A Superior Image Reconstruction Algorithm Based on Total Variation Regularization for Lensless Imaging Systems

In recent years, lensless imaging system has been developed in certain areas. Generally, the objective scene and the measurements of the sensor are in a linear relationship in lensless imaging systems, which requires a computational algorithm to reconstruct an image of the scene. Existing methods include Tikhonov regularization and total variation(TV)-based regularization using partial differential equation(PDE). However, they either can’t reduce noise effectively, or run slowly. We propose a superior TV-based image reconstruction algorithm by employing variable splitting and Bregman iteration. Firstly, we split the objective function into two subproblems via introducing an auxiliary variable, and then solve them by Tikhonov regularization and anisotropic TV regularization separately. Finally, we alternate the two subproblems to achieve the optimal solution. Experiments on synthetic data with different level of degradations show that our algorithm has a better performance than other methods.