DATA FUSION AND UNBALANCED OPTIMAL MASS TRANSPORT
Abstract
Geometric concepts and computational tools have been extensively developed by our team in recent years in the context of spectral analysis of time series, image processing, and more recently, quantum dynamics (i.e., matrix-valued processes). The current proposal aims to develop further some of these concepts as well explore new ideas for data processing and data fusion. In particular, we aim at new ways to co-process and integrate information on dynamical processes that may be available simultaneously at different frequencies, polarizations, and/or collected through a variety of sensors (e.g., multispectral and color). To this end, power from different “channels” (i.e., sensors, polarization directions, frequencies) is seen as a vectorial/matrix/tensorial quantity, and thus new geometric techniques need to be developed to properly account/model energy flow among these various “channels.” In addition to the development of the necessary theory for vector-valued and tensorial data, the proposed effort will focus on the scalability and speed of the resulting signal processing algorithms. Underlying the general methodology of matrix-valued interpolation are mathematical concepts that, unexpectedly, have impacted our view of quantum dynamics, displaying such as a gradient flows, and making contact with key ideas from quantum information theory.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2021
- Source ID
- FA95502010029
Entities
People
- Allen Tannenbaum
Organizations
- Air Force Office of Scientific Research
- Research Foundation for the State University of New York
- United States Air Force