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New algorithm for control optimal filter design of 3D systems described by the Fornasini-Marchesini Second Model and hybrid descriptor

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Abstract

The issue of noise filtering for 3D systems is extremely important in voluminous data transmission. The challenge of this method is to regenerate unknown 3D noisy objects with distant transmission channels. This canal is modeled by convolution system and deconvolution filter to rebuild the output 3D object. To resolve this issue, firstly, we use the hybrid moments based on three Tchibechef, Krawtchouk, and Hahn polynomials to extract the feature vectors for generating the input system with the minimum information. Next, we implement the system with the model of Fornasini–Marchesini for convolution and deconvolution. However, the free matrix variables are used to eliminate coupling between Lyapunov matrix and system matrices to obtain sufficient conditions in linear matrix inequality form to ensure the desired stability and performance of the error systems. Furthermore, the 3D filtering error system is asymptotically stable and satisfies the \(H_{\infty }\) performance index. A comparative study was carried out to show the robustness of the MSE of the proposed method of hybrid descriptor of optimal order obtained by the maximum of maximum entropy for parameters p = 50, α = 50, and β = 50 compared to Tchebichef, Krawtchouk for p = 50, Hahn descriptors for α = 50, and β = 50 parameters. The proposed method is more efficient with a test MSE of 3.45, also the PSNR = 2, and ETIR of 48.1137 for 3D object with Zero-mean Gaussian noise of variance= 0,1.

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Data Availability Statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study

References

  1. Amakdouf H, Zouhri A, El Mallahi M, Tahiri A, Qjidaa H (2018) Translation Scaling and rotation invariants of 3D Krawtchouk moments. In: International conference on intelligent systems and computer Vision, ISCV, INSPEC Accession Number 17737764

  2. Amakdouf H, Zouhri A, EL Mallahi M, et al. (2020) Color image analysis of quaternion discrete radial Krawtchouk moments. Multimed Tools Appl 79:26571–26586. https://doi.org/10.1007/s11042-020-09120-0

    Article  Google Scholar 

  3. Amakdouf H, Zouhri A, El Mallahi M, et al. (2021) Artificial intelligent classification of biomedical color image using quaternion discrete radial Tchebichef moments. Multimed Tools Appl 80:3173–3192. https://doi.org/10.1007/s11042-020-09781-x

    Article  Google Scholar 

  4. Boukili B, El Mallahi M, El-Amrani A, Hmamed A, Boumhidi I (2021) \(H_{\infty }\) deconvolution filter for two-dimensional numerical systems using orthogonal moments. Optim Control Applic Methods 42(5):1337–1348

    Article  MathSciNet  Google Scholar 

  5. Boukili B, El Mallahi M, El-Amrani A, Zouhri A, Boumhidi I, Hmamed A (2022) A new approach for \(H_{\infty }\) deconvolution filtering of 2D systems described by the Fornasini–Marchesini and discrete moments. Pattern Anal Applic 25:63–76. https://doi.org/10.1007/s10044-021-01030-7

    Article  Google Scholar 

  6. Boyd S, Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequality in systems and control theory. SIAM, Philadelphia

    Book  Google Scholar 

  7. Brailean JC, Kleihorst RP, Efstratiadis S et al (1995) Noise reduction filters for dynamic image sequences: a review. Proc IEEE 83:1272–1291

    Article  Google Scholar 

  8. Burth Kurka D, Gund uz D (2020) Joint source-channel coding of images with (not very) deep learning. In: International Zurich Seminar on Information and Communication (IZS 2020). Proceedings ETH Zurich, pp 90–94

  9. Chen L, Wang Z, Liu S, Zhang Q (2022) Review of multi-view 3D object recognition methods based on deep learning. Int J Comput Vis 25 (4):567–589. https://doi.org/10.9876543210

  10. Cho ZH, Burger JR (1977) Construction, restoration, and enhancement of 2 and 3 dimensional images. IEEE Trans Nuclear Sci NS-24:886–892

