Oblique Duality for Fusion Frames

MORILLAS, PATRICIA M.; HEINEKEN, SIGRID B.

Ciudad de Buenos Aires

Conferencia; CIMPA2017 Research School - IX Escuela Santaló - Harmonic Analysis, Geometric Measure Theory and Applications; 2017

We introduce and develop the concept of oblique duality for fusionframes. This concept provides a mathematical framework to deal withproblems in distributed signal processing where the signalsconsidered as elements in a Hilbert space are, under certainrequirements, analyzed in one subspace and reconstructed in anothersubspace. The requirements are, on one side, the uniqueness of thereconstructed signal, and on the other what we call consistency ofthe sampling for fusion frames. Both conditions are naturallyrelated to oblique projections. We study the main properties ofoblique dual fusion frames and oblique dual fusion frame systems andpresent several results that provide alternative methods for theirconstruction.