首页> 外文期刊>BIT numerical mathematics >Unbiased predictive risk estimation of the Tikhonov regularization parameter: convergence with increasing rank approximations of the singular value decomposition
【24h】

Unbiased predictive risk estimation of the Tikhonov regularization parameter: convergence with increasing rank approximations of the singular value decomposition

机译:Tikhonov正则化参数的无偏预测风险估计:随着奇异值分解的秩近似增加而收敛

获取原文
获取原文并翻译 | 示例

摘要

The truncated singular value decomposition may be used to find the solution of linear discrete ill-posed problems in conjunction with Tikhonov regularization and requires the estimation of a regularization parameter that balances between the sizes of the fit to data function and the regularization term. The unbiased predictive risk estimator is one suggested method for finding the regularization parameter when the noise in the measurements is normally distributed with known variance. In this paper we provide an algorithm using the unbiased predictive risk estimator that automatically finds both the regularization parameter and the number of terms to use from the singular value decomposition. Underlying the algorithm is a new result that proves that the regularization parameter converges with the number of terms from the singular value decomposition. For the analysis it is sufficient to assume that the discrete Picard condition is satisfied for exact data and that noise completely contaminates the measured data coefficients for a sufficiently large number of terms, dependent on both the noise level and the degree of ill-posedness of the system. A lower bound for the regularization parameter is provided leading to a computationally efficient algorithm. Supporting results are compared with those obtained using the method of generalized cross validation. Simulations for two-dimensional examples verify the theoretical analysis and the effectiveness of the algorithm for increasing noise levels, and demonstrate that the relative reconstruction errors obtained using the truncated singular value decomposition are less than those obtained using the singular value decomposition.
机译:截断的奇异值分解可用于与Tikhonov正则化结合以找到线性离散不适定问题的解决方案,并且需要估计正则化参数,该参数在拟合数据函数的大小和正则项之间取得平衡。当测量中的噪声以已知方差正态分布时,无偏预测风险估计器是一种用于找到正则化参数的建议方法。在本文中,我们提供了一种使用无偏预测风险估计器的算法,该算法可从奇异值分解中自动找到正则化参数和要使用的项数。该算法的基础是一个新的结果,该结果证明了正则化参数与奇异值分解中的项数一致。为了进行分析,足以假设精确数据满足离散的Picard条件,并且噪声完全污染了所测数据系数的足够多项,具体取决于噪声水平和噪声的不适度。系统。提供正则化参数的下限,从而导致计算效率高的算法。将支持结果与使用广义交叉验证方法获得的结果进行比较。二维示例的仿真验证了理论分析和提高噪声水平的算法的有效性,并证明了使用截短奇异值分解获得的相对重建误差小于使用奇异值分解获得的相对重建误差。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱:kefu@zhangqiaokeyan.com

京公网安备:11010802029741号 ICP备案号:京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有
  • 客服微信

  • 服务号