Comparison of Two Different Interval Techniques for Analyzing the Influence of Measurement Uncertainty in Compressed Sensing for Magnet Resonance Imaging

Magnet resonance imaging (MRI) techniques are well known from the field of medical examinations. Possible applications range from the detection of stenoses in blood vessels, cerebral aneurysms, joint and ligament injuries to X-ray-free methods for mammography. In addition to these medical applications, MRI techniques have gained more and more interest by researchers from the fields of fluid mechanics and other engineering disciplines due to their capability for a non-invasive quantification of multi-dimensional velocity and temperature fields. Especially if engineering applications are of interest, not only qualitative results are required, but also quantitative statements about temperature fields and/or velocity distributions together with quality measures allowing for the description of the influence of measurement uncertainty. This paper aims at the comparison of two different techniques based on interval arithmetic for the signal processing-based analysis of measurement uncertainty with an application to real measured data acquired by a compressed sensing scheme from an MRI scanner available at the Institute of Fluid Mechanics at the University of Rostock.