Blind multiband signal reconstruction: compressed sensing for analog signals
IEEE Transactions on Signal Processing
Compressed sensing of analog signals in shift-invariant spaces
IEEE Transactions on Signal Processing
On the reconstruction of block-sparse signals with an optimal number of measurements
IEEE Transactions on Signal Processing
Compressive-projection principal component analysis
IEEE Transactions on Image Processing
Comparing measures of sparsity
IEEE Transactions on Information Theory
Block sparsity and sampling over a union of subspaces
DSP'09 Proceedings of the 16th international conference on Digital Signal Processing
Explicit thresholds for approximately sparse compressed sensing via l1-optimization
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Robust recovery of signals from a structured union of subspaces
IEEE Transactions on Information Theory
Uncertainty relations for shift-invariant analog signals
IEEE Transactions on Information Theory
Recovering signals from lowpass data
IEEE Transactions on Signal Processing
Time-delay estimation from low-rate samples: a union of subspaces approach
IEEE Transactions on Signal Processing
Block-sparse signals: uncertainty relations and efficient recovery
IEEE Transactions on Signal Processing
Average case analysis of multichannel sparse recovery using convex relaxation
IEEE Transactions on Information Theory
Theoretical and empirical results for recovery from multiple measurements
IEEE Transactions on Information Theory
Randomization of data acquisition and l1-optimization (recognition with compression)
Automation and Remote Control
SIAM Journal on Scientific Computing
Efficient feedback scheme based on compressed sensing in MIMO wireless networks
Computers and Electrical Engineering
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The rapid developing area of compressed sensing suggests that a sparse vector lying in a high dimensional space can be accurately and efficiently recovered from only a small set of nonadaptive linear measurements, under appropriate conditions on the measurement matrix. The vector model has been extended both theoretically and practically to a finite set of sparse vectors sharing a common sparsity pattern. In this paper, we treat a broader framework in which the goal is to recover a possibly infinite set of jointly sparse vectors. Extending existing algorithms to this model is difficult due to the infinite structure of the sparse vector set. Instead, we prove that the entire infinite set of sparse vectors can be recovered by solving a single, reduced-size finite-dimensional problem, corresponding to recovery of a finite set of sparse vectors. We then show that the problem can be further reduced to the basic model of a single sparse vector by randomly combining the measurements. Our approach is exact for both countable and uncountable sets, as it does not rely on discretization or heuristic techniques. To efficiently find the single sparse vector produced by the last reduction step, we suggest an empirical boosting strategy that improves the recovery ability of any given suboptimal method for recovering a sparse vector. Numerical experiments on random data demonstrate that, when applied to infinite sets, our strategy outperforms discretization techniques in terms of both run time and empirical recovery rate. In the finite model, our boosting algorithm has fast run time and much higher recovery rate than known popular methods.