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Minimum Statistics-Based Noise Power Estimation for Parametric Image Restoration

  • Yoo, Yoonjong (Image Processing and Intelligent Systems Laboratory, Department of Advanced Imaging, Graduate School of Advanced Imaging Science, Multimedia, and Film, Chung-Ang University) ;
  • Shin, Jeongho (Department of Web information Engineering Hankyong University) ;
  • Paik, Joonki (Image Processing and Intelligent Systems Laboratory, Department of Advanced Imaging, Graduate School of Advanced Imaging Science, Multimedia, and Film, Chung-Ang University)
  • Received : 2013.11.20
  • Accepted : 2014.02.12
  • Published : 2014.04.30

Abstract

This paper describes a method to estimate the noise power using the minimum statistics approach, which was originally proposed for audio processing. The proposed minimum statistics-based method separates a noisy image into multiple frequency bands using the three-level discrete wavelet transform. By assuming that the output of the high-pass filter contains both signal detail and noise, the proposed algorithm extracts the region of pure noise from the high frequency band using an appropriate threshold. The region of pure noise, which is free from the signal detail part and the DC component, is well suited for minimum statistics condition, where the noise power can be extracted easily. The proposed algorithm reduces the computational load significantly through the use of a simple processing architecture without iteration with an estimation accuracy greater than 90% for strong noise at 0 to 40dB SNR of the input image. Furthermore, the well restored image can be obtained using the estimated noise power information in parametric image restoration algorithms, such as the classical parametric Wiener or ForWaRD image restoration filters. The experimental results show that the proposed algorithm can estimate the noise power accurately, and is particularly suitable for fast, low-cost image restoration or enhancement applications.

Keywords

References

  1. M. Banhamand A. Katsaggelos, "Digital image restoration,"IEEE Signal Processing Magazine, vol. 14, no. 2, pp. 24-41, Mar. 1997.
  2. S. Chang, Y. Bin, and M. Vetterli,"Adaptive wavelet thresholding for image denoising and compression," IEEE Trans. Image Processing, vol. 9, no. 9, pp.1532-1546, Sep. 2000. https://doi.org/10.1109/83.862633
  3. L.Ce, R. Szeliski, K. Sing, C. Zitnick, and W. Freeman, "Automatic estimation and removal of noise from a single image," IEEE Trans. Pattern Analysis, Machine Intelligence, vol. 30, no. 2, pp. 299-314, Feb. 2008. https://doi.org/10.1109/TPAMI.2007.1176
  4. A. Tekalp, H. Kaufman, and J. Woods, "Identification of image and blur parameters for the restoration of noncausal blurs,"IEEE Trans. Acoustics, Speech, Signal Processing, vol. 34, no. 4, pp. 963-972, Aug. 1986. https://doi.org/10.1109/TASSP.1986.1164886
  5. R. Legendijk, A.Tekalp, and J. Biemond, "Maximum likelihood image and blur identification: a unifying approach,"Optical Engineering, vol. 29, no. 5, pp 422-435, May 1990. https://doi.org/10.1117/12.55611
  6. A. Tekalp and H. Kaufman, "On statistical identification of a class of linear space-invariant blurs using nonminimum-phase arma models," IEEE Trans. Acoustics, Speech, Signal Processing,vol. 38, no. 8, pp. 1360-1363, Aug. 1988.
  7. H. Engl, "Discrepancy principles for Tikhonov regularization of ill-posed problems leading to optimal convergence rates," Journal of Optimization Theory and Applications, vol. 52, no. 2, pp. 209-215, 1987. https://doi.org/10.1007/BF00941281
  8. N. Wayrich, and G. Warhola, "Wavelet shrinkage and generalized cross validation for image denoising," IEEE Trans. Image Processing, vol. 7, no.1, pp. 82-90, Jan. 1998. https://doi.org/10.1109/83.650852
  9. P. Hansen, "Analysis of discrete ill-posed problems by means of the L-curve,"SIAM Review, vol. 34, no. 4, pp. 561-580, 1992. https://doi.org/10.1137/1034115
  10. D. Krawczyk-Stando, and M. Rudnicki, "Regularization parameter selection in discrete illposed problems: the use of the U-curve," International Journal of Applied Mathematic Computer Science, vol. 17, no. 2, pp. 157-164,2007.
  11. S. Kayand S. Marple, "Spectrum analysis-A modern perspective,"IEEE Proceeding, vol. 69, no. 11, pp. 1380-1419,Nov. 1981. https://doi.org/10.1109/PROC.1981.12184
  12. R.Martin, "Noise power spectral density estimation based on optimal smoothing and minimum statistics," IEEE Trans. Speech and Audio Processing, vol. 9, no. 5, pp. 504-512,July 2001. https://doi.org/10.1109/89.928915
  13. R.Neelamani,H. Choi, and R.Baraniuk,"ForWaRD: Fourier-wavelet regularized deconvolution for illconditioned systems,"IEEE Trans. Signal Processing, vol. 52, no. 2, pp. 418-433, Feb. 2004. https://doi.org/10.1109/TSP.2003.821103