Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-28T01:18:03.376Z Has data issue: false hasContentIssue false
  • English
  • Français

Image Denoising via Residual Kurtosis Minimization

Part of: Numerical methods in Fourier analysis Statistics Numerical linear algebra

Published online by Cambridge University Press:  05 August 2015

Tristan A. Hearn  and
Lothar Reichel
Tristan A. Hearn
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA
Lothar Reichel*
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA
*
*Email address: [email protected] (T. A. Hearn) and [email protected] (L. Reichel)
Get access

Abstract

A new algorithm for the removal of additive uncorrelated Gaussian noise from a digital image is presented. The algorithm is based on a data driven methodology for the adaptive thresholding of wavelet coefficients. This methodology is derived from higher order statistics of the residual image, and requires no a priori estimate of the level of noise contamination of an image.

Keywords

Denoisingnoise estimationkurtosis minimizationwavelet shrinkage

MSC classification

Secondary: 65F22: Ill-posedness, regularization 62-07: Data analysis 65T60: Wavelets
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 3 , August 2015 , pp. 406 - 424
Copyright
Copyright © Global-Science Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Boncelet, C., Image Noise Models, In: Handbook of Image and Video Processing, ed. Bovik, A., Academic Press, New York, 2000, pp. 325–337.Google Scholar
[2]Buades, A., Coll, B., and Morel, J. M., Image denosing methods. A new nonlocal principle, Siam Review, 52 (2010), pp. 113–147.CrossRefGoogle Scholar
[3]Chang, S. G., Adaptive wavelet thresholding for image denoising and compression, Ieee Transactions on Image Processing, 9 (2000), pp. 1532–1546.CrossRefGoogle ScholarPubMed
[4]Chan, T. F., Golub, G. H., and Mulet, P., A nonlinear primal-dual method for total variation-based image restoration, Siam Journal on Scientific Computing, 20 (1999), pp. 1964–1977.CrossRefGoogle Scholar
[5]Chan, T., Marquina, A., and Mulet, P., High-order total variation-based image restoration, Siam Journal on Scientific Computing, 22 (2000), pp. 503–516.CrossRefGoogle Scholar
[6]Christopoulos, C., Skodras, A., and Ebrahimi, T., The JPEG2000 still image coding system: an overview, Ieee Transactions on Consumer Electronics, 46 (2000), pp. 1103–1127.CrossRefGoogle Scholar
[7]D’Agostino, R. and Pearson, E. S., Tests for departure from normality. Empirical results for the distributions of b2 and , Biometrika, 60 (1973), pp. 613–622.Google Scholar
[8]D’Agostino, R. and Tietjen, G. L., Simulation probability points of b2 for small samples, Biometrika, 58 (1971), pp. 669–672.Google Scholar
[9]Dobson, D. and Vogel, C., Convergence of an iterative method for total variation denoising, Siam Journal on Numerical Analysis, 34 (1997), pp. 1779–1791.CrossRefGoogle Scholar
[10]Donoho, D. and Johnstone, I. M., Adapting to unknown smoothness via wavelet shrinkage, Journal of the American Statistical Association, 90 (1995), pp. 1200–1224.CrossRefGoogle Scholar
[11]Donoho, D., De-noising by soft-thresholding, Ieee Transactions on Information Theory, 41 (1995), pp. 613–627.CrossRefGoogle Scholar
[12]Hearn, T. A. and Reichel, L., Application of denoising methods to regularization of ill-posed problems, Numerical Algorithms, 66 (2014), pp. 761–777.CrossRefGoogle Scholar
[13]Hyvärinen, A., Independent Component Analysis, Adaptive and Learning Systems for Signal Processing, Wiley-Blackwell, 2001.Google ScholarPubMed
[14]Mallat, S., A Wavelet Tour of Signal Processing, 3rd ed., Elsevier, Amsterdam, 2009.Google Scholar
[15]Moisan, L., How to discretize the total variation of an image?, Proceedings in Applied Mathematics and Mechanics, 7 (2007), pp. 1041907–1041908.CrossRefGoogle Scholar
[16]Motwani, M. C., Gadiya, M. C., Motwani, R. C., and Harris, F. C. Jr., Survey of image denoising techniques, Proceedings of the Global Signal Processing Exposition and Conference, 2004.Google Scholar
[17]Pearson, E. S., Tables for percentage points of and b2 in normal samples: a rounding off, Biometrika, 52 (1965), pp. 282–287.Google ScholarPubMed
[18]Rudin, L., Osher, S., and Fatemi, E., Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), pp. 259–268.CrossRefGoogle Scholar