An Introduction To Compressive Sampling
- ISSN: 10535888
- DOI: 10.1109/MSP.2007.914731
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.
An Introduction To Compressive Sampling
Digital Object Identifier 10.1109/MSP.2007.914731
C
onventional approaches to sampling signals or images follow Shannon’s cel-
ebrated theorem: the sampling rate must be at least twice the maximum fre-
quency present in the signal (the so-called Nyquist rate). In fact, this
principle underlies nearly all signal acquisition protocols used in consumer
audio and visual electronics, medical imaging devices, radio receivers, and
so on. (For some signals, such as images that are not naturally bandlimited, the sam-
pling rate is dictated not by the Shannon theorem but by the desired temporal or spatial
resolution. However, it is common in such systems to use an antialiasing low-pass filter
to bandlimit the signal before sampling, and so the Shannon theorem plays an implicit
role.) In the field of data conversion, for example, standard analog-to-digital converter
(ADC) technology implements the usual quantized Shannon representation: the signal is
uniformly sampled at or above the Nyquist rate.
[Emmanuel J. Candès
and Michael B. Wakin]
An Introduction To
Compressive Sampling
[A sensing/sampling paradigm that goes against
the common knowledge in data acquisition]
1053-5888/08/$25.00©2008IEEE IEEE SIGNAL PROCESSING MAGAZINE [21] MARCH 2008
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