Ultrasound plane wave imaging is an ultrafast technique to obtain the reconstructed images in real-time. However, identifying the point targets (such as microcalcifications) is challenging in this imaging technique due to the presence of strong acoustic clutter. In this paper, a compressive sensing (CS)-based algorithm, named modified-CS (M-CS), is proposed which can be used to accurately identify the point targets. In the proposed algorithm, the processing matrix is divided into some non-overlapping sub-matrices, and each part is processed separately. Then, the output passes through the thresholding and localization processes to obtain the locations of the point targets. Compared to the conventional CS algorithm, identifying the point targets in deeper regions of the imaging medium is provided using the M-CS algorithm. Also, due to the usage of smaller sub-matrices, the proposed M-CS algorithm speeds up, and also, needs less memory compared to the conventional CS algorithm. The simulation results confirm the good performance of the proposed algorithm.