Image denoising based on hybrid L0 and L1-norm regularization

In cases of insufficient lighting conditions, the obtained images of optical systems usually suffer from heavy noise, which subsequently has a negative impact on tasks like image segmentation, target detection, and edge extraction. Image denoising requires preserving the integrity of original information while eliminating irrelevant data from the signal. Regularization is an effective way to improve the performance of denoising algorithms, it achieves this by introducing additional constraints to ensure stable solutions. In this paper, we propose a hybrid regularization method which is based on the weighted combination of the L0-norm and L1-norm of image gradients. In order to obtain reliable denoising results, we have also developed a highly efficient alternately minimization algorithm to solve the resulting complex optimization problem. The algorithm utilizes variable splitting and Lagrange multipliers to determine the optimal solution, effectively transforming the initial problem into a simple convex optimization problem and a quadratic optimization problem, which can be rapidly solved in frequency domain. In the end, we conducted experiments to prove the efficiency of the proposed method. The results show that it is stable, efficient and the quality of the denoised images is comparable to some state-of-the-art methods.