journal article·2022-07-27Open access

An Improved Robust Fractal Image Compression Based on M-Estimator

Penghe Huang, Dongyan Li, Huimin Zhao

Applied Sciences· Volume 12· Issue 15

Abstract

In this paper, a robust fractal image compression method based on M-estimator is presented. The proposed method applies the M-estimator to the parameter estimation in the fractal encoding procedure using Huber and Tukey’s robust statistics. The M-estimation reduces the influence of the outliers and makes the fractal encoding algorithm robust to the noisy image. Meanwhile, the quadtree partitioning approach has been used in the proposed methods to improve the efficiency of the encoding algorithm, and some unnecessary computations are eliminated in the parameter estimation procedures. The experimental results demonstrate that the proposed method is insensitive to the outliers in the noisy corrupted image. The comparative data shows that the proposed method is superior in both the encoding time and the quality of retrieved images over other robust fractal compression algorithms. The proposed algorithm is useful for multimedia and image archiving, low-cost consumption applications and progressive image transmission of live images, and in reducing computing time for fractal image compression.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Mathematical Dynamics and Fractals · Image and Signal Denoising Methods · Neural Networks and Applications

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Software Technology Institute, Dalian Jiaotong University, Dalian 116028, China

School of Electronic Information and Automation, Civil Aviation University of China, Tianjin 300300, China

Funding

NSFC

References (58)

