Direction of arrival (DOA) estimation of radio waves is used in many fields such as positioning of radio communication terminals and radar systems, etc. In recent years, as a highly accurate estimation method, some techniques using compressed sensing have been proposed. There are several algorithms to solve solutions for the compressed sensing technique. The authors have used Half-Quadratic Regularization (HQR) method to reconstruct original signals so far. In addition, Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) and Orthogonal Matching Pursuit (OMP) are also typically known as compressed sensing algorithms. In this paper, we compare the performance of HQR, FISTA, and OMP for DOA estimation of multi-band signals. The results indicate that HQR achieves the best performance in the three algorithms although the computational load is large. OMP with less computational load is useful when slightly larger estimation errors are allowable. Additionally, It is shown that compressed sensing works reasonably well even with a small number of snapshots.