Advances in compressed sensing for magnetic resonance imaging

Magnetic resonance imaging (MRI) is a non-invasive imaging modality, which offers high spatial resolution and excellent soft tissue contrast without employing ionizing radiation. MRI is sensitive to a wide range of contrast mechanisms that allow assessment of both morphology and physiology, making it a modality of choice for many clinical applications. A major limitation of MRI is that data acquisition is relatively slow, which besides being unpleasant for the patient, can also seriously degrade the image quality. Modern MR scanners are already operating at the point where further improvements in data acquisition speed by means of hardware and pulse sequence design are constrained by physical and physiological limitations. With the advent of parallel imaging techniques, this problem has partially been addressed. However, further reduction of imaging time is desired, making the development of methods which allow image reconstruction from reduced amount of data necessary. Recently, a new sampling theory under the name compressed sensing (CS) has emerged, suggesting that image reconstruction from reduced amount of data can be achieved by exploiting the signal sparsity. The ability to reconstruct images from small number of measurements provides a new method to accelerate the data acquisition in MRI. Initial studies have shown that compressed sensing has a great potential to improve the imaging speed in MRI. This thesis explores and extends the concept of applying compressed sensing to MRI. A successful CS reconstruction requires incoherent measurements,signal sparsity, and a nonlinear sparsity promoting reconstruction. To optimize the performance of CS, the acquisition, the sparsifying transform and the reconstruction have to be adapted to the application of interest. This work presents new approaches for sampling, signal sparsity and reconstruction, which are applied to three important applications: dynamic MR imaging, MR parameter mapping and chemical-shift based