基于结构风险最小化原则的奇异值分解降噪研究

Study on noise reduction in singular value decomposition based on structural risk minimization

针对奇异值分解降噪中矩阵有效秩的阶次难以确定的问题,提出了利用结构风险最小化原则来确定矩阵的有效秩阶次的新方法。该方法依据统计学习理论,把有效秩阶次的选择看作是一个学习过程,利用结构风险最小化原则来代替传统的经验风险最小化,从而自动得到奇异值分解降噪中矩阵的有效秩。仿真表明,该方法不但具有较好的降噪精度和算法稳定性,而且降低了消噪模型算法的复杂度。

The order of the effective rank of a matrix is difficult to determine for noise reduction in singular value decomposition. A method is presented for solving this problem based on structural risk minimization. Based on statistical learning theory, the determination of the order of an effective rank is considered a learning process. The order of the effective rank can be achieved by using the structural risk minimization (SRM) instead of the experience risk minimization (ERM). Simulation results show that this method has good noise reduction accuracy and deduces the complexity of the algorithm.