Analysis of required measurement number in compressive sensing

Compressive sensing is a new signal processing method which shows that a sparse signal can be constructed using fewer measurements than normal reconstruction methods. Rather taking all Nyquist samples of a sparse signal in any base the signal can be reconstructed correctly by taking small number of linear projections. In compressive sensing an important relation between measurement number and signal length and sparsity level is used as M=K(logN). This relation is examined separately in noiseless and noisy data. It is determined by simulations that this relation is valid for sparse enough signals and a new relation has been developed for more general cases.