Multidimensional and Compressive Super-Resolution: Theory, Computation, and Fundamental Limits

Cuny City College, New York NY

Investigators

Abstract

Novel imaging methods that produce high resolution images are indispensable tools that have enabled important scientific discoveries and technological advancements. Imaging devices have fundamental resolution limits, and super-resolution techniques are computational methods that are used to bypass such limits by leveraging prior information about an imaged object. For many applications including remote sensing, super-resolution fluorescence microscopy and quantum information theory, the imaged objects can be modeled as a collection of point sources and the collected information is a superposition of sinusoidal waves. This project develops novel super-resolution algorithms that will be used for imaging and signal processing and provides their performance guarantees. The City College of New York is one of the most diverse universities in the United States, and this project will support students through research opportunities. Existing super-resolution theory and computational methods primarily pertain to the one-dimensional uniform sampling case. On the other hand many applications are inherently multidimensional and collecting samples may be expensive while new imaging technology allows for the acquisition of specialized information. This project focuses on three themes with the goal of bridging theory and practice. (1) It introduces novel and efficient multidimensional super-resolution algorithms and analyzes their stability and resolution limits. (2) It formulates novel compressive super-resolution algorithms that require fewer samples and rigorously derives their sampling complexities and stability. (3) Use of fluorescence molecules has revolutionized imaging of biological samples and this project formulates a novel model with an accompanying expected min-max error, studying candidate algorithms in search of an optimal one. The theoretical performance guarantees that accompany these methods will provide valuable guidelines for practitioners. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.