Space in Curvelet-type Decomposition Spaces

LI Min; XU Chen; SUN Xiaoli

Article Contents

Article Navigation > Chinese Journal of Electronics > 2013 > 22(4): 702-706

LI Min, XU Chen, SUN Xiaoli, “Iterative Regularization and Nonlinear Inverse Scale Space in Curvelet-type Decomposition Spaces,” Chinese Journal of Electronics, vol. 22, no. 4, pp. 702-706, 2013,

Citation:

LI Min, XU Chen, SUN Xiaoli, “Iterative Regularization and Nonlinear Inverse Scale Space in Curvelet-type Decomposition Spaces,” Chinese Journal of Electronics, vol. 22, no. 4, pp. 702-706, 2013,

LI Min, XU Chen, SUN Xiaoli, “Iterative Regularization and Nonlinear Inverse Scale Space in Curvelet-type Decomposition Spaces,” Chinese Journal of Electronics, vol. 22, no. 4, pp. 702-706, 2013,

Citation:

PDF( 305 KB)

Iterative Regularization and Nonlinear Inverse Scale Space in Curvelet-type Decomposition Spaces

College of Mathematics and Computational Science, Shenzhen University, Shenzhen 518060, China

Funds: This work is supported by the National Natural Science Foundation of China (No.11101292, No.61070087, No.61001183).

More Information

Corresponding author: LI Min, XU Chen, SUN Xiaoli
Received Date: 2012-11-01
Rev Recd Date: 2013-04-01
Publish Date: 2013-09-25

Abstract

Abstract

In this paper we generalize the iterative regularization method and the inverse scale space method, recently developed for wavelet-based image restoration, to curvelet-type decomposition spaces setting. We obtain the result that minimzer of the new model can be derived as curvelet firm shrinkage with curvelet-type weight, which is dynamically changing in the iteration(CDS-IRM). And we obtain a new class of nonlinear inverse scale spaces flow which is dependent on Curvelet-type decomposition scale and smooth order(CDS-ISS). Numerical experiments indicate that the proposed methods are very efficient for denoising.
- Denoising,
- Iterative regularization,
- Inverse scale space,
- Curvelet-type decomposition,
- Shrinkage

FullText(HTML)

References(18)

References

G. Aubert and L. Vese, “A variational method in image recovery”,S IAM J. Numer. Anal., Vol.34, pp.1948-1979, 1997.

T. Chan, S. Esedoglu, F. Park and A. Yip, “Recent developmentsi n total variation image restoration”, UCLA-CAMReport0 5-01, Los Angeles, CA, USA, 2005.

D. Donoho, “Denoising by soft thresholding”, IEEE. Trans. Inform.T heory, Vol.41, No.3, pp.613-627, 1995.

Patrickl. Combettes and Jean-Christophe Pesquet, “Waveletconstrainedi mage restoration”, International Journal of Wavelets, Multiresolution and Information Processing, Vol.2,N o.4, pp.371-389, 2004.

Ashish Khare and Uma Shanker Tiwary, “Soft-thresholding ford enoising of medical images-A Multiresolution Approach”, InternationalJ ournal of Wavelets, Multiresolution and Information Processing, Vol.3, No.4, 2005.

M. Li, X.C. Feng, “Iterative regularization and nonlinear inverses cale space based on translation invariant wavelet shrinkage”,I nternational Journal of Wavelets, Multiresolution and Information Processing, Vol.6, No.1, pp.83-95, 2008.

Liu Guojun, Feng Xiangchu, “Curvelet-based iterative regularization and inverse scale space methods”, Chinese Journal ofE lectronics, Vol.19, No.3, pp.548-552, 2010.

Lasse Borup and Morten Nielsen, “Frame decomposition of decompositions paces”, Journal of Fourier Analysis and Applications,Vol.13, No.1, pp.39-70, 2007.

L.Rudin, S. Osher and E. Fatemi, “Nolinear total variationb ased noise removal algorithms”, Phys. D, Vol.60, PP.259-268,1 992.

S. Osher, M. Burger, D. Goldfarb, J. Xu and W. Yin, “An iterativer egularization method for total variation based imager estoration”, Multiscale Model. and Simul., Vol.4, pp.460-489,2 005.

M. Burger, S. Osher, J. Xu, and G. Gilboa, “Nonlinear inverses cale space methods for image restoration”, Lecture Notes in Computer Science, Vol.3752, pp.25-36, 2005.

M. Burger, G. Gilboa, S. Osher and J. Xu, “Nonlinear inverses cale space methods”, Comm. Math. Sci., Vol.4, No.1, pp.175-2 08, 2006.

M. Nikolova, “Local strong homogeneity of a regularized estimator”,SIAM Journal on Applied Mathematics, Vol.61, No.2,p p.633-658, 2000.

Jinjun Xu and Stanley Osher, “Iterative regularization and nonlineari nverse scale space applied to wavelet based denoising”,I EEE Trans. Image Proc., Vol.16, No.2, pp.534-544, 2007.

Jinjun Xu, “Iterative regularization and nonlinear inverse scales pace methods in image restoration”, Ph.D. Thesis, UCLACAM-R eport 06-33, Los Angeles, CA, USA, 2006.

Youwei Wen, Raymond H. Chan, Andy M. Yip, “A primal-dualm ethod of total-variation based wavelet domain inpainting”,I EEE Trans. Image Proc., Vol.21, No.1, pp.106-113, 2012.

Pooran Singh Negi and Demetrio Labate, “3-D discrete shearlett ransform and video processing”, IEEE Trans. Image Proc.,Vol.21, No.6, pp.2944-2954, 2012.

M. Li, X.C. Feng, “Wavelet shrinkage and a new class of variationalm odels based on Besov spaces and negative Hilbert-S obolev spaces”, Chinese Journal of Electronics, Vol.16, No.2,p p.276-280, 2007.

Relative Articles

Supplements(0)

Cited By

Proportional views