  The problem of recovering signals of high complexity from low quality sensing
devices is analyzed via a combination of tools from signal processing and
harmonic analysis. By using the rich structure offered by the recent
development in fusion frames, we introduce a compressed sensing framework in
which we split the dense information into sub-channel or local pieces and then
fuse the local estimations. Each piece of information is measured by
potentially low quality sensors, modeled by linear matrices and recovered via
compressed sensing -- when necessary. Finally, by a fusion process within the
fusion frames, we are able to recover accurately the original signal.
  Using our new method, we show, and illustrate on simple numerical examples,
that it is possible, and sometimes necessary, to split a signal via local
projections and / or filtering for accurate, stable, and robust estimation. In
particular, we show that by increasing the size of the fusion frame, a certain
robustness to noise can also be achieved. While the computational complexity
remains relatively low, we achieve stronger recovery performance compared to
usual single-device compressed sensing systems.
