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Academic Press Library in Signal Processing by Rama Chellappa, Sergios Theodoridis

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1.23.11.1.3 Compressed Sensing Matching Pursuit (CSMP) algorithms

Strictly speaking, these algorithms are not greedy, yet, as it is stated in [89], they are at heart greedy algorithms. Instead of performing a single term optimization per iteration step, in order to increase the support by one, as it is the case with OMP, these algorithms attempt to obtain first an estimate of the support and then use this information to compute a least squares estimate of the target vector, constrained on the respective active columns. The quintessence of the method lies in the near-orthogonal nature of the sensing matrix, assuming that this obeys the RIP.

Assume that obeys the RIP for some small enough value and sparsity level, , of the unknown vector. ...

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