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An Introduction To Compressive Sampling
Abstract
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/sampling paradigm that goes against the common wisdom in data acquisition. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than traditional methods use.
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“This and other non-equilibrium exchanges between system and environment can have considerable influence on the system dynamics [28-35], influence the direction of energy transfer [28] and may even lead to the generation of long-lived quantum coherence in the system [28, 36-38].”
From Vibrations, quanta and biology (2013) · cites this paper as [36]
In the citing paper
“In the following we will show that the inclusion of significant coupling of electronic motion to long-lived vibrational modes [28, 34] are capable of explaining the observations [36, 37]”
From Vibrations, quanta and biology (2013) · cites this paper as [36]
In the citing paper
“The physical picture presented here illustrates a key point: electronic coherence may emerge from transiently exciting robust, weakly dephasing vibrational coherences which then transfer back coherence to those exciton transitions that are well matched to the mode [28, 36, 37].”
From Vibrations, quanta and biology (2013) · cites this paper as [36]
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Metadata
- Authors
- Candes, E. J., & Wakin, M. B.
- Affiliations
- École Polytechnique (FR)
- ORCID
- Wakin, M.B.
- Venue
- IEEE Signal Processing Magazine
- Published
- 2008-03
- Volume
- 25
- Issue
- 2
- Pages
- 21-30
- ISSN
- 1053-5888 (ISSN-L)
- OpenAlex
- W2119667497
- Cited by
- 10,017
- References
- 32
- Citations by year
- 2026: 233 · 2025: 356 · 2024: 359 · 2023: 437 · 2022: 449 · 2021: 561 · 2020: 545 · 2019: 727 · 2018: 818 · 2017: 792 · 2016: 823 · 2015: 899 · 2014: 803 · 2013: 709 · 2012: 614
- FWCI
- 310.91
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Signal Processing Magazine (publishedVersion)
- HAL (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Signal Processing › Sparse and Compressive Sensing Techniques
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Physical Sciences › Computer Science › Computer Networks and Communications › Distributed Sensor Networks and Detection Algorithms
- Keywords
- compressed sensing, Nyquist rate, undersampling, signal reconstruction, image reconstruction, analog-to-digital conversion, data acquisition
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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