Editing Detection theory (section)

=== Compressed sensing ===
Another field which is closely related to signal detection theory is called '''''[[compressed sensing]]''''' (or compressive sensing). The objective of compressed sensing is to recover high dimensional but with low complexity entities from only a few measurements. Thus, one of the most important applications of compressed sensing is in the recovery of high dimensional signals which are known to be sparse (or nearly sparse) with only a few linear measurements. The number of measurements needed in the recovery of signals is by far smaller than what Nyquist sampling theorem requires provided that the signal is sparse, meaning that it only contains a few non-zero elements. There are different methods of signal recovery in compressed sensing including '''''[[basis pursuit]]''''', '''''expander recovery algorithm'''''<ref>{{cite journal |last1=Jafarpour |first1=Sina |last2=Xu |first2=Weiyu |last3=Hassibi |first3=Babak |last4=Calderbank |first4=Robert |title=Efficient and Robust Compressed Sensing Using Optimized Expander Graphs |journal=IEEE Transactions on Information Theory |date=September 2009 |volume=55 |issue=9 |pages=4299–4308 |doi=10.1109/tit.2009.2025528 |s2cid=15490427 |url=https://authors.library.caltech.edu/15653/1/Jafarpour2009p5830Ieee_T_Inform_Theory.pdf }}</ref>''''', CoSaMP'''''<ref>{{Cite journal|last1=Needell|first1=D.|last2=Tropp|first2=J.A.|title=CoSaMP: Iterative signal recovery from incomplete and inaccurate samples|journal=Applied and Computational Harmonic Analysis|volume=26|issue=3|pages=301–321|doi=10.1016/j.acha.2008.07.002|year=2009|arxiv=0803.2392|s2cid=1642637 }}</ref> and also '''''fast''''' '''''non-iterative algorithm'''''.<ref>Lotfi, M.; Vidyasagar, M."[[arxiv:1708.03608|A Fast Noniterative Algorithm for Compressive Sensing Using Binary Measurement Matrices]]".</ref> In all of the recovery methods mentioned above, choosing an appropriate measurement matrix using probabilistic constructions or deterministic constructions, is of great importance. In other words, measurement matrices must satisfy certain specific conditions such as '''''[[Restricted isometry property|RIP]]''''' (Restricted Isometry Property) or '''''[[Nullspace property|Null-Space property]]''''' in order to achieve robust sparse recovery.