论文标题
在未知的非高斯白噪声下正规化线性逆问题,可以重复测量
Regularising linear inverse problems under unknown non-Gaussian white noise allowing repeated measurements
论文作者
论文摘要
我们处理希尔伯特空间设置中通用线性反问题的解决方案。确切的右侧是未知的,只能通过由未知的任意分布损坏的离散测量来访问。可以重复测量过程,从而可以通过平均来减少和估计测量误差。我们对先验和后正则化方案的无限二维问题的真实解决方案表示,作为测量的数量和离散化的维度倾向于在自然且易于证实的条件下进行离散化。
We deal with the solution of a generic linear inverse problem in the Hilbert space setting. The exact right hand side is unknown and only accessible through discretised measurements corrupted by white noise with unknown arbitrary distribution. The measuring process can be repeated, which allows to reduce and estimate the measurement error through averaging. We show convergence against the true solution of the infinite-dimensional problem for a priori and a posteriori regularisation schemes as the number of measurements and the dimension of the discretisation tend to infinity under natural and easily verifiable conditions for the discretisation.