December 10, 2015
Wen-shin Lee (Universiteit Antwerpen): "How sub-sampling leads to more robustness and higher resolution in signal processing" @ Université des Sciences et Technologies de Lille - Lille I, Laboratoire de Mathématiques Paul Painlevé UMR CNRS 8524, "Analyse Numérique - Equations aux Dérivées Partielles" seminar.
Reconstructing a digital signal from its measurements is an inverse problem that can be extremely ill-posed. Meanwhile, sampling a signal uniformly below the Shannon-Nyquist rate leads to aliasing, an unwanted effect causing different signals to become indistinguishable.
We develop a parametric method to retrieve fine-scale information from coarse-scale measurements. By combining symbolic and numerical tools, we exploit, rather than avoid, aliasing to regularize the problem, hence to increase the frequency resolution or to reduce the number of required measurements.
Our development is motivated by some difficulties encountered in magnetic resonance spectroscopy (MRS) and magnetic resonance imaging (MRI). Both MRS and MRI are based on nuclear magnetic resonance and have found wide applications in medicine, chemistry, physics and many scientific fields. MRS is after a high frequency resolution from a limited amount of data collected from the time domain. It has already become a major tool to study metabolic changes in brain tumors, Alzheimer’s disease, as well as the metabolism of other organs. MRS has been playing an ever more important role in other applications such as drug development and explosive detection. In MRI, one seeks to obtain a high-resolution image in the spatial domain from fewer scans in the k-space: In medical diagnosis, fewer scans can be translated into shorter measuring time, better quality data, thus inevitable economical benefits.