基于交替迭代的均匀噪声消除算法

Uniform Noise Removal Algorithm Based on Alternating Direction

均匀噪声消除在数学上可以表示为一个带有无穷范数L∞约束的最小化问题,但无穷范数的不可微性会造成数值处理困难。为此,利用交替迭代算法求解该问题。引入一个凸示范性函数,根据变量分离的原则将原问题转化为2个具有解析解的最小化子问题。在此基础上,分别对不同的子问题进行求解,从而得到交替迭代公式。实验结果表明,对于一维逆热传导问题和二维逆源问题,交替迭代算法在精度和时间方面都有较好的性能提升效果。

The problem of uniform noise removal can be formulated as an L∞ norm constrained minimization problem.The numerical difficulty arises from the non-differentiability of the L∞ norm. In this paper,the alternating direction algorithm is exploited to solve this problem. Firstly,by introducing a convex speculative function,it decomposes the original problem into two minimization subproblems with analytic solutions due to variables are separable. Secondly,it solves the different subproblems separately,then obtains the alternating direction iteration. Experimental results show that the proposed method has good effects of performance improvement on the one-dimensional inverse heat conduction problem and two-dimensional inverse source problem in accuracy and time.