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CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
TLDR
This extended abstract describes a recent algorithm, called, CoSaMP, that accomplishes the data recovery task and was the first known method to offer near-optimal guarantees on resource usage.
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Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
TLDR
This paper finds a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L1-minimization.
View on Springer
Compressed Sensing with Coherent and Redundant Dictionaries
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Signal Recovery From Incomplete and Inaccurate Measurements Via Regularized Orthogonal Matching Pursuit
TLDR
The algorithm, Regularized Orthogonal Matching Pursuit (ROMP), seeks to provide the benefits of the two major approaches to sparse recovery, and combines the speed and ease of implementation of the greedy methods with the strong guarantees of the convex programming methods.
View on IEEE
Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm
TLDR
An improved finite-sample guarantee on the linear convergence of stochastic gradient descent for smooth and strongly convex objectives is obtained, and it is shown how reweighting the sampling distribution is necessary in order to further improve convergence.
View on Springer
Paved with Good Intentions: Analysis of a Randomized Block Kaczmarz Method
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Linear Convergence of Stochastic Iterative Greedy Algorithms With Sparse Constraints
TLDR
This generalized framework is specialized to the problems of sparse signal recovery in compressed sensing and low-rank matrix recovery, giving methods with provable convergence guarantees that often outperform their deterministic counterparts.
View on IEEE
Stable Image Reconstruction Using Total Variation Minimization
TLDR
It is shown that from nonadaptive linear measurements, an image can be reconstructed to within the best best-term approximation of its gradient up to a logarithmic factor, and this factor can be removed by taking slightly more measurements.
View PDF on arXiv
Signal Space CoSaMP for Sparse Recovery With Redundant Dictionaries
TLDR
This paper describes a variant of the iterative recovery algorithm CoSaMP that utilizes the \mbi D-RIP, a condition on the sensing matrix analogous to the well-known restricted isometry property, and provides provable recovery guarantees.
View on IEEE
Randomized Kaczmarz solver for noisy linear systems
  • D. Needell
  • Computer Science, Mathematics
  • 5 February 2009
TLDR
This work analyzes the case where the Kaczmarz method is corrupted by noise, and proves that in this noisy version, the randomized method reaches an error threshold dependent on the matrix A with the same rate as in the error-free case.
View on Springer
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