On The Acceleration Of PDE-based Differential Schemes In Image Processing

The PDE-based method is one of the most significant techniques in image processing. The paper presents novel accelerated AOS schemes and FP-ADI schemes for the model of mean curvature motion(MCM),CLMC,Total Variation (TV) and high-order TV, which are proved to be relevant. The PDE properties and the computing efficiency are analyzed and the conditions of stability,consistence,convergence and the complexity are given.Theoretical anlysis and implementation demonstrate the superiority of the presented schemes. The accelerated AOS schemes are stable unconditionally and consistent with nonlinear parobolic equations conditionally. They effectively remove the noisy data, preserve the edge and detailed information,and reduce the staircasing effect.Meanwhile, they are at least two times faster than the original schemes, so that the CPU time and memory storage are largely reduced.Accelerated FP-ADI scheme is three times faster than the conventional TV method.It prevents staircasing effect and texture loss effect, which is an ideal method in image restoration.