Accelerated imaging is an active research area in medical imaging. The most intuitive way of image acceleration is to reconstruct images from only a subset of the whole raw data space, so that the acquisition time can be shortened. This concept has been formalized in recent years, and is known as Compressed Sensing (CS).

In this dissertation, we developed a new image reconstruction method, Partial Fourier Compressed Sensing (PFCS), which combines the advantages of partial Fourier transform and compressed sensing techniques. Then, we explore its application on two imaging modalities.

First, we apply PFCS to Electron Paramagnetic Resonance Imaging (EPRI) reconstruction for the purpose of imaging the cycling hypoxia phenomenon. We begin with validating PFCS with the prevailing medical acceleration techniques using CS. Then, we further explore its capability of imaging the oxygen distribution in the tumor tissue. Our results show that PFCS is able to accelerate the imaging process by at least 4 times with-out losing too much image resolution in comparison to conventional CS. Further, the ox-ygen map given by PFCS precisely captures the oxygen change inside the tumor tissue.

In the second part, we apply PFCS to 3D diffusion tensor image (DTI) acquisition. We develop a new sampling strategy specified to diffusion weighted images and optimize the reconstruction cost function for PFCS. The results show that PFCS can reconstruct the accurate color FA map using only 30% of the k-space data. Moreover, PFCS can be further combined with Echo-Planar Imaging (EPI) to achieve an even faster acquisition speed.

In summary, PFCS is shown to be a promising image acceleration method in medical imaging which can potentially benefit many clinical applications.