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.

Wings for Aid is a company which develops an airborne aid-delivery system in emergency-struck areas and wants to use the radar system of Selfly to make an autonomously flying system. The goal of this project is to optimise the current ground-based radar system of Selfly for this application. This is done through the design of a Bi-static radar system, which can be mounted on, and used for drones to detect and avoid other obstacles in the airspace.\ This thesis describes the design process and results of a sub-system of the Bi-static Sense and Avoid System for Drones (BiSAD). This a Bi-static radar system, consisting of three sub-systems that together form the base of the radar system. There will be one transmitter drone and several smaller receiver drones which are designed. Also, an optimal waveform is created for this purpose.\ The report gives a proof of concept and will focus on a proof of concept for the transmitter chain as well as highlight some total system design choices and results.