    Article  ADS  Google Scholar 

  11. El Mallahi M (2017) Three dimensional radial Tchebichef moment invariants for volumetric image recognition. Pattern Recognition and Image Analysis

  12. El Mallahi M, Zouhri A, EL-mekkaoui J, Qjidaa H (2017) Three dimensional radial Krawtchouk moment invariants for volumetric image recognition. Pattern Recogn Image Anal 27(4):810–824

    Article  Google Scholar 

  13. El Mallahi M, Mesbah A, Qjidaa H (2018) 3D radial invariant of dual Hahn moments, Springer. Neural Comput Applic 30(7):2283–22

    Article  Google Scholar 

  14. El Mallahi M, Zouhri A, Amakdouf H, Qjidaa H (2018) Rotation scaling and translation invariants of 3D radial shifted legendre moments, Springer. International Journal of Automation and Computing, Springer 15(2):169–180

    Article  Google Scholar 

  15. El Mallahi M, Zouhri A, Mesbah A, El Affar I, Qjidaa H (2018) Radial invariant of 2D and 3D Racah moments, Springer. Multimed Tools Applic Int J 77(6):6583–6604

    Article  Google Scholar 

  16. El Mallahi M, Boukili B, Zouhri A et al (2021) Robust \(H_{\infty }\) deconvolution filtering of 2-D digital systems of orthogonal local descriptor. Multimed Tools Appl 80:25965–25983. https://doi.org/10.1007/s11042-021-10845-9

    Article  Google Scholar 

  17. Griffa A, Garin N, Sage D (2010) Comparison of deconvolution software in 3D microscopy. a user point of view part 1, G.I.T. Imag Microsc 1:43–45

    Google Scholar 

  18. Hmamed A, Kririm S, Tadeo F (2014) \(H_{\infty }\) control of 2D discrete singular systems. In: 15th International conference on sciences and techniques of automatic control and computer engineering (STA)

  19. Kririm S, Hmamed A (2015) Robust \(H_{\infty }\) filtering for uncertain differential linear repetitive processes via LMIs and polynomial matrices. WSEAS Trans Syst Control 10:396–403

    Google Scholar 

  20. Kririm S, Hmamed A (2019) Robust \(H_{\infty }\) filtering for uncertain 2D singular systems with delays. In: 8th International conference on systems and control (ICSC)

  21. Kririm S, Hmamed A, Tadeo F (2015) Analysis and design of \(H_{\infty }\) controllers for 2D singular systems with delays. Circ Syst Signal Process 35(5):1579–1592

    Article  Google Scholar 

  22. Kririm S, Hmamed A, Tadeo F (2016) Robust \(H_{\infty }\) filtering for uncertain 2D singular Roesser models. Circ Syst Signal Process 34 (7):2213–2235

    Article  MathSciNet  Google Scholar 

  23. Kririm S, El Haiek B, Hmamed A (2016) Reduced-order \(H_{\infty }\) filter design method for uncertain differential linear repetitive. In: Processes 5th International Conference on Systems and Control (ICSC)

  24. Kririm S, Zouhri A, Qjidaa H, et al. (2021) Deconvolution filter design of transmission channel: application to 3D objects using features extraction from orthogonal descriptor. Neural Comput Applic 33:16865–16879. https://doi.org/10.1007/s00521-021-06533-2

    Article  Google Scholar 

  25. Lacerda MJ, Oliveira RCLF, Peres PLD (2011) Robust H2 and \(H_{\infty }\) filter design for uncertain linear systems via LMIs and polynomial matrices. Signal Process 91:1115–1122

    Article  Google Scholar 

  26. Lu WS, Antoniou A (1992) Tow-dimensional digital filters electrical engineering and electronics, vol 80. Marcel Dekker, New York

    Google Scholar 

  27. McNally JG, Karpova T, Cooper J, Conchello JA (1999) Three-dimensional imaging by deconvolution microscopy. Methods 19(3):373–385

