压缩感知理论在矩量法中的应用

Application of compressed sensing theory in the method of moments

矩阵填充与线性方程组求解是矩量法中最耗计算资源的环节.为提高计算效率,提出了一种基于压缩感知理论的矩量法的改进方法.通过引入稀疏变换矩阵实现对待求响应的稀疏表示,从而可在压缩感知理论框架下构造欠定方程,并优化求解.数值仿真实验结果表明:该方法不仅可以减小矩阵填充计算量,还可以有效提高解的求解效率.

Matrix filling and equation solving are the most computationally-expensive steps in the method of moments （MoM）. Based on the compressed sensing （CS） theory, an improved method of MoM is proposed in this paper. Through introducing sparse transform matrix, the unknown response can be expressed sparsely, so we can construct and optimally solving underdetermined equation under the framework of CS. Numerical examples show that the proposed method can reduce the matrix filling cost dramatically, and also can improve the efficiency of equation solving effectively.