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Research On Stochastic Fuzzy Differential Equations In Multiple Blurred Image Repair Models

Author

Listed:
  • JIAN ZHAO

    (School of Information Science and Technology, Northwest University, Xi’an 710127, P. R. China)

  • JIAMING LI

    (School of Information Science and Technology, Northwest University, Xi’an 710127, P. R. China)

  • ABDULLAH K. ALZAHRANI

    (��Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia)

  • JIAN JIA

    (��School of Mathematics, Northwest University, Xi’an 710127, P. R. China)

Abstract

This paper aims to study the processing and repairing methods of blurred images, promote the development of partial differential equations in the field of image processing, and expand the application of stochastic fuzzy differential equations in the field of image processing and repair. This study starts with a typical blurred image repair method. First, a comparative analysis of several common blurred image repair methods including Wiener filtering restoration, inverse filtering restoration, and Lucy–Richardson (L-R) filtering restoration is performed. Second, based on the linear partial differential equation learning model (LPDE), the concept of fuzzy integral is introduced, and an improved stochastic fuzzy partial differential equation learning model (SFCPDE) is proposed. The effect of the learning model before and after improvement on blurred color image processing is compared and analyzed. Finally, based on the total variation (TV) blurred image repair algorithm, an improved TV blurred image repair algorithm is proposed. The comparison and analysis of the repair effects of several blurred image repair algorithms are performed. The results show that there are obvious differences in the repairing methods with or without noise. Inverse filtering works best when there is no noise. L-R filtering has the disadvantage of amplifying noise. Compared with LDPE, the training speed of SFCPDE is significantly improved, and the training error is less than LDPE. The SFCPDE learning model performs better in the processing of blurred color images. After 10 iterations, the improved TV algorithm is significantly better than the TV algorithm and the CDD algorithm in repairing blurred images. The PSNR value of the TV algorithm and the curvature-driven diffusion (CDD) algorithm after 10 iterations corresponds to about 60% of the PSNR value of the improved algorithm. The algorithms and models of stochastic fuzzy partial differential equations proposed in this paper have great application potential in the processing and repair of multiple blurred images.

Suggested Citation

  • Jian Zhao & Jiaming Li & Abdullah K. Alzahrani & Jian Jia, 2022. "Research On Stochastic Fuzzy Differential Equations In Multiple Blurred Image Repair Models," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(02), pages 1-10, March.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:02:n:s0218348x2240076x
    DOI: 10.1142/S0218348X2240076X
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