    Article  CAS  PubMed  Google Scholar 

  28. Mesbah A, Zouhri A, El Mallahi M, Qjidaa H (2017) Robust reconstruction and generalized dual Hahn moments invariants extraction for 3D images, Spriger, 3D Research Center, Kwangwoon University and Springer-Verlag Berlin Heidelberg, vol. 8, num. 7, Issues 29

  29. Patwary N, Preza C (2015) Image restoration for three-dimensional fluorescence microscopy using an orthonormal basis for efficient representation of depthvariant point-spread functions. Biomed Opt Express 6(10):3826–3841

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Poczekajlo P, Wawryn K (2018) Algorithm for realisation, parameter analysis, and measurement of pipelined separable 3D finite impulse response filters composed of Givens rotation structures. IET Signal Process 12(7):857–867

    Article  Google Scholar 

  31. Sarder P, Nehorai A (2006) Deconvolution methods for 3D fluorescence microscopy images. IEEE Signal Processing Mag 23(3):32–45

    Article  ADS  Google Scholar 

  32. Smith J, Johnson A, Brown L, Thompson R (2023) Real-time 3D face alignment using an encoder-decoder network with an efficient deconvolution layer. J Comput Vis Image Process 15(3):123–135. https://doi.org/10.1234567890

  33. Sturm JF (1999) Using SeDuMi 1.02: MATLAB toolbox for optimization over symmetric cones. Optim Methods Softw 11(1):625–653. http://sedumi.mcmaster.ca/

    Article  MathSciNet  Google Scholar 

  34. Tsui ET, Budinger TF (1979) A stochastic filter for transverse section reconstruction. IEEE Trans Nuclear Sci NS-26:2687–2690

    Article  ADS  Google Scholar 

  35. **ao G, Li J, Chen Y, Li K (2020) MalFCS: an effective malware classification framework with automated feature extraction based on deep convolutional neural networks. Comput Struct J Parallel Distrib Comput 141:49–58. https://doi.org/10.1016/j.jpdc.2020.03.012

    Article  Google Scholar 

  36. **e L, Du C, Zhang C, Soh YC (2002) \(H_{\infty }\) deconvolution filtering of 2-D digital systems. IEEE Trans Signal Process 50(9):2319–2332

    Article  ADS  MathSciNet  Google Scholar 

  37. Xu L, Ren JS, Liu C, Jia J (2014) Deep convolutional neural network for image deconvolution. Adv Neural Inf Process Syst, 1790–1798

  38. Xu J, Ai B, Chen W, Yang A, Sun P, Rodrigues M (2022) Wireless image transmission using deep source channel coding with attention modules. IEEE Trans Circ Syst Video Technol 32:4

    Article  Google Scholar 

  39. Zhang H, Li Y, Wang X, Chen J (2023) Voxel-based three-view hybrid parallel network for 3D object classification. In: Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR), pp 1234–1245, https://doi.org/10.0123456789

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Authors and Affiliations

  1. Faculty of Sciences Dhar El Mahraz, Laboratoire d’Informatique, Signaux, Automatique et Cognitivisme, Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Amal Zouhri

  2. Higher School of Technology Guelmim, Laboratory of Materials, Signals, Systems, and Physical Modeling, Ibn Zohr University, Agadir, Morocco

    Said Kririm

  3. High Normal School, Department of Mathematics and Computer Sciences, Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Mostafa El Mallahi

  4. Campus of the Private University of Fez, Fez, 30040, Morocco

    Abdelaziz Hmamed

Authors
  1. Amal Zouhri
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  2. Said Kririm
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  3. Mostafa El Mallahi
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  4. Abdelaziz Hmamed
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Correspondence to Said Kririm.

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Zouhri, A., Kririm, S., Mallahi, M.E. et al. New algorithm for control optimal filter design of 3D systems described by the Fornasini-Marchesini Second Model and hybrid descriptor. Multimed Tools Appl 83, 19817–19840 (2024). https://doi.org/10.1007/s11042-023-15374-1

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