Efficient compressed sensing reconstruction frameworks for accelerated cardiac magnetic resonance imaging

Dynamic magnetic resonance imaging requires rapid data acquisition to provide an appropriate combination of spatial and temporal resolution, and volumetric coverage for clinical studies. In the most challenging clinical situations, conventional dynamic MR scanners are often incapable of simultaneously providing images with sufficient temporal resolution and high spatial resolution. In practice, clinicians are often forced to compromise between these parameters, often resulting in sub-optimal performance. Cardiac MRI is the most challenging and inspiring dynamic MRI application. In cardiac MRI, the main challenge is the sensitivity of reconstruction methods to large inter frame motion. The reconstructions often suffer from temporal blurring and motion related artifacts at high acceleration factors. In this dissertation, three novel approaches are proposed specifically designed to minimize the sensitivity of the reconstructions to inter frame motion. First, a compressed sensing (CS) based image reconstruction method in conjunction with spiral sampling is developed for the reconstruction of dynamic MRI data from highly accelerated / under-sampled Fourier measurements. In the second algorithm, the problem of motion artifacts including respiratory motion and cardiac motion in compressed sensing reconstructions is addressed. A motion estimation/motion compensation algorithm based on a modified search that aids block matching and results in improved residual reconstruction is incorporated into the CS reconstruction for dynamic MRI. In the third algorithm, a novel formulation for the joint estimation of the deformation and the dynamic images in cardiac cine MR imaging is introduced. The motion estimation algorithm estimates the deformation by registering the dynamic data to a reference dataset that is free of respiratory motion, which is derived from the measurements themselves. A variable splitting framework is used to minimize the objective function, and thus derive the deformation and the dynamic images. The validation of the proposed algorithms is illustrated using a numerical phantom and in-vivo cine MRI data to show the feasibility in precisely recovering cardiac MRI data from extensively under-sampled data.