The Compressed Sensing (CS) is a new signal acquisition technique that enables the reduction in the number of measurements required for recovery of sparse signal and the signal recovery is done using optimization techniques. The recovery of the original signal from CS measurements becomes difficult when the CS data acquisition is noisy. Here we are conducting a review of robustness of some of these algorithms in recovering the original signal in presence of data acquisition noise. The algorithms are implemented using Matlab and the performance evaluation are done based on average relative error in recovery and the probability of error in signal support. The results of the experimental evaluation using generic sparse data are presented. In general, the relaxation based algorithms are found to have better recovery precision, when the CS measurement is noisy; and the performance of ANN based RASR algorithm is found to be comparable to basis pursuit and IRLS algorithms. © 2014 IEEE.