Bayesian methods and maximum entropy for ill-posed inverse problems

• 成果类型: Article
• 署名作者: Gamboa, F; Gassiat, E
• 署名单位: Universite Paris Saclay; Universite Paris Saclay; Universite Paris 13
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 328-350
• 关键词: superresolution; probability

摘要

In this paper, we study linear inverse problems where some generalized moments of an unknown positive measure are observed, We introduce a new construction, called the maximum entropy on the mean method (MEM), which relies on a suitable sequence of finite-dimensional discretized inverse problems. Its advantage is threefold: It allows us to interpret all usual deterministic methods as Bayesian methods; it gives a very convenient way of taking into account prior information; it also leads to new criteria for the existence question concerning the linear inverse problem which will be a starting point for the investigation of superresolution phenomena. The key tool in this work is the large deviations property of some discrete random measure connected with the reconstruction procedure.