Improvement in high acceleration parallel Magnetic Resonance Imaging using efficient graph-based energy minimization methods

Magnetic Resonance Imaging is one of the most versatile non invasive tomographic imaging technique. Though MRI is a very powerful but it gets limited by excessive scanning time. MRI scans are of the order of several minutes as compared to a few seconds for Computed Tomography Imaging (CT Scan). This limits the applicability of MRI in scanning anatomical regions that are susceptible to patient motion and breathing; such as heart. This work focuses on parallel imaging modality that has been developed to speed up the scan time. Parallel MR imaging acquires multiple partial spatially encoded scans with the use of multiple receivers. This reduces the scan time and transfers imaging problem to a post data processing step.; The main contribution of this thesis is in reducing parallel MR imaging problem to an energy minimization problem which then is solved with the use of efficient combinatorial optimization algorithms known as graph cuts. Though parallel MR imaging problem is similar to the set of problems where graph cuts are proven technique but unfortunately it falls out of the scope of functions for which graph cuts guarantee an efficient solution. This problem is resolved with an energy relaxation such that relaxed energy function can be efficiently solved with graph cuts. We give quantitative and qualitative evidence of the success of new approach via superior quality in-vivo results in cardiac and brain MRI applications at high acceleration.; The second contribution is in developing a fast graph cuts algorithm to enable efficient energy minimization as an online parallel MR reconstruction method. Traditional graph cuts algorithms scale linearly with the number of discrete labels in an image. Therefore for images with high intensity range, the reconstruction process becomes extremely slow. Fast graph cuts algorithm based on traditional jump move algorithm provides a logarithmic speed up in reconstruction time while maintaining the successful and superior quality in-vivo results at high acceleration cardiac imaging applications.