Performance analysis of support recovery in compressed sensing

Compressed sensing is a new framework to capture sparse signals at sub-Nyquist rate. To guarantee reliable recovery from compressed measurements, the exact reconstruction of the support is necessary. In this letter, we study the probability of exact support reconstruction for maximum likelihood decoding algorithm. The recovery problem is first casted as the one of finding K one-dimensional subspaces containing the maximum energy of the received signal, where K is the sparsity level. Then, the asymptotic probability is developed based on the derived probability density function of the normalized distances between the received signal and all possible subspaces.