论文标题
Tikhonov正规化和非线性统计反问题的过度厚度罚款
Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems
论文作者
论文摘要
在本文中，我们考虑了统计学习环境中嘈杂数据的非线性逆问题。希尔伯特量表中的Tikhonov正则化方案被认为是从随机噪声数据中重建估计器的。在这种统计学习环境中，我们在某些假设对非线性前向操作员和先前的假设的某些假设下得出了正则化解决方案的收敛速率。我们使用复制内核希尔伯特空间的方法讨论重建误差的估计值。
In this paper, we consider the nonlinear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered to reconstruct the estimator from the random noisy data. In this statistical learning setting, we derive the rates of convergence for the regularized solution under certain assumptions on the nonlinear forward operator and the prior assumptions. We discuss estimates of the reconstruction error using the approach of reproducing kernel Hilbert spaces.
