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Levenberg-Marquardt Algorithm Applied for Foggy Image Enhancement
Volume 35, Issue 1 (2024), pp. 47–63
Pub. online: 19 October 2023      Type: Research Article      Open accessOpen Access
Received
1 September 2022
Accepted
1 October 2023
Published
19 October 2023

Abstract

In this paper, we introduce a novel Model Based Foggy Image Enhancement using Levenberg-Marquardt non-linear estimation (MBFIELM). It presents a solution for enhancing image quality that has been compromised by homogeneous fog. Given an observation set represented by a foggy image, it is desired to estimate an analytical function dependent on adjustable variables that best cross the data in order to approximate them. A cost function is used to measure how the estimated function fits the observation set. Here, we use the Levenberg-Marquardt algorithm, a combination of the Gradient descent and the Gauss-Newton method, to optimize the non-linear cost function. An inverse transformation will result in an enhanced image. Both visual assessments and quantitative assessments, the latter utilizing a quality defogged image measure introduced by Liu et al. (2020), are highlighted in the experimental results section. The efficacy of MBFIELM is substantiated by metrics comparable to those of recognized algorithms like Artificial Multiple Exposure Fusion (AMEF), DehazeNet (a trainable end-to-end system), and Dark Channel Prior (DCP). There exist instances where the performance indices of AMEF exceed those of our model, yet there are situations where MBFIELM asserts superiority, outperforming these standard-bearers in algorithmic efficacy.

References

 
Bellavia, S., Gratton, S., Riccietti, E. (2018). A Levenberg-Marquardt method for large nonlinear least-squares problems with dynamic accuracy in functions and gradients. Numerische Mathematik, 140(3), 791–825. https://doi.org/10.1007/s00211-018-0977-z.
 
Cai, B., Xu, X., Jia, K., Qing, C., Tao, D. (2016). DehazeNet: an end-to-end system for single image haze removal. IEEE Transactions on Image Processing, 25(11), 5187–5198. https://doi.org/10.1109/TIP.2016.2598681.
 
Chen, L., Ma, Y. (2023). A new modified Levenberg–Marquardt Method for systems of nonlinear equations. Journal of Mathematics, 45. https://doi.org/10.1155/2023/6043780.
 
Curilă, S., Curilă, M., Curilă (Popescu), D., Grava, C. (2020). A mathematical model and an experimental setup for the rendering of the sky scene in a foggy day. Revue Roumaine des Sciences Techniques – Électrotechnique et Énergétique, 65(3-4), 265–270.
 
Fan, J. (2012). The modified Levenberg-Marquardt method for nonlinear equations with cubic convergence. Mathematics of Computation, 81(277), 447–466.
 
Galdran, A. (2018). Image dehazing by artificial multiple-exposure image fusion. Signal Processing, 149, 135–147. https://doi.org/10.1016/j.sigpro.2018.03.008.
 
He, K., Sun, J., Tang, X. (2011). Single image haze removal using dark channel prior. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33(12), 2341–2353. https://doi.org/10.1109/CVPR.2009.5206515.
 
Karas, E.W., Santos, S.A., Svaiter, B.F. (2016). Algebraic rules for computing the regularization parameter of the Levenberg–Marquardt method. Computational Optimization and Applications, 65(3), 723–751. https://doi.org/10.1007/s10589-016-9845-x.
 
Kim, K., Kim, S., Kim, K.-S. (2018). Effective image enhancement techniques for fog-affected indoor and outdoor images. IET Image Processing, 12(4), 465–471. https://doi.org/10.1049/iet-ipr.2016.0819.
 
Li, B., Gou, Y., S., G., Liu, J.Z., Zhou, J.T., Peng, X. (2021). You only look yourself: unsupervised and untrained single image dehazing neural network. International Journal of Computer Vision, 129, 1754–1767. https://doi.org/10.1007/s11263-021-01431-5.
 
Liu, W., Zhou, F., Lu, T., Duan, J., Qiu, G. (2020). Image defogging quality assessment: real-world database and method. IEEE Transactions on Image Processing, 30, 176–190. https://doi.org/10.1109/IVS.2010.5548128.
 
