This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain non-asymptotic bounds on the reconstruction error attained by maximum a posteriori estimators. The new theory explains how hierarchical Bayesian models that exploit sparsity, group sparsity, and sparse representations of the unknown parameter can achieve accurate reconstructions in high-dimensional settings.

翻译：本文利用高维统计技术分析了分层贝叶斯反问题。我们的分析借助一种称为近似可分解性的分层贝叶斯正则化器性质，获得了最大后验估计器重构误差的非渐近界。这一新理论揭示了利用未知参数的稀疏性、群稀疏性及稀疏表示的分层贝叶斯模型，如何在高维场景下实现精确重构。