Spectrum sensing is an important process in cognitive radio. A number of sensing techniques that have been proposed suffer from high processing time, hardware cost and computational complexity. To address these problems, compressive sensing has been proposed to decrease the processing time and expedite the scanning process of the radio spectrum. Selection of a suitable sparse recovery algorithm is necessary to achieve this goal. A number of sparse recovery algorithms have been proposed. This paper surveys the sparse recovery algorithms, classify them into categories, and compares their performances. For the comparison, we used several metrics such as recovery error, recovery time, covariance, and phase transition diagram. The results show that techniques under Greedy category are faster, techniques of Convex and Relaxation category perform better in term of recovery error, and Bayesian based techniques are observed to have an advantageous balance of small recovery error and a short recovery time.