Inverse Methods for High-dimensional Multi-modal Data
Abstract
This proposal aims to address the fundamental challenge of inverting high-dimensional multi-modal data, that is to simultaneously se""parate and identify the ~eld parameters of different modalities from noisy observations, at a resolution much higher than the natura""l resolution of the sensing platforms, with provable performance guarantees in resource-constrained or sample-starved environments."" This has far-reaching implications in many problems of fundamental importance to the Navy, including identifying sources of informa""tion in signal intelligence, radiating sources in radar and sonar, ~eld elements in electromagnetic, acoustic, and nuclear images, a""nd many more. However, most existing techniques are developed for inverting single-modal datasets, which either cannot be applied or" perform poorly for multi-modal data.The proposed research program will develop a comprehensive framework for inverting multi-moda"l datasets, where computationally ef~cient and robust inverse methods using a limited amount of noisy, incomplete, and/or corrupted"" observations, will be developed with provable near-optimal performance guarantees, complemented by characterizations of fundamental"" trade-offs between sample complexity, resolution limits, and noise level. The proposed theoretical and practical chal-lenges will b""e addressed with a new combination of insights and techniques from statistical signal processing, convex optimization, information t"heory and high-dimensional statistics. The proposed research program confronts the following tasks:~ Exact Inversion of Multi-modal Data: Computationally-ef~cient methods based on convex optimization will be developed to separate and estimate the ~eld parameters" of multi-modal data, where near-optimal performance guarantees of exact inversion are established in terms of sample complexity and" error rate;~ Calibration and Blind Inversion of Multi-modal Data: Computationally-ef~cient methods for blind calibration and blind" inversion of single-modal and multi-modal data with performance guarantees will be developed, where mild assumptions are posed on t"he point spread functions to enable identi~ability;~ Physically-Meaningful Dictionary Learning: Computationally-ef~cient methods fo"r learning physically-meaningful representations of multi-modal data with performance guarantees will be developed, where physically"-meaningful properties such as translation invariance are preserved in the dictionary representation;~ Fundamental Limits: Fundamen"tal limits for inverting multi-modal data will be developed, including analysis of identifiability, Cramer-Rao bound, and trade-offs"" between sample complexity, resolution limits, and noise level.~ Dissemination and Technology Transfer: Substantial interactions wi"th NRL will be actively pursued to foster potential transition avenues for research under this project.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 20, 2018
- Source ID
- N000141812142
Entities
People
- Yuejie Chi
Organizations
- Massachusetts Institute of Technology
- Office of Naval Research
- United States Navy