Comparative Analysis of Spline and Exponential Spline Filters for Gaussian Noise Reduction in Satellite Images: Introducing a Novel Nonlinear Filtering Approach
DOI:
https://doi.org/10.62933/20bvef82Keywords:
Image Denoising , Image Restoration , Gaussian Noise , Spline Filter , Exponential Spline FilterAbstract
Satellite imagery often suffers from noise due to various atmospheric and sensor-related factors, which can significantly degrade image quality and hinder subsequent analysis. This article presents a comprehensive study on denoising satellite images utilizing spline interpolation and exponential spline techniques. We propose a novel nonlinear filter designed to enhance the denoising process, and we compare its performance against traditional spline-based methods. The evaluation metrics employed include the Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM), which are critical for assessing image quality. Our experimental results demonstrate that the proposed nonlinear filter consistently outperforms both spline interpolation and exponential spline methods, achieving superior PSNR and SSIM values. This study highlights the proposed filter's effectiveness in preserving image details while reducing noise and contributes to the ongoing advancements in remote sensing image processing techniques. The findings underscore the potential of nonlinear filtering approaches in enhancing the quality of satellite imagery for various applications.
References
1. Abdul Wadood, M., & Ghalib, A. (2024). Gaussian Denoising for the First Image from The James Webb Space Telescope “Carina Nebula” using Non-Linear Filters. Journal of Economics and Administrative Sciences, 30(143), 420-434.
2. Abdullah, D., Fajriana, F., Maryana, M., Rosnita, L., Putera, A., Siahaan, U., Hadikurniawati, W. (2018). The application of an interpolation image is done using a bi-cubic algorithm. IOP Conf. Series: Journal of Physics: Conf. Series, 1114, 1-7. doi:https://doiorg/10.1088/1742-6596/1114/1/012066
3. Anne, T., & Neri, M. (n.d.). A Heuristic Spline Interpolation Method on Signal Denoising.
4. Averbuch, A. Z., Neittaanmäki, P., & Zheludev, V. (2016). Spline and Spline Wavelet Methods with Applications to Signal and Image Processing Volume II: Non-Periodic Splines. New York: Springer Science and Business Media. doi:https://doi.org/10.1007/978-3-319-22303-2
5. Averbuch, A., Neittaanmki, P., Shabat, G., & Zhelludev, V. (2016). Fast Computation By Subdivision Of Multidimensional Splines And Their Applications. 1(3), 309-341. Retrieved from http://www.ybook.co.jp/online2/oppafa/vol1/p309.html
6. Averbuch, A., Zheludev, V., Neittaanmaki, P., & Kore, J. (2010). Block-based deconvolution algorithm using spline wavelet packets. Journal of Mathematical Imaging and Vision, 38, 197–225. doi:https://doi.org/10.1007/s10851-010-0224-4
7. Basco-Uy, T. A., & Neri, M. C. (2020, 8 1). A Heuristic Spline Interpolation Method on Signal Denoising. 15(1), 1-11.
8. Cassanya, V., Barrutia, M., & Unser. (2007). Locally adaptive smoothing method based on B-splines based on B-splines. 1-7.
9. Chac´on, J., & Duong, T. (2019). Multivariate plug-in bandwidth selection with unconstrained pilot bandwidth matrices. International Journal of Development Research, 7(9), 15048–15053. doi:https://doi.org/10.1007/s11749-009-0168-4
10. Fahmy, G. (2013). Image Super-Resolution and Enhancement Using E-spline. Journal of Communication and Computer, 10, 1497-1501. doi:http://dx.doi.org/10.1109/ISSPIT.2013.6781890
11. Fahmy, M. F., Fahm, G., & Fahm, O. M. (n.d.). E-spline Based Image Interpolators. IEEE International Symposium on Signal Processing and Information Technology (ISSPIT), 32, 61-68. doi:https://doi.org/10.1109/isspit.2014.7300564
12. Fahmy, M., Fahmy, G., & Alkanhal, T. (2013). E-Spline In Image De-Noising Applications. 30th National Radio Science Conference, 7, 274-280. doi:https://doi.org/10.1109/nrsc.2013.6587924
13. Florence, K., Aggrey, A., & Leonard, K. (2018, 5 24). Efficiency of various Bandwidth Selection Methods across Different Kernels. IOSR Journal of Mathematics (IOSR-JM), 15(3), 55-62. doi:https://doi.org/10.9790/5728-1503015562
14. Ghalib, A., & Abdul Wadood, M. (2020). Using multidimensional scaling technique in image dimension reduction for satellite image. Periodicals of Engineering and Natural Sciences, 8(1), p.447-454.
