Compressed sensing (CS) is a new signal acquisition paradigm that enables the reconstruction of signals and images from a low number of samples. A particularly exciting application of CS is Magnetic Resonance Imaging (MRI), where CS significantly speeds up scan time by requiring far fewer measurements than standard MRI techniques. Such a reduction in sampling time leads to less power consumption, less need for patient sedation, and more accurate images. This accuracy increase is especially pronounced in pediatric MRI where patients have trouble being still for long scan periods. Although such gains are already significant, even further improvements can be made by utilizing past MRI scans of the same patient. Many patients require repeated scans over a period of time in order to track illnesses and the prior scans can be used as references for the current image. This allows samples to be taken adaptively, based on both the prior scan and the current measurements. Work by Weizman has shown that so-called reference based adaptive-weighted temporal Compressed Sensing MRI (LACS-MRI) requires far fewer samples than standard Compressed Sensing (CS) to achieve the same reconstruction signal-to-noise ratio (RSNR). The method uses a mixture of reference-based and adaptive-sampling. In this work, we test this methodology by using various adaptive sensing schemes, reconstruction methods, and image types. We create a thorough catalog of reconstruction behavior and success rates that is interesting from a mathematical point of view and is useful for practitioners. We also solve a grayscale compensation toy problem that supports the insensitivity of LACS-MRI to changes in MRI acquisition parameters and thus showcases the reliability of LACS-MRI in possible clinical situations.

Author Bio

Kevin Stangl is a senior studying applied mathematics at UCLA. His main mathematical interest is probability theory. He also enjoys puzzle solving and hiking. His favorite mathematician is Persi Diaconis and he plans to attend grad school in mathematics starting in the fall of 2017.

Samuel Birns completed this paper while participating in the Applied Mathematics REU at UCLA during the summer of 2015, under the direction of Prof. Deanna Needell of Claremont McKenna College. He hopes to obtain a PhD in logic or theoretical computer science. Sam invests the majority of his free time into being a competitive powerlifter, but also enjoys tennis, cooking, and playing the piano.

Stephanie Ku was an applied mathematics major at UCLA and she will be attending Rensselaer Polytechnic Institute for graduate studies. She enjoys hiking, Reddit, crime documentaries, and the board game Settlers of Catan.

Brianna Kim is a recent graduate of mathematics at UCI who will attend to graduate school at UCLA studying applied mathematics.