Combinatorial algorithms for compressed sensing
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Data compression and harmonic analysis
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Explicit constructions for compressed sensing of sparse signals
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Agnostically learning decision trees
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Sketching in adversarial environments
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Space-optimal heavy hitters with strong error bounds
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
On the reconstruction of block-sparse signals with an optimal number of measurements
IEEE Transactions on Signal Processing
Subspace pursuit for compressive sensing signal reconstruction
IEEE Transactions on Information Theory
Sublinear compressive sensing reconstruction via belief propagation decoding
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
A locally encodable and decodable compressed data structure
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Image representation by compressive sensing for visual sensor networks
Journal of Visual Communication and Image Representation
Approximate sparse recovery: optimizing time and measurements
Proceedings of the forty-second ACM symposium on Theory of computing
Fast Manhattan sketches in data streams
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Uncertainty principles and vector quantization
IEEE Transactions on Information Theory
Noisy signal recovery via iterative reweighted L1-minimization
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
CoSaMP: iterative signal recovery from incomplete and inaccurate samples
Communications of the ACM
Space-optimal heavy hitters with strong error bounds
ACM Transactions on Database Systems (TODS)
Sublinear time, measurement-optimal, sparse recovery for all
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Approximate Sparse Recovery: Optimizing Time and Measurements
SIAM Journal on Computing
On the Design of Deterministic Matrices for Fast Recovery of Fourier Compressible Functions
SIAM Journal on Matrix Analysis and Applications
Sketching in Adversarial Environments
SIAM Journal on Computing
Hard Thresholding Pursuit: An Algorithm for Compressive Sensing
SIAM Journal on Numerical Analysis
Strengthening hash families and compressive sensing
Journal of Discrete Algorithms
Compressed sensing construction of spectrum map for routing in cognitive radio networks
Wireless Communications & Mobile Computing
Sketching via hashing: from heavy hitters to compressed sensing to sparse fourier transform
Proceedings of the 32nd symposium on Principles of database systems
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Compressed Sensing is a new paradigm for acquiring the compressible signals that arise in many applications. These signals can be approximated using an amount of information much smaller than the nominal dimension of the signal. Traditional approaches acquire the entire signal and process it to extract the information. The new approach acquires a small number of nonadaptive linear measurements of the signal and uses sophisticated algorithms to determine its information content. Emerging technologies can compute these general linear measurements of a signal at unit cost per measurement. This paper exhibits a randomized measurement ensemble and a signal reconstruction algorithm that satisfy four requirements: 1. The measurement ensemble succeeds for all signals, with high probability over the random choices in its construction. 2. The number of measurements of the signal is optimal, except for a factor polylogarithmic in the signal length. 3. The running time of the algorithm is polynomial in the amount of information in the signal and polylogarithmic in the signal length. 4. The recovery algorithm offers the strongest possible type of error guarantee. Moreover, it is a fully polynomial approximation scheme with respect to this type of error bound. Emerging applications demand this level of performance. Yet no otheralgorithm in the literature simultaneously achieves all four of these desiderata.