Data-Driven Priors in the Maximum Entropy on the Mean Method for Linear Inverse Problems
Abstract
Abstract. We establish the theoretical framework for implementing the maximum entropy on the mean (MEM) method for linear inverse problems in the setting of approximate (data-driven) priors. We prove a.s. convergence for empirical means and further develop general estimates for the difference between the MEM solutions with different priors [Formula: see text] and [Formula: see text] based on the epigraphical distance between their respective log-moment generating functions. These estimates allow us to establish a rate of convergence in expectation for empirical means. We illustrate our results with denoising on the MNIST and Fashion-MNIST datasets.
Fields of Study & Subjects
Numerical methods in inverse problems
Image and Signal Denoising Methods
Optimization and Variational Analysis
Publication details
- Journal / source
- SIAM Journal on Mathematics of Data Science
- Volume
- 8
- Issue
- 1
- Pages
- 108–140
- Publication date
- 12 February 2026
- Language
- EN