Analysis of Wavelet Transform Multiscale Products for Step Detection and Estimation

Abstract

We consider discrete wavelet transform (DWT) multiscale products for detection and estimation of steps. Here the DWT is an overcomplete approximation to smoothed gradient estimation, with smoothing varied over dyadic scale. We show that the multiscale product approach for edge detection is a nonlinear whitening transformation. We characterize the resulting non-Gaussian heavy tailed densities. The results may be applied to edge detection with a false alarm constraint. The response to impulses, steps, and pulses is also characterized. A general closed form expression for the Cramer Rao bound (CRB) for discrete and continuous time step change location estimation in independent identically distributed non-Gaussian noise is developed, generalizing previous results. We consider location estimation using multiscale products, and compare results to the appropriate CRB.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1998
Accession Number
ADA351960

Entities

People

  • Ananthram Swami
  • Brian M. Sadler

Organizations

  • United States Army Research Laboratory

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Change Detection
  • Data Science
  • Detection
  • Estimators
  • False Alarms
  • Filtration
  • Frequency
  • Frequency Response
  • Gaussian Noise
  • Image Processing
  • Information Processing
  • Information Science
  • Mathematical Filters
  • Order Statistics
  • Statistical Analysis
  • Statistics

Fields of Study

  • Engineering

Readers

  • Image Processing and Computer Vision.
  • Statistical inference.