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.