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An Introduction To Compressive Sampling

by E J Candes, M B Wakin
IEEE Signal Processing Magazine ()

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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An Introduction To Compressive Sa...

�� DIGITAL VISION Digital Object Identifier 10.1109/MSP.2007.914731 Caudio 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 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. Cand��s 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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