Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Algorithms for simultaneous sparse approximation: part I: Greedy pursuit
Signal Processing - Sparse approximations in signal and image processing
Algorithms for simultaneous sparse approximation: part II: Convex relaxation
Signal Processing - Sparse approximations in signal and image processing
Spectrum-blind minimum-rate sampling and reconstruction of multiband signals
ICASSP '96 Proceedings of the Acoustics, Speech, and Signal Processing, 1996. on Conference Proceedings., 1996 IEEE International Conference - Volume 03
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
Theoretical Results on Sparse Representations of Multiple-Measurement Vectors
IEEE Transactions on Signal Processing
A Theory for Sampling Signals From a Union of Subspaces
IEEE Transactions on Signal Processing
Reduce and Boost: Recovering Arbitrary Sets of Jointly Sparse Vectors
IEEE Transactions on Signal Processing - Part I
Sparse solutions to linear inverse problems with multiple measurement vectors
IEEE Transactions on Signal Processing
Minimum rate sampling and reconstruction of signals with arbitrary frequency support
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Compressed sensing of analog signals in shift-invariant spaces
IEEE Transactions on Signal Processing
Block sparsity and sampling over a union of subspaces
DSP'09 Proceedings of the 16th international conference on Digital Signal Processing
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
Sampling piecewise sinusoidal signals with finite rate of innovation methods
IEEE Transactions on Signal Processing
Spectral analysis of nonuniformly sampled data -- a review
Digital Signal Processing
Multirate synchronous sampling of sparse multiband signals
IEEE Transactions on Signal Processing
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
Beyond Nyquist: efficient sampling of sparse bandlimited signals
IEEE Transactions on Information Theory
Regularized sampling of multiband signals
IEEE Transactions on Signal Processing
Fast block-sparse decomposition based on SL0
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Reconstruction of compressed samples in shift-invariant space base on matrix factorization
Computers and Electrical Engineering
Group polytope faces pursuit for recovery of block-sparse signals
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
Block-sparse recovery via redundant block OMP
Signal Processing
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We address the problem of reconstructing a multi-band signal from its sub-Nyquist pointwise samples, when the band locations are unknown. Our approach assumes an existing multi-coset sampling. To date, recovery methods for this sampling strategy ensure perfect reconstruction either when the band locations are known, or under strict restrictions on the possible spectral suppprts. In this paper, only the number of bands and their widths are assumed without any other limitations on the support. We describe how to choose the parameters of the multicoset sampling so that a unique multiband signal matches the given samples. To recover the signal, the continuous recontruction is replaced by a single finite-dimensional problem without the need for discretization. The resulting problem is studied within the framework of compressed sensing, and thus can be solved efficiently using known tractable algorithms from this emerging area. We also develop a theoretical lower bound on the average sampling rate required for blind signal reconstruction, which is twice the minimal rate of known-spectrum recovery. Our method ensures perfect reconstruction for a wide class of signals sampled at the minimal rate, and provides a first systematic study of compressed sensig in a truly analog setting. Numerical experiments are presented demonstrating blind sampling and reconstruction with minimal sampling rate.