Multiscale System Theory

Abstract

In many applications, it is of interest to analyze and recognize phenomena occurring at different scales. The recently introduced wavelet transforms provide a time-and-scale decomposition of signals that offers the possibility of such an analysis. Until recently, however, there has been no corresponding statistical framework to support the development of optimal, multiscale statistical signal processing algorithms. A recent work of some of the present authors and co-authors proposed such a framework via models of "stochastic fractals" on the dyadic tree. In this paper we investigate some of the fundamental issues that are relevant to system theories on the dyadic tree, both for systems and signals.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Feb 21, 1990
Accession Number
ADA455882

Entities

People

  • Alan S. Willsky
  • Albert Benveniste
  • Ramine Nikoukhah

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Coefficients
  • Covariance
  • Differential Equations
  • Equations
  • Frequency Domain
  • Partial Differential Equations
  • Power Series
  • Sequences
  • Signal Processing
  • Standards
  • Stationary Processes
  • Stochastic Processes
  • Transfer Functions
  • Two Dimensional
  • Wavelet Transforms

Fields of Study

  • Computer science

Readers

  • Image Processing and Computer Vision.
  • Theoretical Analysis.