The images captured under adverse weather conditions suffer from poor visibility and contrast problems. Such images are not suitable for computer vision analysis and similar applications. Therefore, image defogging/dehazing is one of the most intriguing topics. In this paper, a new, fast, and robust defogging/dehazing algorithm is proposed by combining the Retinex theory with independent component analysis, which performs better than existing algorithms. Initially, the foggy image is decomposed into two components: reflectance and luminance. The former is computed using the Retinex theory, while the latter is obtained by decomposing the foggy image into parallel and perpendicular components of air-light. Finally, the defogged image is obtained by applying Koschmieder's law. Simulation results demonstrate the absence of halo effects and the presence of high-resolution images. The simulation results also confirm the effectiveness of the proposed method when compared to other conventional techniques in terms of NIQE, FADE, SSIM, PSNR, AG, CIEDE2000, (r) over bar, and implementation time. All foggy and defogged results are available in high quality at the following link: https://drive.google.com/file/d/1OStXrfzdnF43gr6PAnBd8BHeThOfj33z/view?usp=drive_link.