Compression serves as a significant feature for efficient storage and transmission of medical, satellite, and natural images. Transmission speed is a key challenge in transmitting a large amount of data especially for magnetic resonance imaging and computed tomography scan images. Compressive sensing is an optimization-based option to acquire sparse signal using sub-Nyquist criteria exploiting only the signal of interest. This chapter explores compressive sensing for correct sensing, acquisition, and reconstruction of clinical images. In this chapter, distinctive overall performance metrics like peak signal to noise ratio, root mean square error, structural similarity index, compression ratio, etc. are assessed for medical image evaluation by utilizing best three reconstruction algorithms: basic pursuit, least square, and orthogonal matching pursuit. Basic pursuit establishes a well-renowned reconstruction method among the examined recovery techniques. At distinct measurement samples, on increasing the number of measurement samples, PSNR increases significantly and RMSE decreases.