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AbstractDynamic cardiac Magnetic Resonance Imaging (CMR) demands fast imaging techniques to obtain high spatial-resolution, large spatial-coverage and high temporal-resolution images for accurate prognosis and diagnosis. Compressed sensing (CS), a fast imaging technique of growing importance, is making a major impact on MRI. Using CS, high-quality images can be recovered from data sampled well below the Nyquist rate. Because of the high temporal and spatial redundancy inherent to dynamic images, these data are well-suited for acceleration by CS.However, the complex dynamics which include both object motions and image contrast variations encountered in dynamic CMR pose challenging tasks for CS techniques. The complexity, if not handled correctly, leads to largely degraded reconstruction quality.This dissertation presents a novel CS method to accelerate dynamic CMR imaging, especially those with complex dynamics, with a motion-compensated CS method that exploits regional spatiotemporal sparsity: Block LOw-rank Sparsity with Motion-guidance (BLOSM). In one iteration of the BLOSM calculation, blocks of image pixels are motion-tracked through time and low-rank sparsity is exploited within the tracked blocks. The de-noised blocks are merged back into complete images and compensated for data fidelity.The BLOSM method was first developed and validated using retrospectively accelerated first-pass cardiac perfusion images with prominent respiratory motion and computer simulated motion phantoms. Systematic experiments were conducted to compare BLOSM to several other II competing CS methods. The BLOSM showed great quality improvement for the images presenting complex dynamics.Two CMR applications of great clinical importance, both of which present distinct and extremely challenging tasks for CS, were prospectively accelerated using BLOSM.First-pass cardiac perfusion imaging was accelerated on patients with suspected heart disease. With prospective rate 4 acceleration, multi-slice high spatial resolution perfusion images were acquired. A Poisson-disc-distributed sampling pattern was implemented. BLOSM was extended to incorporate parallel imaging. The image quality offered by BLOSM showed significant improvement over the other CS methods when respiratory motion occurred.2D cine DENSE imaging was accelerated using BLOSM. The scan time was shortened from two separate breathholds of total 28 heartbeats to one single breathhold of 8 heartbeats.Variable-density spiral trajectory with golden angle rotation was designed for accelerated data sampling. Both retrospective and prospective studies were conducted in healthy volunteers and BLOSM provided high image quality and the cardiac function assessed from BLOSM reconstructed images matched well with the fully-sampled reference data.III