Randomized algorithms
Finding Frequent Items in Data Streams
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
What's hot and what's not: tracking most frequent items dynamically
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
An improved data stream summary: the count-min sketch and its applications
Journal of Algorithms
One sketch for all: fast algorithms for compressed sensing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Deterministic constructions of compressed sensing matrices
Journal of Complexity
Near-Optimal Sparse Recovery in the L1 Norm
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Efficient and robust compressed sensing using optimized expander graphs
IEEE Transactions on Information Theory
Approximate sparse recovery: optimizing time and measurements
Proceedings of the forty-second ACM symposium on Theory of computing
Lower bounds for sparse recovery
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
(1 + eps)-Approximate Sparse Recovery
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Sublinear time, measurement-optimal, sparse recovery for all
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Combinatorial algorithms for compressed sensing
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
IEEE Transactions on Information Theory
On the Design of Deterministic Matrices for Fast Recovery of Fourier Compressible Functions
SIAM Journal on Matrix Analysis and Applications
A Mathematical Introduction to Compressive Sensing
A Mathematical Introduction to Compressive Sensing
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A compressed sensing method consists of a rectangular measurement matrix, M@?R^m^x^N with m@?N, together with an associated recovery algorithm, A:R^m-R^N. Compressed sensing methods aim to construct a high quality approximation to any given input vector x@?R^N using only Mx@?R^m as input. In particular, we focus herein on instance optimal nonlinear approximation error bounds for M and A of the form @?x-A(Mx)@?"p@?@?x-x"k^o^p^t@?"p+Ck^1^/^p^-^1^/^q@?x-x"k^o^p^t@?"q for x@?R^N, where x"k^o^p^t is the best possible k-term approximation to x. In this paper we develop a compressed sensing method whose associated recovery algorithm, A, runs in O((klogk)logN)-time, matching a lower bound up to a O(logk) factor. This runtime is obtained by using a new class of sparse binary compressed sensing matrices of near optimal size in combination with sublinear-time recovery techniques motivated by sketching algorithms for high-volume data streams. The new class of matrices is constructed by randomly subsampling rows from well-chosen incoherent matrix constructions which already have a sub-linear number of rows. As a consequence, fewer random bits than previously required are needed in order to select the rows utilized by the fast reconstruction algorithms considered herein.