A wavelet-based multiresolution regularized least squares reconstruction approach for optical tomography

Wenwu Zhu, Yao Wang, Yining Deng, Yuqi Yao, Randall L. Barbour

Research output: Contribution to journalArticle

Abstract

In this paper we present a wavelet-based multigrid approach to solve the perturbation equation encountered in optical tomography. With this scheme the unknown image the data as well as the weight matrix are all represented by wavelet expansions thus yielding a multiresolution representation of the original perturbation equation in the wavelet domain. This transformed equation is then solved using a multigrid scheme by which an increasing portion of wavelet coefficients of the unknown image are solved in successive approximations. One can also quickly identify regions of interest (ROI's) from a coarse level reconstruction and restrict the reconstruction in the following fine resolutions to those regions. At each resolution level a regularized least squares solution is obtained using the conjugate gradient descent method. This approach has been applied to continuous wave data calculated based on the diffusion approximation of several two-dimensional (2-D) test media. Compared to a previously reported one grid algorithm the multigrid method requires substantially shorter computation time under the same reconstruction quality criterion.

Original languageEnglish (US)
Pages (from-to)210-217
Number of pages8
JournalIEEE Transactions on Medical Imaging
Volume16
Issue number2
DOIs
StatePublished - 1997

Keywords

  • Image reconstruction
  • Multigrid method
  • Optical tomography
  • Wavelet transform

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering

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