Images taken in low-light conditions are frequently affected by limited visibility, diminished contrast and severe noise, adversely impacting the performance of various computer vision tasks. Most variational-based Retinex decomposition methods mainly depend on integer norms to constrain the illumination and reflectance components. However, this strategy may fail to achieve the ideal Retinex decomposition. In this paper, we propose a Retinex-based variational model that incorporates flexible constraints for both illumination and reflectance. Specifically, we impose the Lpnorm constraints with varying values of p to ensure the piece-wise smoothness of the illumination and promote the presence of abundant textures in the reflectance. Moreover, we develop two effective pixel-wise weight matrices that consider variance and gradients of the input image respectively, with the objective of preserving the structural edges of the illumination and retaining more details in the reflectance. In addition, we use an L2norm to estimate the overall noise level and avoid noise amplification. Through incorporating these above constraints, our proposed variational model can obtain a structure-aware illumination and a detail-revealed reflectance. Qualitative and quantitative comparisons on real-world and synthetic datasets indicate that our approach yields results with superior visual quality and outperforms several state-of-the-art algorithms on objective metrics. Besides, our algorithm can also address similar low-level computer vision challenges, such as image dehazing and underwater image enhancement. The source code is available at https://github.com/Enping-Hu/dual weighted lp.

The visibility of images plays a crucial role in Intelligent Transportation Systems (ITS). However, images captured under hazy environments can degrade visual quality, significantly reducing the working performance of ITS. Although existing dehazing methods have achieved remarkable performance for daytime hazy images, they struggle to overcome the unique degradations under nighttime haze conditions such as glows, weak illumination, hidden noise, and color distortions. To simultaneously address these degradations, we propose VNDHR, a novel Variational Nighttime Dehazing framework using Hybrid Regularization focusing on enhancing the perceptual visibility of nighttime hazy scenarios. Specifically, a new physical model that accounts for multiple degradations under nighttime haze conditions is first constructed. Then, a novel hybrid variational model comprising an$\ell _{p}$norm, a weighted$\ell _{2}$norm, and a total variation regularization is developed to obtain a structure-aware illumination and a noise-free reflectance, simultaneously. To remove the nonhomogeneous haze in the illumination, we employ the dark channel prior to estimate parameters in each grid patch. Furthermore, a simple but effective nonlinear stretching function is designed to enhance the texture in the decomposed reflectance component. Finally, the dehazed illumination and the stretched reflectance are combined to generate a haze-free result. Experiments performed on synthetic and real-world nighttime hazy images prove that our VNDHR framework achieves state-of-the-art dehazing performance, providing results with clear details and less noise. Besides, our VNDHR can also handle various types of degraded images well, such as low-light images, daytime hazy images, sandstorm images, and underwater images.