Perhaps medical imaging has seen the largest application of compressed sensing (CS) since its inception. Application of sparse recovery-based techniques can make X-Ray computed tomography (CT) safer and magnetic resonance imaging (MRI) faster. This chapter presents a study about CT and MRI. CT imaging is mathematically a linear inverse problem. In theory, there exists analytical solution for solving the inverse problem in the continuous domain; this is called the back propagation (BP). MRI is a versatile medical imaging modality that can produce high-quality images and is safe when operated within approved limits. Single-channel static MRI is further segregated into two parts: single-echo MRI and multi-echo MRI. Single-echo MRI is routinely used for medical diagnosis. Owing to its versatility, MRI has one-to-many correspondence and hence is not quantitative. The MR image is dependent on the scanning parameters.