Magnetic resonance imaging (MRI) is a non-invasive tool to image the body’s anatomy and physiology, but suffers from long scan times. Compressed Sensing (CS) is used to accelerate MRI scans by incoherently taking fewer measurements and using a nonlinear optimization algorithm to image the undersampled data. Convex optimization techniques are generally used for image reconstruction. Minimizing a data fidelity term along with two regularization terms, which are a total variation (TV) based and a wavelet transform based function, is a standard procedure in CS-MRI. Regularization parameters are needed to balance the different terms, but it is impossible to know upfront what the optimal regularization parameters are to get the desired output. A consequence is that the algorithm of choice needs to be executed many times for many different values of the regularization parameters, which is a time-consuming process requiring knowledge of the algorithm.

In this work we rewrite and implement the regularization functions in a multiplicative manner by multiplying the data fidelity term with the regularization terms, thereby eliminating the need to tune the regularization parameters. Moreover, we include a region of support (ROS) mask to further accelerate reconstruction. The performance of different combinations of regularization functions and reconstruction algorithms are validated on a simulation study and various experiments on a low-field MRI scanner. This also shows the capability of CS applied to low-field MRI, which has lower signal-to-noise ratio compared to conventional MRI. Of all proposed methods, a nonlinear conjugate gradient method applied to the fully multiplicatively regularized objective function shows the most robust performance.

MRI is an non-invasive imaging technique used by many physicians to diagnose and treat diseases. The technique however is still very expensive and thus out of reach for developing countries. This has led to the goal to design a low-cost MRI system. The challenges that arise from this system make it necessary to design coils in a different way than conventional MRI. In this work the inverse boundary element method is used to create a coil design method for an arbitrary surface. This method is described and the mathematical framework is analyzed. A regularization method for the inverse problem has been designed in the form of a regularization matrix. This regularization matrix is constructed such that it can handle arbitrary surfaces. The regularization matrix is applied using Tikhonov regularization. To validate the design method a proof of concept radiofrequency coil for the low field MRI system at the LUMC has been realized. This coil is designed and has been used to image the human brain of an adult. The results from simulations beforehand are in agreement with the physically built coil showing that this method makes it possible to design and construct a physically feasible coil on an arbitrary surface.