Estimation of piecewise constant coefficients of parabolic equations: Applications to the detection of buried objects

Nguyen Trung Thành, Hichem Sahli, Dinh Nho Hao

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

A one-dimensional inverse problem arising in infrared thermography for the detection and characterization of buried objects is introduced. Mathematically, the problem is to reconstruct a piecewise constant coefficient of a scalar heat equation in a finite rod from measurements taken at one of its extremities. The problem is posed in the well known least-squares setting and solved by a quasi-Newton method. The contributions of this article include: (i) the parameterization of a piecewise constant function by a small number of unknown parameters which represent its constant values and locations of discontinuities; (ii) the application of the adjoint field technique in the calculation of the gradient of a discretized objective function and (iii) the application of the considered inverse problem in the detection and characterization of buried objects. Numerical results illustrate the good performance of the proposed algorithm.

Original languageEnglish (US)
Pages (from-to)903-925
Number of pages23
JournalInverse Problems in Science and Engineering
Volume16
Issue number7
DOIs
StatePublished - Oct 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Computer Science Applications
  • Applied Mathematics

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