An enhanced fractal image denoising algorithm. (English) Zbl 1152.94316

Summary: In recent years, there has been a significant development in image denoising using fractal-based method. This paper presents an enhanced fractal predictive denoising algorithm for denoising the images corrupted by an additive white Gaussian noise (AWGN) by using quadratic gray-level function. Meanwhile, a quantization method for the fractal gray-level coefficients of the quadratic function is proposed to strictly guarantee the contractivity requirement of the enhanced fractal coding, and in terms of the quality of the fractal representation measured by PSNR, the enhanced fractal image coding using quadratic gray-level function generally performs better than the standard fractal coding using linear gray-level function. Based on this enhanced fractal coding, the enhanced fractal image denoising is implemented by estimating the fractal gray-level coefficients of the quadratic function of the noiseless image from its noisy observation. Experimental results show that, compared with other standard fractal-based image denoising schemes using linear gray-level function, the enhanced fractal denoising algorithm can improve the quality of the restored image efficiently.


94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
28A80 Fractals
Full Text: DOI


[1] Barnsley, M. F., Fractals everywhere (1998), Academic: Academic New York · Zbl 0691.58001
[2] Barnsley, M. F.; Demko, S., Iterated function systems and the global construction of fractals, Proc Roy Soc London, A399, 243-275 (1985) · Zbl 0588.28002
[3] Barnsley, M. F.; Jacquin, A. E., Application of recurrent iterated function systems to images, Proc SPIE, 1001, 122-131 (1988)
[4] Jacquin, A. E., Image coding based on a fractal theory of iterated contractive image transformation, IEEE Trans Image Process, 1, 18-30 (1992)
[5] (Fisher, Y., Fractal image compression: theory and application (1994), Springer-Verlag: Springer-Verlag New York) · Zbl 0814.68143
[6] Truong, T. K.; Kung, C. M.; Jeng, J. H.; Hsieh, M. L., Fast fractal image compression using spatial correlation, Chaos, Solitons & Fractals, 22, 1071-1076 (2004) · Zbl 1062.68594
[7] Wu, M. S.; Teng, W. C.; Jeng, J. H.; Hisieh, J. G., Spatial correlation genetic algorithm for fractal image compression, Chaos, Solitons & Fractals, 28, 497-510 (2006) · Zbl 1084.68941
[8] Chung, K. L.; Hsu, C. H., Novel prediction- and subblock-based algorithm for fractal image compression, Chaos, Solitons & Fractals, 29, 215-222 (2006) · Zbl 1096.68757
[9] He, C. J.; Li, G. P.; Shen, X. N., Interpolation decoding method with variable parameters for fractal image compression, Chaos, Solitons & Fractals, 32, 1429-1439 (2007) · Zbl 1127.94003
[10] Davis, G. M., A wavelet-based analysis fractal image compression, IEEE Trans Image Process, 7, 141-154 (1998) · Zbl 0993.94509
[11] Vrscay, E. R., A generalized class of fractal-wavelet transforms for image representation and compression, Can J Elect Comput Eng, 23, 69-84 (1998)
[12] Ghazel, M.; Freeman, G. H.; Vrscay, E. R., Fractal image denoising, IEEE Trans Image Process, 12, 1560-1578 (2003)
[14] Ghazel, M.; Freeman, G. H.; Vrscay, E. R., Fractal-wavelet image denoising, IEEE Proc Image Process, 836-839 (2002)
[15] Ghazel, M.; Freeman, G. H.; Vrscay, E. R., Fractal-wavelet image denoising revisited, IEEE Trans Image Process, 15, 2669-2675 (2006)
[17] Zhao, Y.; Yuan, B. Z., A new affine transformation: its theory and application to image coding, IEEE Trans Circ Syst Video Technol, 8, 3, 269-274 (1998)
[18] Roman, S., Coding and information theory (1992), Springer-Verlag: Springer-Verlag New York · Zbl 0752.94001
[19] Coifman, R. R.; Donoho, D. L., Translation-invariant denoising, Wavelets Stat, 103, 125-150 (1995) · Zbl 0866.94008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.