Name
Abstract | ||
|---|---|---|
Sparse representations have emerged as a powerful tool in signal and
information processing, culminated by the success of new acquisition and
processing techniques such as Compressed Sensing (CS). Fusion frames are very
rich new signal representation methods that use collections of subspaces
instead of vectors to represent signals. This work combines these exciting
fields to introduce a new sparsity model for fusion frames. Signals that are
sparse under the new model can be compressively sampled and uniquely
reconstructed in ways similar to sparse signals using standard CS. The
combination provides a promising new set of mathematical tools and signal
models useful in a variety of applications. With the new model, a sparse signal
has energy in very few of the subspaces of the fusion frame, although it does
not need to be sparse within each of the subspaces it occupies. This sparsity
model is captured using a mixed l1/l2 norm for fusion frames.
A signal sparse in a fusion frame can be sampled using very few random
projections and exactly reconstructed using a convex optimization that
minimizes this mixed l1/l2 norm. The provided sampling conditions generalize
coherence and RIP conditions used in standard CS theory. It is demonstrated
that they are sufficient to guarantee sparse recovery of any signal sparse in
our model. Moreover, an average case analysis is provided using a probability
model on the sparse signal that shows that under very mild conditions the
probability of recovery failure decays exponentially with increasing dimension
of the subspaces. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1109/TIT.2011.2143890 | Clinical Orthopaedics and Related Research |
Keywords | Field | DocType |
rich new signal representation,sparse recovery,sparse signal,signal sparse,new model,mixed l1,combined fusion frame measurements,fusion frame,signal model,l2 norm,sparse representation,signal detection,sensors,convex optimization,mutual coherence,compressive sampling,probabilistic logic,sparse matrices,compressed sensing,coherence,information processing,sensor fusion,probabilistic analysis,stochastic model,convex programming,minimization,stochastic processes,null space,probability,random matrices,signal processing | Signal processing,Pattern recognition,Computer science,Sparse approximation,Sensor fusion,Artificial intelligence,Fusion frame,Convex optimization,Sparse matrix,Mutual coherence,Compressed sensing | Journal |
Volume | Issue | ISSN |
57 | 6 | 0018-9448 |
Citations | PageRank | References |
26 | 1.25 | 28 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Petros T. Boufounos | 1 | 828 | 56.77 |
| Gitta Kutyniok | 2 | 325 | 34.77 |
| Holger Rauhut | 3 | 816 | 67.21 |