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不适定逆问题的贝叶斯方法与最大熵AI 解读

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;…

离散线性系统的盲反卷积AI 解读

We study the blind deconvolution problem in the case where the input noise has a finite discrete support and the transfer linear system is not necessarily minimum phase. We propose a new family of estimators built using algebraic considerations. The estimates are consistent under very wide assumptions: The input signal need not be independently distributed; the cardinality of the finite support may be estimated simultaneously. We consider in particular AR systems: In this…