Compressed Sensing: From Theory to Praxis

Authored by: Axel Flinth , Ali Hashemi , Gitta Kutyniok

Compressive Sensing of Earth Observations

Print publication date:  June  2017
Online publication date:  May  2017

Print ISBN: 9781498774376
eBook ISBN: 9781315154626
Adobe ISBN:

10.1201/9781315154626-1

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Abstract

For a long time, the Shannon sampling theorem was the ruling paradigm in the signal processing community when it came to choosing sampling rates. The theorem, proved in 1949 by Claude E. Shannon, states that any function f : ℝ → ℂ having limited bandwidth W (meaning that the support of the Fourier transform f ̂ is contained in the interval [ − W , W ] ) can be exactly reconstructed from its values f ( n 2 W ) n ∈ ℤ . Put differently, sampling a function at a rate at least two times higher than the bandwidth of the function will provide enough information for perfect reconstruction of the signal of interest. The rate two times higher than the bandwidth of a signal is often referred to as the Nyquist rate.

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