2 boyutlu sıfıra çeken LMS algoritmasıyla görüntü iyileştirme

Öz

Bu yazıda, iki boyutlu en küçük kare algoritmasının (2D-LMS) maliyet fonksiyonuna seyrekliği farkeden l₁-norm ceza terimi yükleyen yeni bir 2D sıfıra çeken en küçük ortalama kare (ZALMS) uyarlamalı filtreyi önermekteyiz. 2D-LMS ve BM3D algoritmaları ile karşılaştırmalar hem seyrek hem de seyrek olmayan görüntülerde yürütülmüştür. Simülasyon sonuçları, önerilen algoritmanın hem yatay hem de dikey doğrultuda filtre katsayılarının güncellenmesinde iyi yeteneklere sahip olduğunu göstermiştir ve performansı düşük hesaplama zamanına sahip 2D-LMS algoritması ile aynı/daha iyidir. Ancak 2D-ZALMS, BM3D algoritmasından daha iyi performans göstermektedir.

Anahtar Kelimeler

• LMS,Görüntü iyileştirme,Seyrek sinyaller

Image denoising with two-dimensional zero attracting LMS algorithm

Abstract

In this paper, we propose a new two-dimensional (2D) zero-attracting least-mean-square (ZALMS) adaptive filter by imposing a sparsity aware l₁-norm penalty term into the cost function of the 2D-LMS algorithm. Comparisons with 2D-LMS and BM3D algorithms were conducted both on sparse and non-sparse images. The carried-out simulations show that the proposed algorithm has good capabilities in updating the filter coefficients along both horizontal and vertical directions, and its performance is similar with the 2D-LMS algorithm with lower computation time. But 2D-ZALMS performs better than BM3D algorithm.

Keywords

• LMS,Image restoration,Sparse signals

References

1. Widrow B, Hoff M.E. “Associative storage and retrieval of digital information in networks of adaptive neurons”. Biological Prototypes and Synthetic Systems, 160-160, 1962.
2. Haykin S. Adaptive Filter Theory. 5th ed. USA, Pearson, 2014.
3. Hussain U, Kumar S. “Adaptive echo canceller using LMS algorithm”. International Journal of Advance Engineering and Research Development, 2(8), 54-59, 2015.
4. Wang X, Gu Y, Chen L. “Proof of convergence and performance analysis for sparse recovery via zero-point attracting projection”. IEEE Transactions Signal Processing, 60(8), 4081-4093, 2012.
5. Wright J, Ma Y, Mairal J, Sapiro G, Huang TS, Yan S. “Sparse representation for computer vision and pattern recognition”. IEEE Proceedings, 98(6), 1031-1044, 2010.
6. Czink N, Yin X, Ozcelik H, Herdin M, Bonek E, Fleury B. “Cluster characteristics in a MIMO indoor propagation environment”. IEEE Transactions on Wireless Communications, 6 (4), 1465–1475, 2007.
7. Vuokko L, Kolmonen VM, Salo J, Vainikainen P. “Measurement of large-scale cluster power characteristics for geometric channel models”. IEEE Transactions on Antennas and Propagation, 55(11), 3361–3365, 2007.
8. Gui G, Peng W, Adachi F. “Improved adaptive sparse channel estimation based on the least mean square algorithm”. IEEE Wireless Communication and Networking Conference, Shanghai, China, 07-10 April 2013.

9. Chen Y, Gu Y, Hero AO. “Sparse LMS for system identification”. IEEE International Conference on Acoustics, Speech and Signal Processing, Taipei, Taiwan, 4 April 2009.
10. Wang X, Gu Y, Chen L. “Proof of Convergence and Performance Analysis for Sparse Recovery via Zero-Point Attracting Projection”. IEEE Transactions on Signal Processing, 60(8), 4081-4093. 2012.
11. Taheri O, Vorobyov SA. “Sparse channel estimation with lp-norm and reweighted l1-norm penalized least mean square”. IEEE Conference on Acoustics Speech and Signal Processing (ICASSP), Prague, Czech Republic, 22-27 May 2011.
12. Gu Y, Jin J, Mei S. “l0-Norm constraint LMS algorithm for sparse system identification”. IEEE Signal Processing Letters, 16(9), 774–777. 2009.
13. Su G, Jin J, Gu Y, Wang J. “Performance analysis of l0-norm constraint least mean square algorithm”. IEEE Transactions on Signal Processing, 60(5), 2223-2235, 2012.
14. Mancera L, Portilla J. “l0-Norm-Based sparse representation through alternate projections”. IEEE International Conference on Image Processing, Georgia, USA, 08-11 October 2006.
15. Hadhoud MM, Thomas DW. “The two-dimensional adaptive LMS (TDLMS) algorithm”. IEEE Transactions on Circuits and Systems , 35(5), 485-494, 1988.
16. Abadi MSE, Nikbakht S. “Image denoising with two-dimensional adaptive filter algorithms”. Iranian Journal of Electrical & Electronic Engineering, 7, 84-105. 2011.
17. Zhang X, Jiang T, Li Y. “2D sparsity-information-aided least mean square algorithm for sparse image de-noising”. Wireless Communications & Signal Processing Conference, Yangzhou, China, 13-15 October 2016.
18. Kockanat S, Karaboga N. “A novel 2D-ABC adaptive filter algorithm: A comparative study”. Journal of Digital Signal Processing, 40, 140-153, 2015.
19. Lebrun M. “An analysis and implementation of the BM3D image denoising method”. Image Processing On Line, 2, 175-213, 2012.
20. Muneyasu M, Uemoto E, Hinamoto T. “A novel 2-D adaptive filter based on the 1-D RLS algorithm”. IEEE International Symposium Circuits and Systems, Hong Kong, 12 June 1997.
21. Yang J. Adaptive Filter Design for Sparse Signal Estimation. Ph.D. Dissertation, University of Minnesota, Minnesota, USA, 2011.