A speed preserving Hilbert gradient flow for generalized integral Menger curvature

We establish long-time existence for a projected Sobolev gradient flow of generalized integral Menger curvature in the Hilbert case and provide C 1 , 1 C^{1,1} -bounds in time for the solution that only depend on the initial curve. The self-avoidance property of integral Menger curvature guarantees that the knot class of the initial curve is preserved under the flow, and the projection ensures that each curve along the flow is parametrized with the same speed as the initial configuration. Finally, we describe how to simulate this flow numerically with substantially higher efficiency than in the corresponding numerical L 2 L^{2} gradient descent or other optimization methods.

An Efficient Local Block Sobolev Gradient and Laplacian Approach for Elimination of Atmospheric Turbulence

A long range observing systems can be sturdily affected by scintillations. These scintillations are caused by changes in atmospheric conditions. In recent years, various turbulence mitigation approaches for turbulence mitigation have been exhibiting a promising nature. In this paper, we propose an effectual method to alleviate the effects of atmospheric distortion on observed images and video sequences. These sequences are mainly affected through floating air turbulence which can severely degrade the image quality. The existing algorithms primarily focus on the removal of turbulence and provides a solution only for static scenes, where there is no moving entity (real motion). As in the traditional SGL algorithm, the updated frame is iteratively used to correct the turbulence. This approach reduces the turbulence effect. However, it imposes some artifacts on the real motion that blurs the object. The proposed method is an alteration of the existing Sobolev Gradient and Laplacian (SGL) algorithm to eliminate turbulence. It eliminates the ghost artifact formed on moving object in the existing approach. The proposed method alleviates turbulence without harming the moving objects in the scene. The method is demonstrated on significantly distorted sequences provided by OTIS and compared with the SGL technique. The information conveyed in the scene becomes clearly visible through the method on exclusion of turbulence. The proposed approach is evaluated using standard performance measures such as MSE, PSNR and SSIM. The evaluation results depict that the proposed method outperforms the existing state-of-the-art approaches for all three standard performance measures.