Deconvolution of Temporally Under-Resolved Image Sequences for Coupled Dynamical Systems
Abstract
The Hall-effect thruster, a pervasive in-space propulsion device, can be effectively modelled as a coupled dynamical system using a strange attractor. This fact allows the use of Takens' Embedding Theorem (and therefore convergent cross mapping) to analyze different component variables in the system. Namely, if the system state is given by (X(t); Y (t)) and Y (t) is corrupted by noise while X(t) remains comparatively clear, X(t) can be used to retrieve the denoised Y (t) signal. Previous work by the Air Force Research Laboratory (AFRL) and past RIPS-AFRL research teams has yielded methods to denoise corrupted signals, as well as reconstruct underlying signals from temporally under-resolved time series (deconvolution). Both denoising and deconvolution involve mapping a clean reference signal to phase space and averaging the corrupted signal within partitions of phase space. The original work by the AFRL utilized a grid-based partition, while the 2020 RIPS-AFRL research team used Voronoi diagram-based partitions of phase space. In this work, we primarily extend the capabilities of the Voronoi diagram-based partition to work with deconvolution and substantially decrease the computational runtime of the deconvolution algorithm so that it can be applied to a system where many corrupted signals are coupled to the same clean reference signal. Additionally, we develop optimization strategies that increase the accuracy of our reconstructions of target signals.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 20, 2021
- Accession Number
- AD1202421
Entities
People
- Addie Mccurdy
- Benjamin Maloy
- Nagaprasad Rudrapatna
- Sharadiant Turner
Organizations
- Duke University
- Spelman College
- Tufts University
- University of St. Thomas