Maximum entropy and the nearly black object.(With discussion). (English) Zbl 0788.62103

Donoho, David L.; Johnstone, Iain M.; Hoch, Jeffrey C.; Stern, Alan S.

J. R. Stat. Soc., Ser. B 54, No. 1, 41-81 (1992).

The authors give a description of the properties of the so-called ‘maximum entropy’ method. The paper is written against a background of some controversy with regard to the importance of the maximum entropy method for solving inverse problems. It deals with the application of this method to spectroscopy. It is shown that near-blackness is required, both for signal-to-noise enhancement and superresolution. The maximum entropy method is compared with other methods – in particular, minimum \(\ell_ 1\)-norm reconstruction. An appendix contains a critical discussion of the paper by proponents and users of the maximum entropy method.

Reviewer: B.Mathiszik (Halle)

MSC:

62P99	Applications of statistics
62B10	Statistical aspects of information-theoretic topics
62C20	Minimax procedures in statistical decision theory

Keywords:

magnetic resonance spectroscopy; minimum l1-norm reconstruction; maximum entropy method; inverse problems; near-blackness; signal-to-noise enhancement; superresolution