Magnetic Resonance Imaging (MRI) is a safe medical imaging modality that can acquire high quality scans. However, MRI has a relatively long acquisition time compared to other medical imaging modalities like X-Ray Computer Tomography and Ultrasonography. Reducing the MRI data acquisition time had been a challenge to researchers for the last two decades. Broadly there are two approaches to reduce the scan time – i) the hardware based approach by which the design of the scanner is changed to accommodate faster scans and ii) the software based approach where the sampling and reconstruction methods are changed to make faster scans. In this book, we propose techniques to reduce MRI acquisition time from the software based approach.