Modern imaging modalities, such as Computed Tomography (CT), Digital Breast Tomosynthesis (DBT) or Magnetic Resonance Tomography (MRT) are able to acquire volumetric images with an isotropic resolution in micrometer (um) or millimeter (mm) range. When used in interactive telemedicine applications, these raw images need a huge storage unit, thereby necessitating the use of high bandwidth data communication link. To reduce the cost of transmission and enable archiving, especially for medical applications, image compression is performed. Recent advances in compression algorithms have resulted in a vast array of data compression techniques, but because of the characteristics of these images, there are challenges to overcome to transmit these images efficiently. In addition, the recent studies raise the low dose mammography risk on high risk patient. Our preliminary studies indicate that by bringing the compression before the analog-to-digital conversion (ADC) stage is more efficient than other compression techniques after the ADC. The linearity characteristic of the compressed sensing and ability to perform the digital signal processing (DSP) during data conversion open up a new area of research regarding the roles of sparsity in medical image registration, medical image analysis (for example, automatic image processing algorithm to efficiently extract the relevant information for the clinician), further Xray dose reduction for mammography, and contrast enhancement.