Analysis, algorithms and applications of compressed sensing - Yang, Zai (2014)
Compressed sensing (CS) is an emerging research area which studies the problem of recovering a high dimensional sparse signal from its low dimensional linear samples. While CS can acquire a signal with a sub-Nyquist sampling rate, it requires a nonlinear signal reconstruction strategy which is computationally expensive compared to the simple linear reconstruction procedure in the traditional Nyquist sampling case. Given the exact information of the sampling/sensing system, existing results have shown that the signal of interest can be accurately recovered via convex relaxation (l_1 minimization) and/or other approaches provided the signal is sufficiently sparse.