Structured sampling of structured signals

The paper considers structured sampling of structured signals, more specifically, using block diagonal (BD) measurement matrices to sense signals with uniform partitions that share the same sparsity profile. This model arises in distributed compressive sensing systems. In general, the fact that the number of nonzero entries in the measurement matrix is smaller than in a dense matrix leads to the need for more measurements. However, taking advantage of a certain structure in the sparse signal allows one to relax the conditions on the measurement matrix for the restricted isometry property (RIP) to hold, thus allowing for higher compression rate. We systematically provide guarantees for a unique solution, and also an efficient recovery method. The analysis relies on the RIP of the random BD matrix for signals in a particular union of subspaces. Also, we show how our theoretical results can be used to analyze the multiple measurement vector (MMV) problem.

[1]  R. DeVore,et al.  A Simple Proof of the Restricted Isometry Property for Random Matrices , 2008 .

[2]  Richard G. Baraniuk,et al.  Distributed Compressive Sensing , 2009, ArXiv.

[3]  J. Tropp,et al.  SIGNAL RECOVERY FROM PARTIAL INFORMATION VIA ORTHOGONAL MATCHING PURSUIT , 2005 .

[4]  Yonina C. Eldar,et al.  Robust Recovery of Signals From a Structured Union of Subspaces , 2008, IEEE Transactions on Information Theory.

[5]  Joel A. Tropp,et al.  Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit , 2007, IEEE Transactions on Information Theory.

[6]  Jie Chen,et al.  Theoretical Results on Sparse Representations of Multiple-Measurement Vectors , 2006, IEEE Transactions on Signal Processing.

[7]  Yonina C. Eldar,et al.  Rank Awareness in Joint Sparse Recovery , 2010, IEEE Transactions on Information Theory.

[8]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[9]  Yonina C. Eldar,et al.  Average Case Analysis of Multichannel Sparse Recovery Using Convex Relaxation , 2009, IEEE Transactions on Information Theory.

[10]  Yonina C. Eldar,et al.  Structured Compressed Sensing: From Theory to Applications , 2011, IEEE Transactions on Signal Processing.

[11]  Michael B. Wakin,et al.  The Restricted Isometry Property for Random Block Diagonal Matrices , 2012, ArXiv.

[12]  Volkan Cevher,et al.  Model-Based Compressive Sensing , 2008, IEEE Transactions on Information Theory.

[13]  Mike E. Davies,et al.  Sampling Theorems for Signals From the Union of Finite-Dimensional Linear Subspaces , 2009, IEEE Transactions on Information Theory.

[14]  Michael B. Wakin,et al.  Concentration of Measure for Block Diagonal Matrices With Applications to Compressive Signal Processing , 2011, IEEE Transactions on Signal Processing.