论文标题
在无约束的白噪声下，一般线性反问题的无噪声水平无噪声正则化
Noise level free regularisation of general linear inverse problems under unconstrained white noise
论文作者
论文摘要
在本说明中，我们通过应用（修改的）启发式差异原理解决了噪声水平和噪声分布的知识，解决了一般的统计反问题。在此，通过引入辅助离散维度并以自适应方式选择它，从而控制了无界（非高斯）噪声。我们首先显示了完全任意的紧凑型远期操作员和地面解决方案的收敛性。然后，在特定的类似贝叶斯的环境中量化了达到最佳收敛速率的不确定性。
In this note we solve a general statistical inverse problem under absence of knowledge of both the noise level and the noise distribution via application of the (modified) heuristic discrepancy principle. Hereby the unbounded (non-Gaussian) noise is controlled via introducing an auxiliary discretisation dimension and choosing it in an adaptive fashion. We first show convergence for completely arbitrary compact forward operator and ground solution. Then the uncertainty of reaching the optimal convergence rate is quantified in a specific Bayesian-like environment.
