Gradient-based compressive sensing for noise image and video reconstruction

In this study, a fast gradient-based compressive sensing (FGB-CS) for noise image and video is proposed. Given a noise image or video, the authors first make it sparse by orthogonal transformation, and then reconstruct it by solving a convex optimisation problem with a novel gradient-based method. The main contribution is twofold. Firstly, they deal with the noise signal reconstruction as a convex minimisation problem, and propose a new compressive sensing based on gradient-based method for noise image and video. Secondly, to improve the computational efficiency of gradient-based compressive sensing, they formulate the convex optimisation of noise signal reconstruction under Lipschitz gradient and replace the iteration parameter by the Lipschitz constant. With this strategy, the convergence of our FGB-CS is reduced from O(1/k) to O(1/k²). Experimental results indicate that their FGB-CS method is able to achieve better performance than several classical algorithms.