Over time, engineers have improved their understanding of which assumptions are practical and how they can be generalized.Īn early breakthrough in signal processing was the Nyquist–Shannon sampling theorem.
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Nevertheless, with prior knowledge or assumptions about the signal, it turns out to be possible to perfectly reconstruct a signal from a series of measurements (acquiring this series of measurements is called sampling). In general, this task is impossible because there is no way to reconstruct a signal during the times that the signal is not measured. OverviewĪ common goal of the engineering field of signal processing is to reconstruct a signal from a series of sampling measurements.
The second one is incoherence, which is applied through the isometric property, which is sufficient for sparse signals. The first one is sparsity, which requires the signal to be sparse in some domain. There are two conditions under which recovery is possible. This is based on the principle that, through optimization, the sparsity of a signal can be exploited to recover it from far fewer samples than required by the Nyquist–Shannon sampling theorem. Compressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems.
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