15. Getreuer, P. (2012). Rudin–Osher–Fatemi Total Variation Denoising using Split Bregman. Image Processing On Line, 2, 74–95. doi:https://doi.org/10.5201/ipol.2012.g-tvd
16. Hong, Q., Hong, Q., Messi, L., & Wang, J. (2019). Galerkin method with splines for total variation minimization. Journal of Algorithms & Computational Technology, 13, 1-16. doi:http://dx.doi.org/10.1177/1748301819833046
17. Horiuchi, Y. (n.d.). Reducing Image Noise Using Spline Smoothing. 1-4.
18. Horova, I., Kolacek, J., Zelinka, J., & Vopatova, K. (2008, 12). Bandwidth choice for kernel density estimates. 1-10. Retrieved from https://link.springer.com/article/10.1007/s10182-013-0216-y
19. Islam, T., & Righetti, R. (2020). A Spline Interpolation–based Data Reconstruction Technique for Estimating Strain Time Constant in Ultrasound Poroelastography. Electrical Engineering and Systems Science, 42(1), 5-14. doi:https://us.sagepub.com/en-us/journals-permissions
20. Jones, M. C., Marron, J. S., & Sheather, S. J. (1996, 3). A Brief Survey of Bandwidth Selection for Density Estimation. Journal of the American Statistical Association, 91(433), 401-407. Retrieved from https://www.jstor.org/stable/pdf/2291420.pdf
21. Kawasakia, T., Jayaraman, P., Shida, K., Zheng, J., & Maekawa, T. (2018). An Image Processing Approach to Feature-Preserving B-Spline Surface Fairing. 1-14.
22. Lakshmi, M., Murthy, S., & Rao, N. (2017). A Novel Algorithm for Impulse Noise Removal using B-Splines for Finger Print Forensic Images. International Journal of Applied Engineering Research, 12(1), 127-131.
23. Lee, J. C., Li, J., Musco, C., Phillips, J., & Tai, W. M. (2021). Finding an Approximate Mode of a Kernel Density Estimate. 29th Annual European Symposium on Algorithms (ESA 2021)(61), 1-19.
24. Mccartixn, B. J. (1991). Theory Of Exponential Splines. Journal Of Approximation Theory, 1-23.
25. Mohammed, A., Jamil, B., Ali, F. (2020). Bootstrap technique for image detection. Periodicals of Engineering and Natural Sciences. 8(3), 1280-1287. https://api.semanticscholar.org/CorpusID:221757811.
26. Mohammed, F., Fahmy, G., & Fahmy, O. (2011, 7). B-spline wavelets for signal denoising and image compression. Signal Image and Video Processing, 5, 141–153. doi:https://doi.org/10.1007/s11760-009-0148-x
27. Oliveira, E. F., Melo, S. B., Dantas, C. C., Mota, Í. V., & Lira, M. (2011, 10 24). Tomographic Reconstruction With B-Splines Surfaces. 2011 International Nuclear Atlantic Conference - INAC 2011, 1-14.
28. Ortelli, F., & van de Geer, S. (2020). Adaptive Rates for Total Variation Image Denoising. Journal of Machine Learning Research, 21, 1-38.
29. Pana, H., Wena, Y.-W., & Zhu, H.-M. (2019, 11 23). A regularization parameter selection model for total variation-based image noise removal. Applied Mathematical Modelling, 68, 353-376. doi:https://doi.org/10.1016/j.apm.2018.11.032
30. Parsania, P. S., & Virparia, P. V. (2016, 1). A Comparative Analysis of Image Interpolation Algorithms. International Journal of Advanced Research in Computer and Communication Engineering, 5(1), 29-34. doi:https://doi.org/ 10.17148/IJARCCE.2016.5107
31. Parveen, S., & Tokas, R. (2015). Faster Image Zooming using the Cubic Spline Interpolation Method. International Journal on Recent and Innovation Trends in Computing and Communication, 3(1), 22 - 26. doi:https://doi.org/10.17762/ijritcc2321-8169.150106
32. Rothfuss, J., Ferreira, F., Walther, S., & Ulrich, M. (2019, 4 3). Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks. 1-36. Retrieved from https://arxiv.org/abs/1903.00954
33. Salgado-Ugarte, I. H., & Perez-Hernandez, M. A. (2003). Exploring the use of variable bandwidth kernel density estimators. The Stata Journal, 3(2), 133-137. Retrieved from https://www.stata-journal.com/abstracts/st0036.pdf
34. Sharma, A., Lall, U., & Tarboton, D. G. (1998). Kernel bandwidth selection for a first-order nonparametric streamflow simulation model. Statistic Hydrology and Hydraulics, 12, 33-52. Retrieved from https://link.springer.com/article/10.1007/s004770050008
35. Singh, R. B., Jain, A., & Lipton, M. (2012, 12). Image Enhancement Method using E-spline. International Journal of Emerging Trends & Technology in Computer Science (IJETTCS), 1(4), 35-43.
36. Takeda, H., Farsiu, S., & Milanfar, P. (2007, 2). Kernel Regression for Image Processing and Reconstruction. IEEE Transactions On Image Processing, 16(2), 349-366. doi:https://doi.org/10.1109/TIP.2006.888330
37. Xu, G., Ling, R., Deng, L., Wu, Q., & Ma, W. (2020). Image Interpolation via Gaussian-Sinc Interpolators with Partition of Unity. Computers, Materials & Continua, 62(1), 309-319.
38. Zeng, X., & Li, S. (2013). An efficient adaptive total variation regularization for image denoising. Conference: Image and Graphics (ICIG), 7, 1-6. doi:https://doi.org/10.1109/ICIG.2013.17
39. Zhou, K., Zheng, L., & Lin, F. (2012). Image Denoising Using Orthogonal Spline. Physics Procedia; 2012 International Conference on Medical Physics and Biomedical Engineering, 33, 798 – 803. doi:https://doi.org/10.1016/j.phpro.2012.05.137
40. Zhu, J., Li, K., & Hao, B. (2019, 5 6). Image Restoration by Second-Order Total Generalized Variation and Wavelet Frame Regularization. Complexity, 1-17. doi:https://doi.org/10.1155/2019/3650128
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