This first chapter formulates the objectives of compressive sensing. It introduces the
standard compressive problem studied throughout the book and reveals its ubiquity in many …

Randomized algorithms for very large matrix problems have received a great deal of
attention in recent years. Much of this work was motivated by problems in large-scale data …

This article presents novel results concerning the recovery of signals from undersampled
data in the common situation where such signals are not sparse in an orthonormal basis or …

An oblivious subspace embedding (OSE) given some parameters ε, d is a distribution D over
matrices Π∈ R m× n such that for any linear subspace W⊆ R n with dim (W)= d, P Π~ D (∀ …

We give two different and simple constructions for dimensionality reduction in ℓ 2 via linear
mappings that are sparse: only an O (ε)-fraction of entries in each column of our embedding …

This paper presents an improved analysis of a structured dimension-reduction map called
the subsampled randomized Hadamard transform. This argument demonstrates that the …

Low-distortion embeddings are critical building blocks for developing random sampling and
random projection algorithms for common linear algebra problems. We show that, given a …

Consider an instance of Euclidean k-means or k-medians clustering. We show that the cost
of the optimal solution is preserved up to a factor of (1+ ε) under a projection onto a random …

The nearest neighbor problem is defined as follows: Given a set P of n points in some metric
space (X, D), build a data structure that, given any point q, returns a point in P that is closest …

Consider an m*N matrix Φ with the restricted isometry property of order k and level δ; that is,
the norm of any k-sparse vector in R^N is preserved to within a multiplicative factor of 1±δ …