Fractal Estimation using Models on Multiscale Trees

Abstract

In this paper we estimate the fractal dimension of stochastic processes with 1/f-like spectra by applying a recently-introduced multiresolution framework. This framework admits an efficient likelihood function evaluation, allowing us to compute the maximum likelihood estimate of this fractal parameter with relative ease. In addition to yielding results that compare well to other proposed methods. and in contrast to other approaches, our method is directly applicable, with at most very simple modification, in a variety of other contexts including fractal estimation given irregularly sampled data or nonstationary measurement noise and the estimation of fractal parameters for 2-D random fields.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1995
Accession Number
ADA459845

Entities

People

  • Alan S. Willsky
  • Paul W. Fieguth

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Brownian Motion
  • Computer Science
  • Covariance
  • Electrical Engineering
  • Estimators
  • Gaussian Noise
  • Information Science
  • Information Theory
  • Maximum Likelihood Estimation
  • Multiscale Models
  • Signal Processing
  • Standards
  • Statistical Analysis
  • Statistics
  • Stochastic Processes
  • Two Dimensional

Readers

  • Computational Fluid Dynamics (CFD)
  • Graph Algorithms and Convex Optimization.
  • Statistical inference.