A Multiscale Approach to Solving One Dimensional Inverse Problems

Abstract

In this paper we explore a multiresolution approach to solving one dimensional inverse problems. The approach we take is motivated by the work of Chon, Golden, and Willsky [ and Beylkin, Coifman, and Rokhlin. Specifically, we consider inverse problems described by that class of operators which are made sparse under the action of the wavelet transform. Moreover, statistically-based inversion procedures utilizing multiscale a priori stochastic models are considered. As a concrete example, we examine a deconvolution problem arising in wellbore induction measurement of conductivity.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1992
Accession Number
ADA459602

Entities

People

  • Alan Willsky
  • Eric L. Miller

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Algorithms
  • Coefficients
  • Computer Science
  • Concrete
  • Equations
  • Integrals
  • Inverse Problems
  • Inversion
  • Measurement
  • Military Research
  • Models
  • Probabilistic Models
  • Scientific Research
  • Transmitters
  • Wavelet Transforms

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Operations Research
  • Wave Propagation and Nonlinear Chaotic Dynamics.