Geometric and Graph Structures in Information Characterization and Extraction
Abstract
Research problem: Our goal is to develop a theory to both, characterize and extract information from data having geometric and graph structures. The research program starts from the observation that signal structure is a fundamental enabler for the characterization and extraction of information. Our contention is that for the specific case of time signals we have well developed tools in statistics, signal processing, and information theory. These tools do not generalize well to data sources such as images and signals supported on graphs. Yet, these signals have some form of structure that can be leveraged to extract information efficiently. Our goal is the development of this theory and corresponding methodologies. Technical approach. Our technical approach is that the challenges in processing different data modalities is the presence of different structures and that different tasks require different representations. We have identified two types of structure that will be exploited for suitable representations: Geometric structure. Such is the nature of images and videos. Considerable variability within image classes is often uninformative. Part of this variability is due to rigid translations, rotations, or scaling and we must therefore search for techniques and measures of information that are invariant to this variability. Graph structured signals. This arises when data is collected over an irregular domain that renders the conventional notions of smoothness and proximity not applicable. We resort to endowing the signal with a support graph that defines proximity between different elements and search for representations over these irregular domains. In our proposed research thrusts we also observe that the state of art for the processing of geometric signals is more advanced than our current understanding of graph signals. In the case of the former modern efforts center on nonlinear processing. Most notably, on convolutional neural networks (CNNs) which have achieved fantastic results in the recent past. In the case of graph signals we don t have neither a rich theory nor a well developed practice for linear processing. Recent efforts in Graph Signal Processing (GSP) are concerned with developing such a theory. If our experience with image and video processing translates to graph signals, and there is no reason to suspect it won t, nonlinear processing of graph signals will result in dramatic improvements relative to linear processing. Our ultimate goal is to develop such a theory but to get there we need to advance the sate of the art of nonlinear geometric information processing and linear graph information processing. This motivates a research program built around three research thrusts: (i) Nonlinear geometric information processing. (ii) Linear graph information processing. (iii) Nonlinear graph information processing. Anticipated outcomes and impact on DoD capabilities: We will develop new metrics to measure information in images and signals supported on graphs as well as new tools to extract such information. The applications range from intelligence gathering and automated reconnaissance to mission evaluation. We will engage our DoD partners to ensure our research is grounded in real-world constraints and to identify technology transition paths. The are committed to transition their results to the DoD. The senior PI has a proven track record of collaboration with the armed forces research labs.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Sep 11, 2018
- Source ID
- W911NF1710438
Entities
People
- Alejandro Ribeiro
Organizations
- Army Contracting Command
- United States Army
- University of Pennsylvania