An Introduction To Compressive Sampling

@article{Cands2008AnIT,
  title={An Introduction To Compressive Sampling},
  author={Emmanuel J. Cand{\`e}s and Michael B. Wakin},
  journal={IEEE Signal Processing Magazine},
  year={2008},
  volume={25},
  pages={21-30}
}
  • E. CandèsM. Wakin
  • Published 21 March 2008
  • Computer Science
  • IEEE Signal Processing Magazine
Conventional approaches to sampling signals or images follow Shannon's theorem: the sampling rate must be at least twice the maximum frequency present in the signal (Nyquist rate). In the field of data conversion, standard analog-to-digital converter (ADC) technology implements the usual quantized Shannon representation - the signal is uniformly sampled at or above the Nyquist rate. This article surveys the theory of compressive sampling, also known as compressed sensing or CS, a novel sensing… 
View on IEEE
authors.library.caltech.edu
9,168 Citations
Highly Influential Citations
675
Background Citations
4,210
Methods Citations
1,836
Results Citations
41

Figures from this paper

9,168 Citations

Compressive Sampling of Image and its comparison with JPEG Compressed Image

This report surveys the theory of compressive sampling, also known as compressed sensing or CS, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition that asserts that one can recover certain signals and images from far fewer samples or measurements than traditional methods use.

Recent Advances in Compressive Sensing

This paper presents a brief historical background, mathematical foundation, and a theory behind compressive sensing and its emerging applications with a special emphasis on communication, network design, signal processing, and image processing.

Demystifying Compressive Sensing [Lecture Notes]

  • H. Laue
  • Computer Science
    IEEE Signal Processing Magazine
  • 2017
The theory of compressive sensing/sampling (CS) presents a sampling framework based on the rate of information of a signal and not the bandwidth, thereby minimizing redundancy during sampling.

Compressive Video Sensing: Algorithms, architectures, and applications

The design of conventional sensors is based primarily on the Shannon?Nyquist sampling theorem, which states that a signal of bandwidth W Hz is fully determined by its discrete time samples provided…

CS-Video : Algorithms , Architectures , and Applications for Compressive Video Sensing

Compressive sensing (CS) is a powerful sensing paradigm that seeks to alleviate the daunting sampling rate requirements imposed by the Shannon-Nyquist principle.

Compressive Sampling Techniques for Integrating Video Acquisition and Coding

In this paper a simulation of an efficient system for integrating video coding/compression with acquisition through compressive sampling is developed in detail and simulation is implemented for the Y-components of video frames and qualitative comparison is done with traditionally acquired frames.

Compressive Sensing

This paper overviews the recent work on compressive sensing, a new approach to data acquisition in which analog signals are digitized for processing not via uniform sampling but via measurements…

Compressive Sampling Using EM Algorithm

This work proposes a naive approach which has certain computational difficulties and subsequently modify it to a new approach which performs better than the conventional methods of compressive sampling using EM algorithm.

A Comprehensive Review on Compressive Sensing

This study aims to present an overview of existing Compressive Sensing approaches so that researchers can better understand existing limitations and seek to improve accuracy and precision.

Compressed sensing based multi-rate sub-Nyquist sampling system

...

References

SHOWING 1-10 OF 38 REFERENCES

Signal Reconstruction From Noisy Random Projections

  • J. HauptR. Nowak
  • Computer Science, Engineering
    IEEE Transactions on Information Theory
  • 2006
A practical iterative algorithm for signal reconstruction is proposed, and potential applications to coding, analog-digital (A/D) conversion, and remote wireless sensing are discussed.

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: .

Spectrum-blind minimum-rate sampling and reconstruction of multiband signals

  • Ping FengY. Bresler
  • Mathematics
    1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings
  • 1996
We propose a universal sampling pattern and corresponding reconstruction algorithms that guarantee well-conditioned reconstruction of all multiband signals with a given spectral occupancy bound…

Distributed Compressed Sensing Dror

A new theory for distributed compressed sensing (DCS) is introduced that enables new distributed coding algorithms for multi-signal ensembles that exploit both intraand inter-Signal correlation structures.

Rapid MR Imaging with "Compressed Sensing" and Randomly Under-Sampled 3DFT Trajectories

A method to evaluate the effective randomness of a randomly under-sampled trajectory by analyzing the statistics of aliasing in the sparse transform domain is provided and a 5fold scan time reduction is demonstrated.

Stable signal recovery from incomplete and inaccurate measurements

It is shown that it is possible to recover x0 accurately based on the data y from incomplete and contaminated observations.

Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements

The first guarantees for universal measurements (i.e. which work for all sparse functions) with reasonable constants are proved, based on the technique of geometric functional analysis and probability in Banach spaces.

Enhancing Sparsity by Reweighted ℓ1 Minimization

A novel method for sparse signal recovery that in many situations outperforms ℓ1 minimization in the sense that substantially fewer measurements are needed for exact recovery.

On sparse reconstruction from Fourier and Gaussian measurements

This paper improves upon best‐known guarantees for exact reconstruction of a sparse signal f from a small universal sample of Fourier measurements by showing that there exists a set of frequencies Ω such that one can exactly reconstruct every r‐sparse signal f of length n from its frequencies in Ω, using the convex relaxation.

Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit

This paper demonstrates theoretically and empirically that a greedy algorithm called orthogonal matching pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln…