A Unified Framework for Multi-level Processing of Complex Data
Abstract
Complex data are lifted to a high-dimensional point-cloud for exploring data similarities, with each point representing an image thumb-nail, highlight of a medical record, spectral curve for every pixel of an HSI cube, etc. A weighted graph, with data similarities as weights, is constructed to connect the points of the point-cloud, and embedded to some binary tree by applying the shortest-path algorithm. The objective is to map the tree to the unit interval of the real-line, allowing us to extend the theory and methods from harmonic analysis to the study of functions on the given complex data. To build a unified framework for multi-level processing of the given complex data, spline and wavelet methods and algorithms have been developed with emphasis on real-time implementation. Toward the end of the funding period, an innovative theory, along with local methods, was developed for separating nonlinear and non-stationary signals from a blind source embedded with noise, via extraction of polynomial-like trends, point-set clustering, and estimation of instantaneous frequencies. This development has also been extended to the multivariate setting, including separation of image data.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 04, 2014
- Accession Number
- ADA623286
Entities
People
- Charles K. Chui
Organizations
- University of Missouri