An Introduction to Wavefield and Magnetic Resonance Imaging

In many sensing and imaging problems (geophysical exploration, radio astronomy, nondestructive testing, medical X-ray tomography, etc.) one is interested in information about an object that is not directly accessible and possibly obscured by a surrounding medium. Waves, fields, or a stream of particles may be used as probes to obtain this information. By measuring the fields or particles after they have traveled through an object, the goal is to retrieve the location of this object or its internal constitution or both. This may be realized via sophisticated imaging and inversion algorithms that process the signals as measured by the receivers. These algorithms are often computationally intensive especially for 3D real-world problems. Moreover, inverse problems are usually ill-posed and solutions may be very sensitive to noise or other perturbations of the data. Developing efficient and robust imaging and inversion algorithms is therefore an extremely challenging problem. In this course, we present a general overview of this exciting research field. We follow a multidisciplinary approach and introduce various imaging principles, methods, and applications in a uniform framework. The commonalities that exist between different problems in different fields are emphasized and both linear and nonlinear state-of-the-art solution techniques are discussed.