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Applied Math Seminar
Sparse MRI: The Application of Compressed Sensing for Rapid Magnetic
Resonance Imaging
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Magnetic Resonance Imaging (MRI) is a non-invasive non-toxic imaging modality. The vast number of control parameters in MRI provides flexibility in image contrast. For example, MRI can distinguish between different type of soft tissues, it can image functional activity in the brain, measure flow velocities, monitor temperature changes and more. So far, MRI has been very successful in imaging parts of the body that are easily immobilized, such as the brain and joints. Its success has been much more limited for rapidly changing settings, as in imaging the heart and dynamic imaging. MRI requires a relatively long scan time compared to other imaging modalities, a requirement that limits and sometimes prevents its use in important applications. Recently, the theory of Compressed Sensing (CS) was introduced. According to CS, compressible images can be recovered from a significantly small number of measurements, well beyond the Nyquist rate. The recovery is possible as long as the measurements are random projections and the recovery is a special non-linear procedure. One of the most promising applications of compressed sensing (CS) is to MRI. MRI images in general, and dynamic MRI images in particular are often highly compressible. The MRI data are collected in the spatial frequency domain (k-space) and in most imaging scenarios, scan time is directly related to the number of data samples needed for proper reconstruction. Therefore, MRI scans can be significantly accelerated by obtaining fewer samples. All of these facts as well as that the data sampling of frequency is controllable (For example, it is possible with some restrictions to obtain random Fourier samples that can serve as approximately random projections ) makes MRI a natural compressed sensing imaging system. This talk aims to review the current development and applications of compressed sensing in MRI. The talk starts with a short overview of the MR system as well as some of the physics that is essential to understanding the imaging mechanism in MRI. This is followed by a brief review of the CS theory that is directly related to MRI, e.g. , transform sparsity of MRI images and dynamic sequences, incoherent sampling and the non-linear reconstruction. Finally examples are given from a variety of applications in which scan time can be significantly reduced such as: angiography, coronary artery imaging, dynamic heart imaging and brain imaging. Joint work with David L. Donoho, Statistics Department Stanford University, Juan M Santos and John M Pauly, EE Department Stanford |