D. Needell

Publications
Influence

CoSaMP: Iterative signal recovery from incomplete and inaccurate samples

J. Tropp, D. Needell
Computer Science, Mathematics
Commun. ACM
16 March 2008

This paper presents and analyzes a novel signal reconstruction algorithm, called, CoSaMP, that accomplishes the data recovery task. Expand

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Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit

D. Needell, R. Vershynin
Computer Science, Mathematics
Found. Comput. Math.
28 July 2007

This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements—L1-minimization methods and iterative methods (Matching Pursuits). Expand

Compressed Sensing with Coherent and Redundant Dictionaries

E. Candès, Yonina C. Eldar, D. Needell
Computer Science, Mathematics
ArXiv
14 May 2010

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 incoherent dictionary, but in a truly redundant dictionary. Expand

Signal Recovery From Incomplete and Inaccurate Measurements Via Regularized Orthogonal Matching Pursuit

D. Needell, R. Vershynin
Mathematics, Computer Science
IEEE Journal of Selected Topics in Signal…
9 December 2007

We demonstrate a simple greedy algorithm that can reliably recover a vector <i>v</i> ¿ ¿<sup>d</sup> from incomplete and inaccurate measurements . Expand

CoSaMP: Iterative signal recovery from incomplete and inaccurate samples

D. Needell, J. Tropp
Mathematics
1 May 2009

Abstract Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to… Expand

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Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm

D. Needell, R. Ward, Nathan Srebro
Mathematics, Computer Science
NIPS
21 October 2013

We obtain an improved finite-sample guarantee on the linear convergence of stochastic gradient descent for smooth and strongly convex objectives, improving from a quadratic dependence on the conditioning $$(L/\mu )^2$$ (L/μ)2 (where $$L$$L is a bound on the smoothness and $$\mu $$μ on the strong convexity) to a linear dependence on $$L/ \mu $$ L/μ. Expand

Linear Convergence of Stochastic Iterative Greedy Algorithms With Sparse Constraints

Nam Nguyen, D. Needell, Tina Woolf
Mathematics, Computer Science
IEEE Transactions on Information Theory
30 June 2014

We develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints that outperform their deterministic counterparts. Expand

Paved with Good Intentions: Analysis of a Randomized Block Kaczmarz Method

D. Needell, J. Tropp
Mathematics, Computer Science
ArXiv
18 August 2012

This paper introduces a randomized version of the block Kaczmarz method that converges with an expected linear rate, and we characterize the performance of this algorithm using geometric properties of the blocks of equations. Expand

Stable Image Reconstruction Using Total Variation Minimization

D. Needell, Rachel Ward
Computer Science, Mathematics
SIAM J. Imaging Sci.
29 February 2012

This paper presents near-optimal guarantees for stable and robust image recovery from undersampled noisy measurements using total variation minimization. Expand

Signal Space CoSaMP for Sparse Recovery With Redundant Dictionaries

M. Davenport, D. Needell, M. Wakin
Computer Science, Mathematics
IEEE Transactions on Information Theory
1 August 2012

Compressive sensing (CS) has recently emerged as a powerful framework for acquiring sparse signals. Expand

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