Speaker.  Yuanchang Sun, Math & Stats, FIU.

Title. Enhanced Peak Separation and Signal Recovery in Overlapped and Noisy Spectral Data.

Abstract. Substances such as chemical compounds and biological agents are invisible to human eyes, they are usually captured by sensing equipment with their spectral fingerprints.  The work in this talk is motivated by the analysis of Nuclear Magnetic Resonance (NMR) spectra, which presents challenges due to signal overlap and the presence of noise.

In the first part of this talk, we propose a novel approach for enhancing peak separation and signal recovery in overlapped and mixing noisy NMR spectra without the knowledge of the mixing process and the mixing substances (so called blind source separation).  

Moving on to the second part, we consider a problem where the knowledge of spectral references of the substances are available, the task of data fitting is to solve their weights, which usually can be solved by least squares. Complications occur if a shift of the source signal peaks occurs in the mixtures. we formulate mathematical model for such distortions and build them into data fitting algorithms.