Low-Light Image Enhancement Using a Retinex-Based Variational Model With Weighted $L_{p}$ Norm Constraint

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 L<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> norm 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 L<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm 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.