Noisy Image Decomposition Based On Texture Detecting Function

Full Text (PDF, 1337KB), PP.15-21

Views: 0 Downloads: 0

Author(s)

Ruihua Liu 1,2,* Ruizhi Jia 1 Liyun Su 2

1. School of Mathematics and Statistics, Chongqing University of Technology, Chongqing, China

2. Institute of Automation, Chinese Academy of Sciences, Beijing, China

* Corresponding author.

DOI: https://doi.org/10.5815/ijigsp.2012.03.03

Received: 12 Jan. 2012 / Revised: 8 Feb. 2012 / Accepted: 14 Mar. 2012 / Published: 8 Apr. 2012

Index Terms

Texture detecting function, texture, cartoon, image decomposition

Abstract

At present, most of image decomposition models only apply to some ideal images, such as, noise-free, without blurring and super resolution images, and so on. In this paper, they propose a novel decomposition model based on dual method and texture detecting function for noisy image. Firstly, they prove the existence of minimal solutions of the noisy decomposition model functional. Secondly, they write down an alterative implementation algorithm. Finally, they give some numerical experiments, which show that their model can effectively work for Gaussian noisy image decomposition.

Cite This Paper

Ruihua Liu, Ruizhi Jia, Liyun Su,"Noisy Image Decomposition Based On Texture Detecting Function", IJIGSP, vol.4, no.3, pp.15-21, 2012. DOI: 10.5815/ijigsp.2012.03.03 

Reference

[1]G. Aubert and J. Aujol, A variational approach to remove multi- -plicative noise, SIAM Journal on Applied Mathematics, 2008, 68 (4), pp. 925-946.

[2]J. Aujol, G. Aubert, L. Blanc and A. Chambolle, Image decompo--sition into a bounded variation component and an oscillating component, Journal of Mathematical Imaging and Vision, 2005, 22(1), pp. 71-88. 

[3]X. Bresson, S. Esedoglu, P. Vandergheynst, J. Thiran and S. Osher, Fast global minimization of the active contour/snake model, J. Math. Imag. Vis., 2007, 28(2), pp.151-167.

[4]A. Chambolle and P. Lions, Image recovery via total variational minimization and related problem, Numerical Mathematics, 1997, 76(3), pp. 167-188.

[5]T. Chan and S. Eaedoglu, Aspects of total variation regularized L1 function approximation, SIAM, 2005, 65(5), pp. 1817-1837.

[6]S. Chao and D. Tsai, An improved anisotropic diffusion model for detail and edge-preserving smoothing, Pattern Recognition Letters, 2010, 31(13), pp. 2012-2023. 

[7]G. Gilboa, N. Sochen and Y. Zeevi, Variational denoising of partly textured images by spatially varying constraints, IEEE Transactions on Image Processing, 2006, 15(8), pp. 2281-2289.

[8]K. Krissian, K. Vosburgh, R. Kikins and C. Westin, Anisotropic diffusion of ultrasound constrained by speckle noise model, Tech. report, Harvard Med. School, 2004.

[9]F. Li, C. Shen, C.-L. Shen and G. Zhang, Variational denoising of partly textured images, Journal of Visual Communication and Image Representation, 2009, 20(4), pp. 293-300.

[10]R. Liu, R. Jia and F. Li, Image Variational decomposition based on dual method, ISRN Singal Processing, under reviewing, 2011.

[11]Y. Meyer, Oscillating patterns in image processing and in some nonlinear evolution equations, The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures, University Lectures Series, 22, 2001.

[12]M. Nikolova, A variational approach to remove outliers and impulse noise, Journal of Math. Imaging and Vision, 2004, 20(1-2), pp. 99-120.

[13]L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 1992, 60, pp. 259-268.

[14]L. Vese and S. Osher, Modeling textures with total variation minimization and oscillating patterns in image processing, Journal of Scientific Computing, 2003, 19(1-3), pp. 553-572.

[15]L. Vese and S. Osher, Image denoising and decomposition with total variation minimization and oscillatory functions, Journal of Mathematical Imaging and Vision, 2004, 20(1/2), pp. 7-18.