A maximum entropy statistical treatment of an inverse problem concerning frame theory is presented. The problem arises from the fact that a frame is an overcomplete set of vectors that defines a mapping with no unique inverse. Although any vector in the concomitant space can be expressed as a linear combination of frame elements, the coefficients of the expansion are not unique. Frame theory guarantees the existence of a set of coefficients which is “optimal” in a minimum norm sense. We show here that these coefficients are also “optimal” from a maximum entropy viewpoint.
Bibliographical noteCopyright 1997 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Rebollo - Neira, Laura; Fernandez-Rubio, J.; Fern, J. and Plastino, A. (1997) Frames: a maximum entropy statistical estimate of the inverse problem. Journal of Mathematical Physics, 38 (9). pp. 4863-4871. ISSN 0022-2488 and may be found at http://jmp.aip.org/jmapaq/v38/i9/p4863_s1
- maximum entropy statistical treatment
- inverse problem
- frame theory
- overcomplete set of vectors
- no unique inverse
Rebollo-Neira, L., Fernandez-Rubio, J., & Plastino, A. (1997). Frames: a maximum entropy statistical estimate of the inverse problem. Journal of Mathematical Physics, 38(9), 4863-4871. https://doi.org/10.1063/1.532130