Signal expansions using frames may be considered as generalizations of signal representations based on transforms and filter banks. Frames for sparse signal representations may be designed using an iterative method with two main steps: (1) Frame vector selection and expansion coefficient determination for signals in a training set, – selected to be representative of the signals for which compac...

We describe some contributions of the knowledge representation system FROME to the exploitation of class hierarchies. In order to cope with incomplete, subjective and changing knowledge, FROME proposes multiple and evolutive representation of frames. Multiple representation in FROME allows to describe and manipulate entities from different points of view. Point of view selection on frames contr...

‎in this paper‎, ‎first we develop the duality concept for $g$-bessel sequences‎ ‎and bessel fusion sequences in hilbert spaces‎. ‎we obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎we also expand every $g$-bessel ‎sequence to a frame by summing some elements‎. ‎we define the restricted isometry property for ‎$g$-frames and generalize some resu...