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For the course, the student is supposed to be familiar with the fundamentals of Compressive Sensing. At the end of this modul, the students will be familiar with MRI acquisition and modern optimization techniques to improve MRI images via Compressive Sensing. The students can apply the learned algorithms and methods for the enhancements of Magnetic resonance imaging .

Compressive Sensing (CS) describes a new paradigm in signal processing to sample signals in a parsimonious and efficient way. Its aim is to establish reconstruction methods using fewer measurements than were traditionally thought necessary by exploiting the parsimony of the data. Since its introduction in 2006, several applications arose like in the fields of radars, seismology or medical imaging. Particularly in the last one, Magnetic resonance imaging (MRI) turned to be a fruitful application for Compressive Sensing because of its inherent slow data acquisition process. The application of CS to MRI offered significant scan time reductions. The goal of this seminar is to discuss the application of Compressive Sensing to MRI and implement them. The students will be able to understand the theoretical basis of MRI and how CS algorithms are able to improve it.

Basic knowledge in: linear algebra, system theory, probability theory, convex optimization, signal representations in time- and frequency domain, compressive sensing The following moduls should be completed: analysis 1-3, signal- and system theory

After a basic introduction to the physics of MRI and some optimization methods, the students will have small projects to present every week and tasks to discuss and collaborate with other colleagues

There will be exercise sheets every week to be delivered in the following week and seminars to be presented along the course. The sheets will be divided into a theoretical part, where the students need to work with concepts of optimization and probability, and a practical part, where the students will need to implement the state-of-the-art version of Compressive Sensing algorithms for MRI and deal with real data.

A. Majumdar - "Compressed Sensing for Engineers" S. Foucart, H. Rauhut - "A mathematical Introduction to Compressed Sensing" A. Majumdar - "Compressed Sensing for Magnetic Resonance Image Reconstruction" S. Boyd - "Convex Optimization" D. Bertsekas - "Convex Optimization Algorithms"