Tomography limitations in vivo due to incomplete, inconsistent and intricate measurements require solution of inverse problems. The new strategies disclosed in this application are capable of providing faster data acquisition, higher image quality, lower radiation dose, greater flexibility, and lower system cost. Such benefits can be used to advance research in cardiovascular diseases, regenerative medicine, inflammation, and nanotechnology. The present invention relates to the field of medical imaging. More particularly, embodiments of the invention relate to methods, systems, and devices for imaging, including tomography-based and MRI-based applications. For example, included in embodiments of the invention are compressive sampling based tomosynthesis methods, which have great potential to reduce the overall x-ray radiation dose for a patient. To name a few, compressive sensing based carbon nano-tube based interior tomosynthesis systems, tomography-based dynamic cardiac elastography systems, cardiac elastodynamic biomarkers from interior MR imaging, exact and stable interior ROI reconstructions for radial MRI, and interior reconstruction based ultrafast tomography systems are provided.