Compressive sensing (CS) is one of the important theories developed in signal processing in the recent decade, and MRI is it's one of, if not biggest, field of practical application. The use of compressive sensing can greatly reduce the number of measurements required during an MRI scan which result in faster acquisition. By the time I started researching this topic, the use of CS in MRI has already been researched, but it was limited to static subjects, ex. brain scans. However the real challenge of MRI is for the dynamic scans when the time of acquision is really limited, and the subject is changing in time, often moving.
As a part of this project, I have developed regularization methods for the reconstruction of temporally varying MRI scans from heavily incomplete samples (in Fourier domain). I have also developed new convex optimization approaches to be used for inverse problems regarding MRI which can be significantly parallelized and accelerated using GPUs.
This work formed the basis of my PhD. thesis, and helped me understand not only compressed sensing and inverse problems but also convex optimization and MRI. Having implemented all the algorithms that I used by myself, I also had immense experience on implementations with Matlab, linear algebra and parallel processing.