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Abstract
We consider the problem of constructing a linear map from a Hilbert space H (possibly infinite dimensional) to Rm that satisfies a restricted isometry property (RIP) on an arbitrary signal model, i.e., a subset of H. We present a generic framework that handles a large class of lowdimensional subsets but also unstructured and structured linear maps. We provide a simple recipe to prove that a random linear map satisfies a general RIP with high probability. We also describe a generic technique to construct linear maps that satisfy the RIP. Finally, we detail how to use our results in several examples, which allow us to recover and extend many known compressive sampling results.
Original language  English 

Pages (fromto)  2171  2187 
Journal  IEEE Transactions on Information Theory 
Volume  63 
Issue number  4 
Early online date  6 Feb 2017 
DOIs  
Publication status  Published  Apr 2017 
Keywords
 compressed sensing
 restricted isometry property
 boxcounting dimension
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Dive into the research topics of 'Recipes for stable linear embeddings from Hilbert spaces to R^m'. Together they form a unique fingerprint.Projects
 2 Finished

Exploiting low dimensional models in sensing, computation and signal processing
1/09/16 → 31/08/22
Project: Research

Profiles

Michael Davies
 School of Engineering  Jeffrey Collins Chair of Signal Processing
Person: Academic: Research Active