Inverse Methods for High-dimensional Multi-modal Data
Abstract
Statement of Work: The PI will develop new analytical and computational tools for inverse problems involving high-dimensional multi-modal Data. Objective: This proposal aims to address the fundamental challenge of inverting high-dimensional multimodal data, that is to simultaneously separate and identify the field parameters of different modalities from noisy observations, at a resolution much higher than the natural resolution of the sensing platforms, with provable performance guarantees in resource-constrained or sample-starved environments. The PI will develop a comprehensive framework for inverting multimodal datasets, where computationally efficient 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. Approach: The PI will attempt to complete the following tasks: 1) Exact Inversion of Multi-modal Data: Computationally-efficient methods based on convex optimization will be developed to separate and estimate the field parameters of multi-modal data, where near-optimal performance guarantees of exact inversion are established in terms of sample complexity and error rate; 2) Calibration and Blind Inversion of Multi-modal Data: Computationally-efficient methods for blind calibration and blind inversion of single-modal and multi-modal data with performance guarantees will be developed, where the point spread functions are assumed unknown but mildly constrained in a low-dimensional subspace; 3) Physically-Meaningful Dictionary Learning: Computationally-efficient methods for 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; 4) Fundamental Limits: Fundamental 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. Overall Merit and ONR Mission/Relevance: The PI will apply rigorous mathematical results to obtain practical computational tools to address inverse problems, in the presence of noisy data. This effort will enhance the Navy and the DoD s capabilities in inverse problems, including identifying sources of information in signal intelligence, radiating sources in radar and sonar, field elements in electromagnetic, acoustic, and nuclear images, among others.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2016
- Source ID
- N000141512387
Entities
People
- Yuejie Chi
Organizations
- Office of Naval Research
- Ohio State University
- United States Navy