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Fuzzy Transform and Least-Squares Fuzzy Transform: Comparison and Application

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Abstract

Fuzzy transform is a novel and well-founded soft computing method for reconstruction and denoising of image data. Recently, a least-squares fuzzy transform that combines a fuzzy transform with a least-squares algorithm for function reconstruction has been proposed. However, the least-squares fuzzy transform has a drawback because it uses an estimation process based on the least-squares algorithm, unlike the fuzzy transform that uses the weighted average of the original function over the fuzzy partition. In this paper, we discuss the similarities and differences between fuzzy transform and least-squares fuzzy transform. Simulation results for various image sizes and noisy images show that the fuzzy transform outperforms the least-squares fuzzy transform in terms of image reconstruction and image denoising.

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References

  1. Quan, Y., Chen, Y., Shao, Y., Teng, H., Xu, Y., Ji, H.: Image denoising using complex-valued deep CNN. Pattern Recogn. 111, 107639 (2021)

    Article  Google Scholar 

  2. Shah, Z.H., Müller, M., Wang, T.C., Scheidig, P.M., Schneider, A., Schüttpelz, M., et al.: Deep-learning based denoising and reconstruction of super-resolution structured illumination microscopy images. Photonics Res. 9(5), B168-B181 (2021)

  3. Tian, C., Fei, L., Zheng, W., Xu, Y., Zuo, W., Lin, C.W.: Deep learning on image denoising: an overview. Neural Netw. 131, 251–275 (2020)

    Article  Google Scholar 

  4. Choi, S.H., Jung, H.Y., Kim, H.: Ridge fuzzy regression model. Int. J. Fuzzy Syst. 21(7), 2077–2090 (2019)

    Article  MathSciNet  Google Scholar 

  5. Roh, S.B.: Design of face recognition system based on fuzzy transform and radial basis function neural networks. Soft. Comput. 23(13), 4969–4985 (2019)

    Article  Google Scholar 

  6. Di Martino, F., Hurtik, P., Perfilieva, I., Sessa, S.: A color image reduction based on fuzzy transforms. Inf. Sci. 266, 101–111 (2014)

    Article  Google Scholar 

  7. Novák, V., Perfilieva, I., Holčapek, M., Kreinovich, V.: Filtering out high frequencies in time series using F-transform. Int. J. Approx. Reason. 48(1), 110–131 (2008)

    Article  Google Scholar 

  8. Novák, V., Štěpnička, M., Dvořák, A., Perfilieva, I., Pavliska, V., Vavříčková, L.: Analysis of seasonal time series using fuzzy approach. Int. J. Gen. Syst. 39(3), 305–328 (2010)

    Article  MathSciNet  Google Scholar 

  9. Perfilieva, I., De Baets, Bernard: Fuzzy transforms of monotone functions with application to image compression. Inf. Sci. 180(17), 3304–3315 (2010)

    Article  MathSciNet  Google Scholar 

  10. Perfilieva, I., Dubois, D., Prade, H., Esteva, F., Godo, L., Hodáková, P.: Interpolation of fuzzy data: analytical approach and overview. Fuzzy Sets Syst. 192, 134–158 (2012)

    Article  MathSciNet  Google Scholar 

  11. Woo-Joo, Lee, Hye-Young, Jung, Jin-Hee, Yoon, Seung-Hoe, Choi: A novel forecasting method based on F-transform and fuzzy time series. Int. J. Fuzzy Syst. 19(6), 1793–1802 (2017)

    Article  Google Scholar 

  12. Perfilieva, I.: Fuzzy transforms: theory and applications. Fuzzy Sets Syst. 157(8), 993–1023 (2006)

    Article  MathSciNet  Google Scholar 

  13. Rividhya, K., Ramya, M.M.: Fuzzy-based adaptive denoising of underwater images. Int. J. Fuzzy Syst. 19(4), 1132–1143 (2017)

    Article  MathSciNet  Google Scholar 

  14. Chen, Bor-Sen., Min-Yen, Lee, Dain-Long, Chen: Robust Fuzzy filter design for nonlinear parabolic partial differential systems with continuous wiener noise and discontinuous Poisson noise. Int. J. Fuzzy Syst. 21(1), 1–18 (2019)

    Article  MathSciNet  Google Scholar 

  15. Patané, G.: Fuzzy transform and least-squares approximation: analogies, differences, and generalizations. Fuzzy Sets Syst. 180(1), 41–54 (2011)

    Article  MathSciNet  Google Scholar 

  16. Gaeta, M., Loia, V., Tomasiello, S.: Multisignal 1-D compression by F-transform for wireless sensor networks applications. Appl. Soft Comput. 30, 329–340 (2015)

    Article  Google Scholar 

  17. Tomasiello, S.: Least-squares Fuzzy transforms and autoencoders: some remarks and application. IEEE Trans. Fuzzy Syst. 29(1), 129–136 (2020)

    Article  MathSciNet  Google Scholar 

  18. Di Martino, F., Loia, V., Perfilieva, I., Sessa, S.: An image coding/decoding method based on direct and inverse fuzzy transforms. Int. J. Approx. Reason. 48(1), 110–131 (2008)

    Article  Google Scholar 

  19. Boyat, A.K., Joshi, B.K.: A review paper: noise models in digital image processing, signal & image processing. Int. J. (SIPIJ) 6(2) (2015)

  20. Daňková, M., Štěpnička, M.: Fuzzy transform as an additive normal form. Fuzzy Sets Syst. 158(9), 1024–1035 (2006)

    Article  MathSciNet  Google Scholar 

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Author notes

  1. Hee-Jun Min and Jae-Won Shim have contributed equally to this work.

Authors and Affiliations

  1. Department of Applied Mathematics, Hanyang University, Gyeonggi, Republic of Korea

    Hye-Young Jung

  2. Department of Applied Mathematics, Hanyang University Graduate School, Seoul, Republic of Korea

    Hee-Jun Min, Jae-Won Shim, Hye-Ju Han & Chang-Hee Park

Authors
  1. Hee-Jun Min
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  2. Jae-Won Shim
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  3. Hye-Ju Han
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  4. Chang-Hee Park
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  5. Hye-Young Jung
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Corresponding author

Correspondence to Hye-Young Jung.

Additional information

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1I1A1A01046810) and Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2020-0-01343), and Artificial Intelligence Convergence Research Center (Hanyang University).

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Min, HJ., Shim, JW., Han, HJ. et al. Fuzzy Transform and Least-Squares Fuzzy Transform: Comparison and Application. Int. J. Fuzzy Syst. 24, 2740–2752 (2022). https://doi.org/10.1007/s40815-022-01277-0

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  • DOI: https://doi.org/10.1007/s40815-022-01277-0

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