Show source-provided references
1. Iterated function systems and the global construction of fractals
2. Image coding based on a fractal theory of iterated contractive image transformations
3. Barnsley, M.F. (1993). Fractal Everywhere, Elsevier. [2nd ed.].
4. Fisher, Y. (1995). Fractal Image Compression Theory and Appplication, Springer.10.1007/978-1-4612-2472-3 ↗
5. Fractal image compression using visual-based particle swarm optimization10.1016/j.imavis.2008.01.003 ↗
6. An improved no-search fractal image coding method based on a fitting plane10.1016/j.imavis.2010.01.008 ↗
7. Fractal image compression based on spatial correlation and hybrid genetic algorithm10.1016/j.jvcir.2009.07.002 ↗
8. Fractal compression coding based on wavelet transform with diamond search10.1016/j.nonrwa.2011.07.017 ↗
9. Fast intra-prediction algorithms for high efficiency video coding standard10.1117/1.JEI.25.1.013028 ↗
10. Parameter adaptation-based ant colony optimization with dynamic hybrid mechanism10.1016/j.engappai.2022.105139 ↗
11. Wu, D., and Wu, C. (2022). Research on the time-dependent split delivery green vehicle routing problem for fresh agricultural products with multiple time windows. Agriculture, 12.10.3390/agriculture12060793 ↗
12. Li, X., Shao, H., Lu, S., Xiang, J., and Cai, B. (2022). Highly-efficient fault diagnosis of rotating machinery under time-varying speeds using LSISMM and small infrared thermal images. IEEE Trans. Syst. Man Cybern. Syst., 1–13.10.1109/TSMC.2022.3151185 ↗
13. End-to-end learnt image compression via non-local attention optimization and improved context modeling10.1109/TIP.2021.3058615 ↗
14. Solving the family traveling salesperson problem in the adleman–lipton model based on DNA computing10.1109/TNB.2021.3109067 ↗
15. An, Z., Wang, X., Li, B., Xiang, Z.L., and Zhang, B. (2022). Robust visual tracking for UAVs with dynamic feature weight selection. Appl. Intell.10.1007/s10489-022-03719-6 ↗
16. Unsupervised domain-share CNN for machine fault transfer diagnosis from steady speeds to time-varying speeds10.1016/j.jmsy.2021.11.016 ↗
17. A robust meaningful image encryption scheme based on block compressive sensing and SVD embedding10.1016/j.sigpro.2020.107629 ↗
18. Wu, J., and Wang, Z. (2022). A hybrid model for water quality prediction based on an artificial neural network, wavelet transform, and long short-term memory. Water, 14.10.3390/w14040610 ↗
19. Deep transfer multi-wavelet auto-encoder for intelligent fault diagnosis of gearbox with few target training samples10.1016/j.knosys.2019.105313 ↗
20. Feature extraction using parameterized multisynchrosqueezing transform10.1109/JSEN.2022.3179165 ↗
21. Pyramid particle swarm optimization with novel strategies of competition and cooperation10.1016/j.asoc.2022.108731 ↗
22. Secure outsourcing algorithm of BTC feature extraction in cloud computing10.1109/ACCESS.2020.3000683 ↗
23. SG-PBFT: A secure and highly efficient distributed blockchain PBFT consensus algorithm for intelligent Internet of vehicles10.1016/j.jpdc.2022.01.029 ↗
24. An enhanced MSIQDE algorithm with novel multiple strategies for global optimization problems10.1109/TSMC.2020.3030792 ↗
25. A hyperspectral image classification method using multifeature vectors and optimized KELM10.1109/JSTARS.2021.3059451 ↗
26. Xu, G., Dong, W., Xing, J., Lei, W., and Liu, J. (2022). Delay-CJ: A novel cryptojacking covert attack method based on delayed strategy and its detection. Digit. Commun. Netw.10.1016/j.dcan.2022.04.030 ↗
27. Transfer fault diagnosis of bearing installed in different machines using enhanced deep auto-encoder10.1016/j.measurement.2019.107393 ↗
28. A novel mathematical morphology spectrum entropy based on scale-adaptive techniques10.1016/j.isatra.2021.07.017 ↗
29. Zhao, H.M., Liu, J., Chen, H.Y., Chen, J., Li, Y., Xu, J.J., and Deng, W. (2022). Intelligent diagnosis using continuous wavelet transform and gauss convolutional deep belief network. IEEE Trans. Reliab., 1–11.
30. Jin, T., Xia, H., Deng, W., Li, Y., and Chen, H. (2021). Uncertain fractional-order multi-objective optimization based on reliability analysis and application to fractional-order circuit with Caputo type. Circ. Syst. Signal Pr.10.1007/s00034-021-01761-2 ↗
31. Self-paced dynamic infinite mixture model for fatigue evaluation of pilots’ brains10.1109/TCYB.2020.3033005 ↗
32. Compound fault diagnosis using optimized MCKD and sparse representation for rolling bearings10.1109/TIM.2022.3159005 ↗
33. Rolling element fault diagnosis based on VMD and sensitivity MCKD10.1109/ACCESS.2021.3108972 ↗
34. Enhancing comprehensive learning particle swarm optimization with local optima topology10.1016/j.ins.2018.08.049 ↗
35. Adaptive comprehensive learning particle swarm optimization with cooperative archive10.1016/j.asoc.2019.01.047 ↗
36. Saturated control design of a quadrotor with heterogeneous comprehensive learning particle swarm optimization10.1016/j.swevo.2019.02.008 ↗
37. Reliability analysis of the uncertain heat conduction model10.1016/j.camwa.2022.05.033 ↗
38. Liu, Q., Jin, T., Zhu, M., Tian, C., Li, F., and Jiang, D. (2022). Uncertain currency option pricing based on the fractional differential equation in the Caputo sense. Fractal Fractional, 6.10.3390/fractalfract6080407 ↗
39. Li, G., Li, Y., Chen, H., and Deng, W. (2022). Fractional-order controller for course-keeping of underactuated surface vessels based on frequency domain specification and improved particle swarm optimization algorithm. Appl. Sci., 12.10.3390/app12063139 ↗
40. Optimal reactive power dispatch using an improved slime Mould algorithm10.1016/j.egyr.2021.11.138 ↗
41. Fractal image denoising10.1109/TIP.2003.818038 ↗
42. An enhanced fractal image denoising algorithm10.1016/j.chaos.2007.06.048 ↗
43. Study on Huber fractal image compression10.1109/TIP.2009.2013080 ↗
44. Robust estimation of parameter for fractal inverse problem10.1016/j.camwa.2010.07.051 ↗
45. A Novel fast fractal image compression method based on distance clustering in high dimensional sphere surface10.1142/S0218348X17400047 ↗
46. Wei, G., Jiang, H., and Rui, Y. (2010, January 17–18). Linear-regression model based wavelet filter evaluation for image compression. Proceedings of the 2010 Asia-Pacific Conference on Wearable Computing Systems, Shenzhen, China.
47. Impact of spatial dynamic search with matching threshold strategy on fractal image compression algorithm performance: Study10.1109/ACCESS.2020.2980747 ↗
48. Fractal image compression using block indexing technique: A review10.24996/ijs.2020.61.7.29 ↗
49. A fast-encoding fractal image compression using quantized quad—tree partitioning techniques
50. Controlled hardware architecture for fractal image compression10.1504/IJNBM.2020.107415 ↗
51. A nonlocal low-rank regularization method for fractal image coding10.1142/S0218348X21501255 ↗
52. Genetic algorithm based on discrete wavelet transformation for fractal image compression10.1016/j.jvcir.2014.09.001 ↗
53. On fractal image compression technology based on genetic algorithm
54. Huber, P. (1981). Robust Statistics, Wiley.10.1002/0471725250 ↗
55. Tukey, J. (1977). Explortary Data Analysis, Addison-Wesley.
56. Hampel, F., Ronchetti, E., Rousseeuw, P., and Stahel, W. (1986). Robust Statistics: The Approach Based on Influence Functions, John Wiley & Sons.
57. Robust estimation of a local parameter10.1214/aoms/1177703732 ↗
58. Rey, W. (1983). Introduction to Robust and Quasi-Robust Statistical Methods, Springer.10.1007/978-3-642-69389-2 ↗