Performance Bounds for Grouped Incoherent Measurements in Compressive Sensing

@article{Polak2012PerformanceBF,
  title={Performance Bounds for Grouped Incoherent Measurements in Compressive Sensing},
  author={Adam C. Polak and Marco F. Duarte and Dennis L. Goeckel},
  journal={IEEE Transactions on Signal Processing},
  year={2012},
  volume={63},
  pages={2877-2887}
}
Compressive sensing (CS) allows for acquisition of sparse signals at sampling rates significantly lower than the Nyquist rate required for bandlimited signals. Recovery guarantees for CS are generally derived based on the assumption that measurement projections are selected independently at random. However, for many practical signal acquisition applications, including medical imaging and remote sensing, this assumption is violated as the projections must be taken in groups. In this paper, we… 

Compressed sensing with structured sparsity and structured acquisition

An Analysis of Block Sampling Strategies in Compressed Sensing

A new random sampling approach that consists of projecting the signal over blocks of sensing vectors, which provides a good insight on the possibilities and limits of block compressed sensing in imaging devices, such as magnetic resonance imaging, radio-interferometry, or ultra-sound imaging.

A Bayesian recovery technique with Toeplitz matrix for compressive spectrum sensing in cognitive radio networks

The proposed method addresses the previously mentioned problems by exploiting the Bayesian model strengths and the Toeplitz matrix structure and demonstrates the superiority of the proposed method over the 2 other techniques in speed, robustness, recovery success, and handling uncertainty.

Variable Density Sampling with Continuous Trajectories

This paper discusses the choice of an optimal sampling subspace (smallest subset) allowing perfect reconstruction of sparse signals and shows that a mixed strategy involving partial deterministic sampling and independent drawings can help breaking the so-called "coherence barrier".

New Results - Variable density sampling with continuous trajectories. Application to MRI.

This paper discusses the choice of an optimal sampling subspace (smallest subset) allowing perfect reconstruction of sparse signals and shows that a mixed strategy involving partial deterministic sampling and independent drawings can help breaking the so-called "coherence barrier".

An Algorithm for Variable Density Sampling with Block-Constrained Acquisition

A new way to draw the blocks in order to mimic CS strategies based on isolated measurements and an efficient minimization algorithm based on Nesterov's accelerated gradient descent in metric spaces are proposed.

Close Encounters of the Binary Kind: Signal Reconstruction Guarantees for Compressive Hadamard Sampling With Haar Wavelet Basis

This work compute an explicit sample-complexity bound for Hadamard-Haar systems as well as uniform and non-uniform recovery guarantees; a seemingly missing result in the related literature.

Comparison of MRI Under-Sampling Techniques for Compressed Sensing with Translation Invariant Wavelets Using FastTestCS: A Flexible Simulation Tool

The addition of FastTestCS is proven to be a fast, flexible, portable and reproducible simulation aid for CS research, and the TIWT in CS reconstruction performs well, even for cases where TV does not improve the mean squared error.

Generalized notions of sparsity and restricted isometry property. Part I: a unified framework

  • M. JungeKiryung Lee
  • Mathematics, Computer Science
    Information and Inference: A Journal of the IMA
  • 2019
This work proposes generalized notions of sparsity and provides a unified framework for the corresponding RIP, which applies to high-order tensor products when combined with isotropic group actions.

Investigation of Sparsifying Transforms in Compressed Sensing for Magnetic Resonance Imaging with Fasttestcs

INVESTIGATION OF SPARSIFYING TRANSFORMS IN COMPRESSED SENSING FOR MAGNETIC RESONANCE IMAGING WITH FASTTESTCS

References

SHOWING 1-10 OF 20 REFERENCES

Grouped incoherent measurements for compressive sensing

A penalty factor on the number of required measurements with respect to the standard CS scheme that employs conventional independent measurement selection is found and the predicted penalty is verified through simulations.

Sparsity and incoherence in compressive sampling

It is shown that ℓ1 minimization recovers x0 exactly when the number of measurements exceeds S, and μ is the largest entry in U properly normalized: .

Recovery of sparse signals from amplitude-limited sample sets

This work introduces three techniques to improve the quality of recovery of a frequency-sparse signal from samples of small magnitude, and concludes that each of the proposed techniques show the promise of substantially improving recovery performance.

Compressive Domain Interference Cancellation

It is demonstrated that it is possible to efficiently filter out the interference from the compressive measurements in a manner that preserves the ability to recover the signal of interest.

Interference rejection by time selective sampling

A time sampling scheme that keeps only samples that do not exceed a threshold amplitude and thus are not distorted by amplifier nonlinearities is proposed.

Compressed sensing

  • D. Donoho
  • Mathematics
    IEEE Transactions on Information Theory
  • 2006
It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.

Compressed Sensing MRI

The authors emphasize on an intuitive understanding of CS by describing the CS reconstruction as a process of interference cancellation, and there is also an emphasis on the understanding of the driving factors in applications.

Compressed Synthetic Aperture Radar

A new synthetic aperture radar (SAR) imaging modality which can provide a high-resolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms is introduced.

Probing the Pareto Frontier for Basis Pursuit Solutions

A root-finding algorithm for finding arbitrary points on a curve that traces the optimal trade-off between the least-squares fit and the one-norm of the solution is described, and it is proved that this curve is convex and continuously differentiable over all points of interest.

Column subset selection, matrix factorization, and eigenvalue optimization

A randomized, polynomial-time algorithm that produces the submatrix promised by Bourgain and Tzafriri, and an approximation algorithm for the (∞, 1) norm of a matrix, which is generally NP-hard to compute exactly.