自适应全变分(adaptive total variation,ATV)模型可以利用差分曲率自适应地选择基于Lp范数的正则项,并且能自适应调节正则项与保真项的权重,能够有效地去除噪声和保持图像边缘.使用半隐式梯度下降法求解ATV模型时,误差的高频分量会快...自适应全变分(adaptive total variation,ATV)模型可以利用差分曲率自适应地选择基于Lp范数的正则项,并且能自适应调节正则项与保真项的权重,能够有效地去除噪声和保持图像边缘.使用半隐式梯度下降法求解ATV模型时,误差的高频分量会快速衰减而低频分量却衰减缓慢,从而导致收敛速度缓慢.为了加快低频误差衰减的速度,利用半隐式梯度下降法设计了光滑化方法,构造了求解ATV模型的非线性多重网格法,并通过与不动点迭代法、半隐式梯度下降法的对比实验,验证了新方法的去噪效果更好且计算速度更快.展开更多
We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of the nonlinear eigenvalue problem into a series of solutions of the corresponding linear ...We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of the nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and nonlinear eigenvalue problems on the coarsest finite element space. The linearized boundary value problems are solved by some multigrid iterations.Besides the multigrid iteration, all other efficient iteration methods for solving boundary value problems can serve as the linear problem solver. We prove that the computational work of this new scheme is truly optimal,the same as solving the linear corresponding boundary value problem. In this case, this type of iteration scheme certainly improves the overfull efficiency of solving nonlinear eigenvalue problems. Some numerical experiments are presented to validate the efficiency of the new method.展开更多
文摘自适应全变分(adaptive total variation,ATV)模型可以利用差分曲率自适应地选择基于Lp范数的正则项,并且能自适应调节正则项与保真项的权重,能够有效地去除噪声和保持图像边缘.使用半隐式梯度下降法求解ATV模型时,误差的高频分量会快速衰减而低频分量却衰减缓慢,从而导致收敛速度缓慢.为了加快低频误差衰减的速度,利用半隐式梯度下降法设计了光滑化方法,构造了求解ATV模型的非线性多重网格法,并通过与不动点迭代法、半隐式梯度下降法的对比实验,验证了新方法的去噪效果更好且计算速度更快.
基金supported by National Natural Science Foundation of China (Grant Nos. 91330202, 11371026, 11201501, 11571389, 11001259 and 11031006)National Basic Research Program of China (Grant No. 2011CB309703)the National Center for Mathematics and Interdisciplinary Science, Chinese Academy of Sciences, the President Foundation of Academy of Mathematics and Systems Science, Chinese Academy of Sciences and the Program for Innovation Research in Central University of Finance and Economics
文摘We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of the nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and nonlinear eigenvalue problems on the coarsest finite element space. The linearized boundary value problems are solved by some multigrid iterations.Besides the multigrid iteration, all other efficient iteration methods for solving boundary value problems can serve as the linear problem solver. We prove that the computational work of this new scheme is truly optimal,the same as solving the linear corresponding boundary value problem. In this case, this type of iteration scheme certainly improves the overfull efficiency of solving nonlinear eigenvalue problems. Some numerical experiments are presented to validate the efficiency of the new method.
