A New Method for TSVD Regularization Truncated Parameter Selection
A New Method for TSVD Regularization Truncated Parameter Selection
复制标题
DOI：
10.1155/2013/161834
复制
发表时间：
2013-11
影响因子：
--
通讯作者：
Z. Wu;S. Bian;C. Xiang;Yude Tong
中科院分区：
文献类型：
--
作者：
Z. Wu;S. Bian;C. Xiang;Yude Tong
研究了截断奇异值分解（TSVD）正则化在不适定问题中的应用。通过数学分析，提出了一种新的截断参数选择方法，并应用于TSVD正则化。该方法首先考虑观测噪声的区间估计，选取所有局部最优截断参数，然后从局部最优截断参数中选取最优截断参数。在将新方法与传统的广义交叉验证法（GCV）和曲线法进行比较时，为了使比较结果尽可能具有统计意义，提出了一种随机不适定矩阵模拟方法.仿真实验表明，新方法求解的解具有最小的均方误差，且计算量最小。
The truncated singular value decomposition (TSVD) regularization applied in ill-posed problem is studied. Through mathematical analysis, a new method for truncated parameter selection which is applied in TSVD regularization is proposed. In the new method, all the local optimal truncated parameters are selected first by taking into account the interval estimation of the observation noises; then the optimal truncated parameter is selected from the local optimal ones. While comparing the new method with the traditional generalized cross-validation (GCV) and curve methods, a random ill-posed matrices simulation approach is developed in order to make the comparison as statistically meaningful as possible. Simulation experiments have shown that the solutions applied with the new method have the smallest mean square errors, and the computational cost of the new algorithm is the least.