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. 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. There are two conditions under which recovery is possible. The first one is sparsity, which requires the signal to be sparse in some domain. The second one is incoherence, which is applied through the isometric property, which is sufficient for sparse signals.[1][2] Compressed sensing has applications in, for example, MRI where the incoherence condition is typically satisfied.[3]
^Donoho, David L. (2006). "For most large underdetermined systems of linear equations the minimal 1-norm solution is also the sparsest solution". Communications on Pure and Applied Mathematics. 59 (6): 797–829. doi:10.1002/cpa.20132. S2CID 8510060.
^M. Davenport, "The Fundamentals of Compressive Sensing", SigView, April 12, 2013.
^Candès, E.J., & Plan, Y. (2010). A Probabilistic and RIPless Theory of Compressed Sensing. IEEE Transactions on Information Theory, 57, 7235–7254.
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