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Image Denoising using a Novel Frobenius Norm Filter for a Class of Noises

International Journal of Computer Applications
© 2010 by IJCA Journal
Number 5 - Article 2
Year of Publication: 2010
Sutanshu Saksena Raj
Palak Jain
Divij Babbar

Sutanshu Saksena Raj, Palak Jain and Divij Babbar. Article:Image Denoising using a Novel Frobenius Norm Filter for a Class of Noises. International Journal of Computer Applications 10(5):8–12, November 2010. Published By Foundation of Computer Science. BibTeX

	author = {Sutanshu Saksena Raj and Palak Jain and Divij Babbar},
	title = {Article:Image Denoising using a Novel Frobenius Norm Filter for a Class of Noises},
	journal = {International Journal of Computer Applications},
	year = {2010},
	volume = {10},
	number = {5},
	pages = {8--12},
	month = {November},
	note = {Published By Foundation of Computer Science}


In this paper, we present a novel Frobenius Norm Filter (FNF), which is a spatially selective noise filtration technique in the wavelet subband domain. We address the issue of denoising of images corrupted with additive, multiplicative, and uncorrelated noise. The proposed nonlinear filter is an adaptive order statistic filter functioning on the L^2 space, which modulates itself according to the noise level. We have applied the comparative Frobenius Norm under a given window set and pixel connectivity for removal of noise. We prove the existence of a minimizer, and its convergence, of our specialized filter. We present a comparative study between FNF and certain standard filters, and find that our method is capable of reducing large noise blotches, and is an adequate preprocess to improving the quality of segmentation and facilitating the feature extraction process. We obtained better restoration results, especially when the images were highly corrupted and having a high noise density.


  • D. T. Kuan, et al, Adaptive Noise smoothing filter for Images with signal-dependent Noise, IEEE Trans. on Pattern Anal. And Machine Intell., vol. 7, pp. 165, 1985.
  • E. Kolaczyk, Wavelet shrinkage estimation of certain Poisson intensity signals using corrected thresholds, Statist. Sinica, 9, pp. 119{135, 1999.
  • G. Demoment, “Image reconstruction and restoration: Overview of common estimation structures and problems,” IEEE Trans. Acoustic, Speech, Signal Processing, vol. 37, no. 12, pp. 2024–2036, 1989.
  • I. Daubechies, Ten Lectures on Wavelets, Vol. 61 of Proc. CBMS-NSF Regional Conference Series in Applied Mathematics. Philadelphia, PA:SIAM, 1992.
  • J. S. Lee, Digital Image Enhancement and Noise Filtering by use of Local Statistics, IEEE Trans. on Pattern Anal. and Machine Intell., vol. 2, pp. 165, 1980.
  • Martin Welk, Joachim Weickert, et al, “Median and Related Local Filters for Tensor-Valued Images”, Tensor Signal Processing, 87:291–308, 2007.
  • M. K. Mihcak, et al, "Low-complexity image denoising based on statistical modeling of wavelet coefficients," IEEE Signal Processing Letters, Vol. 6, Dec. 1999.
  • P. Moulin and J. Liu, "Analysis of Multiresolution Image Denoising Schemes Using Generalized Gaussian and Complexity Priors," IEEE Trans. on Information Theory, Vol. 45, No. 3, pp. 909-919, April 1999.
  • P. Besbeas, I. D. Fies and T. Sapatinas, A comparative simulation study of wavelet shrinkage estimators for Poisson counts, Int. Stats Rev., Vol. 72, pp. 209, 2004.
  • R. Chan, C. Ho, and M. Nikolova, “Salt-and-pepper noise removal by median-type noise detectors and edge-preserving regularization,” IEEE Trans. Image Processing, vol. 14, no. 10, pp. 1479–1485, 2005.
  • R.C Gonzalez & R.E Woods, DIPUM Toolbox.
  • R.R. Coifman and D.L. Donoho, “Translation-Invariant Denoising”, Lecture Notes in Statistics, pp. 125–150, Springer Verlag, 1995.
  • S. Mallat, “A theory for multiresolution signal decomposition: The wavelet representation”, IEEE Trans. Pattern Anal. Machine Intell., vol. 11, 1989.
  • ___, “Analysis of Wavelet Family with Frobenius Norm for the Removal of Noise.”, ICALIP ’10, Accepted.
  • T.F Chan and K. Chen, An optimization-based multilevel algorithm for total variation image denoising, SIAM J. Multiscale Modeling and Simulations, 5, pp. 615, 2006.
  • T. Rockafellar, Convex Analysis, volume 224 of Grundlehren der mathematischen Wissenschaften. Princeton University Press, second edition, 1983.
  • Y. Hawwar and A. Reza, “Spatially adaptive multiplicative noise image denoising technique,” IEEE Trans. on Image Processing, vol. 11, pp. 1397, Dec. 2002.