Performance analysis of partial support recovery and signal reconstruction of compressed sensing

Recent work in the area of compressed sensing mainly focuses on the perfect recovery of the entire support for sparse signals. However, partial support recovery, where a part of the signal support is correctly recovered, may be adequate in many practical scenarios. In this study, in the high-dimensional and noisy setting, the authors develop the probability of partial support recovery of the optimal maximum-likelihood (ML) algorithm. When a large part of the support is available, the asymptotic mean-square-error (MSE) of the reconstructed signal is further developed. The simulation results characterise the asymptotic performance of the ML algorithm for partial support recovery, and show that there exists a signal-to-noise ratio (SNR) threshold, beyond which the increase of SNR cannot bring any obvious MSE gain.