允许重复测量的未知非高斯白噪声下正则化线性逆问题
Regularising linear inverse problems under unknown non-Gaussian white noise allowing repeated measurements
摘要：
我们在希尔伯特空间中讨论了一般线性反问题的解。准确的右手侧是未知的，并且只能通过被具有未知任意分布的白噪声破坏的离散测量来访问。测量过程可以重复，这允许通过平均来减少和估计测量误差。我们显示收敛对真正的解决方案的无穷维问题的先验和后验正则化计划的测量和离散化的维数趋于无穷大的自然和易于验证的条件下的离散化。
英文摘要：
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.
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