СИСТЕМЫ АНАЛИЗА И ОБРАБОТКИ ДАННЫХ

The algorithms based on the decomposition of a noisy image in an orthogonal basis of wavelet functions have been widely used to filter images (especially contrasting ones) over the past four decades. In this case, most wavelet filtering algorithms are of a threshold nature, namely: the decomposition coefficient smaller in an absolute value of a certain threshold value is reset to zero; otherwise the coefficient undergoes some (most often nonlinear) transformation. A certain (and very significant) drawback of threshold algorithms is that all coefficients of a certain decomposition level are processed with one identical threshold value (i.e., a constant value for all de-composition coefficients). This does not allow taking into account the “individual energy” of each decomposition coefficient for its more optimal processing. Therefore, we propose its own filtering factor for each coefficient, built on the basis of the optimal Wiener filtering and where a filtering parameter is introduced to compensate for incomplete a priori information on the value of the processed decomposition coefficients. In order to select a filtering parameter, a statistical approach has been proposed that makes it possible to estimate the optimal value of this parameter with acceptable accuracy. The performed computational experiment has shown the developed algorithm effectiveness for wavelet filtering of images.

1. Chui C.K. An introduction to wavelets. New York, London, Academic Press, 2001. 213 p.

2. Daubechies I. Ten Lectures on Wavelets. Philadelphia, Pa., Society for Industrial and Applied Mathematics, 1992. 357 p.

3. Gao R.X., Yan R. Wavelets: theory and applications for manufacturing. Springer, 2011. 243 p. DOI: 10.1007/978-1-4419-1545-0.

4. Voskoboinikov Yu.E. Wavelet filtering algorithms with examples in the MathCAD package. Palmarium Academic Publishing, 2016. 196 p. (In Russian).

5. Baleanu D. Advances in wavelet theory and their applications in engineering, physics and technology. InTech, 2012. 326 p.

6. Om H., Biswas M. An improved image denoising method based on wavelet thresholding. Journal of Signal and Information Processing, 2012, vol. 3, no. 1, pp. 109–116.

7. Voskoboinikov Yu.Е., Gochakov A.V. Estimation of optimal threshold values in algorithms of wavelet filtration of images. Optoelectronics, Instrumentation and Data Processing, 2011, vol. 47, no. 2, pp. 105–113.

8. Debalina J. Kaushik S. Wavelet thresholding for image noise removal. International Journal on Recent and Innovation Trends in Computing and Communication, 2014, vol. 2, no. 6, pp. 1400–1405.

9. Voskoboinikov Y.Е., Gochakov A.V. Quasi-optimal algorithm of estimating the coefficients of wavelet expansions during signal filtration. Optoelectronics, Instrumentation and Data Processing, 2010, vol. 46, no. 1. Pp. 27–36. DOI: 10/3103/S8756699010010048.

10. Chen G.Y., Bui T.D. Multiwavelet denoising using neighbouring coefficients. IEEE Signal Processing Letters, 2003, vol. 10, no. 7, pp. 211–214.

11. Krishna G.C., Nagarjuna R., Dhanaraj C. An adaptive wavelet thresholding image denoising method using neighboring wavelet coefficients. International Journal of Innovation Research in Engineering and Science, 2013, vol. 9, no. 2, pp. 46–59.

12. Rao B.C., Latha M.D. Selective neighbouring wavelet coefficients approach for image denoising. International Journal of Computer Science and Communication, 2011, vol. 2, no. 1, pp. 73–77.

13. Kumar R., Saini B.S. Improved image denoising technique using neighboring wavelet coefficients of optimal wavelet with adaptive thresholding. International journal of computer theory and engineering, 2012, vol. 4, no. 3, pp. 395–400. DOI: 10.7763/IJCTE.2012.V4.491.

14. Voskoboinikov Y.E. Estimation of optimal parameters of the multiplicative algorithm of wavelet filtering of images. Optoelectronics, Instrumentation and Data Processing, 2017, vol. 53, no. 4, pp. 402–407. DOI: 10/3103/S8756699017040136.

15. Mallat S. Multiresolution approximation and wavelet orthonormal bases of L²(R). Transactions of the American Mathematical Society, 1989, vol. 315, no. 1, pp. 69–87. DOI: 10.2307/2001373.

16. Mallat S. А theory of multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1989, vol. 11, no. 7, pp. 674–693. DOI:10.1109/34.192463.