The new notion of fusion frames will be presented in this article. Fusion frames provide an extensive framework
not only to model sensor networks, but also to serve as a means to improve robustness or develop efficient and
feasible reconstruction algorithms. Fusion frames can be regarded as sets of redundant subspaces each of which
contains a spanning set of local frame vectors, where the subspaces have to satisfy special overlapping properties.
Main aspects of the theory of fusion frames will be presented with a particular focus on the design of sensor
networks. New results on the construction of Parseval fusion frames will also be discussed.
Detection of military and civilian targets from airborne platforms using hyperspectral imaging (HSI) sensors is of great interest. Relative to multispectral sensing, hyperspectral sensing can increase the detectability of targets by exploiting finer detail in spectral signatures. A multitude of adaptive detection algorithms have appeared in the literature or have found their way into software packages and end-user systems. The most widely known among them is the linear matched filter. However, despite its popularity, the fact that the matched filter is used under conditions that deviate from the implicit optimality assumptions has not been investigated. The optimum linear matched filter assumes that the target and background spectra follow normal distributions with identical covariance matrices. However, in HSI data, the fundamental assumption about equal covariance matrices is likely violated. An analytic matched filter performance expression assuming unequal covariance matrices is derived, which also allows performance estimates under incomplete class descriptions (only a few principal components are known). Examples based on HSI data show that theoretical performance can be overly optimistic compared to actual performance. Example performance estimates based on incomplete class descriptions are shown to be more realistic because of the elongation of typical HSI data distribution hyperellipses.