A Statistical view of Iterative Methods for Linear Inverse Problems

Maxiset point of view for signal detection in inverse problems

This paper extends the successful maxiset paradigm from function estimation to signal detection in inverse problems. In this context, the maxisets do not have the same shape compared to the classical estimation framework. Nevertheless, we introduce a robustified version of these maxisets, allowing to exhibit tail conditions on the signals of interest. Under this novel paradigm we are able to compare direct and indirect testing procedures.

面向对称正定矩阵的迭代分块矩阵求逆（IBMI）算法及其在协方差矩阵中的应用

An Iterative Block Matrix Inversion (IBMI) Algorithm for Symmetric Positive Definite Matrices with Applications to Covariance Matrices

针对大型对称正定矩阵直接求逆复杂度极高的难题，提出迭代分块矩阵求逆算法IBMI，通过分块迭代逼近逆矩阵，证明两块非重叠方法收敛，数值结果支持多块重叠方法也收敛。

分层贝叶斯逆问题：高维统计视角

Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint

本文从高维统计视角分析分层贝叶斯逆问题，利用正则化器的近似可分性获得最大后验估计重建误差的非渐近界，并解释了利用稀疏性的模型在高维环境下的准确重建机制。

On a Dynamic Variant of the Iteratively Regularized Gauss-Newton Method with Sequential Data

For numerous parameter and state estimation problems, assimilating new data as they become available can help produce accurate and fast inference of unknown quantities. While most existing algorithms for solving those kind of ill-posed inverse problems can only be used with a single instance of the observed data, in this work we propose a new framework that enables existing algorithms to invert multiple instances of data in a sequential fashion. Specifically we will work with the well-known iteratively regularized Gauss-Newton method (IRGNM), a variational methodology for solving nonlinear inv…