Masoud, A., Francisco, A.A. J., Ronan, M.T.F., Phan, T.V. (2019). Local convergence of the Levenberg-Marquardt method under Hölder metric subregularity. Advances in Computational Mathematics, 45, 2771–2806. https://doi.org/10.1007/s10444-019-09708-7.
 
Musa, Y.B., Waziri, M.Y., Halilu, A.S. (2017). On computing the regularization parameter for the Levenberg-Marquardt method via the spectral radius approach to solving systems of nonlinear equations. Journal of Numerical Mathematics and Stochastics, 9(1), 80–94.
 
Sejal, R., Mitul, P. (2014). Removal of the fog from the image using filters and colour model. International Journal of Engineering Research & Technology, 3(1), 553–557.
 
Sokolik, I.N. (2021). Principles of passive remote sensing using emission and applications: remote sensing of atmospheric path-integrated quantities (cloud liquid water content and precipitable water vapor). http://irina.eas.gatech.edu/EAS8803_Fall2017/Petty_8.pdf Accessed November 2021; https://www.docsity.com/en/basic-radiometric-quantities-the-beer-bouguer-lambert-law-eas-8803/6417363/ Accessed July 2023.
 
Tarel, J.-P., Hautière, N., Cord, A., Gruyer, D., Halmaoui, H. (2010). Improved visibility of road scene images under heterogeneous fog. In: Intelligent Vehicles Symposium, (IV’10), La Jolla, CA, USA, pp. 478–485. http://perso.lcpc.fr/tarel.jean-philippe/bdd/frida.html. https://doi.org/10.1109/IVS.2010.5548128.
 
Umar, A.O., Sulaiman, I.M., Mamat, M., Waziri, M.Y., Zamri, N. (2021). On damping parameters of Levenberg-Marquardt algorithm for nonlinear least square problems. Journal of Physics: Conference Series, 1734(1), 012018. https://doi.org/10.1088/1742-6596/1734/1/012018.
 
Xu, Y., Wen, J., Fei, L., Zhang, Z. (2016). Review of video and image defogging algorithms and related studies on image restoration and enhancement. IEEE Access, 4, 165–188. https://doi.org/10.1109/ACCESS.2015.2511558.

Biographies

Curila Sorin
https://orcid.org/0000-0001-9865-9855
scurila@uoradea.ro

S. Curila graduated in 1994 with the applied electronics specialization from the Technical University of Cluj-Napoca, Romania, and received in 2000 his PhD in electrical engineering from the University of Oradea, Romania (Compression of 3D polygonal models). He holds a university professor position at the Department of Electronics and Telecommunications of University of Oradea, Romania. His research interests include: pattern recognition, signal and image processing, programming languages.

Curila Mircea
mcurila@uoradea.ro

M. Curila graduated in 1994 with the applied electronics specialization from the Technical University of Cluj-Napoca, Romania, and in 1995 with the mathematics specialization from the Babes-Bolyai University of Cluj-Napoca, Romania. He received in 2003 his PhD in electrical engineering from the University of Oradea, Romania. He holds a university professor position at the Department of Environmental Engineering of University of Oradea, Romania. His research interests include: virtual reality, signal and image processing, programming languages.

Curila (Popescu) Diana
curila_diana@yahoo.com

D. Curila (Popescu) graduated in 1995 with the mathematics specialization from the Babes-Bolyai University of Cluj-Napoca, Romania. She is a PhD student at the Faculty of Informatics and Science, University of Oradea, Romania. She is currently a mathematics teacher at Dacia School, Oradea, Romania.

Grava Cristian
https://orcid.org/0000-0002-6316-1368
cgrava@uoradea.ro

C. Grava is a senior member of IEEE. He received his PhD in electronics and telecommunications from the Politehnica University of Bucharest, Romania, and in images and systems, from the National Institute of Applied Sciences from Lyon, France, in 2003. He is a professor at the University Oradea, Romania, a member of the Department of Electronics and Telecommunications. His research interests include signal and image processing, modelling of complex systems and artificial intelligence.


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Keywords
least squares problem Levenberg-Marquardt foggy images image enhancement

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