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 discretized 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 regularization schemes as the number of measurements and the dimension of the discretization tend to infinity under natural and easily verifiable conditions for the discretization.

中文翻译：

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在未知的非高斯白噪声下正则化线性逆问题，允许重复测量

我们处理希尔伯特空间设置中的一般线性逆问题的解决方案。确切的右手边是未知的，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。我们展示了针对先验和后验正则化方案的无限维问题的真实解决方案的收敛性，因为在离散化的自然且易于验证的条件下，离散化的测量次数和维数趋于无穷大。