Regularized total least squares approach for nonconvolutional linear inverse problems

Wenwu Zhu, Yao Wang, Nikolas P. Galatsanos, Jun Zhang

Research output: Contribution to journalArticle

Abstract

In this correspondence, a solution is developed for the regularized total least squares (RTLS) estimate in linear inverse problems where the linear operator is nonconvolutional. Our approach is based on a Rayleigh quotient (RQ) formulation of the TLS problem, and we accomplish regularization by modifying the RQ function to enforce a smooth solution. A conjugate gradient algorithm is used to minimize the modified RQ function. As an example, the proposed approach has been applied to the perturbation equation encountered in optical tomography. Simulation results show that this method provides more stable and accurate solutions than the regularized least squares and a previously reported total least squares approach, also based on the RQ formulation.

Original languageEnglish (US)
Pages (from-to)1657-1661
Number of pages5
JournalIEEE Transactions on Image Processing
Volume8
Issue number11
DOIs
StatePublished - 1999

Fingerprint

Linear Inverse Problems
Total Least Squares
Rayleigh quotient
Inverse problems
Optical tomography
Mathematical operators
Optical Tomography
Conjugate Gradient Algorithm
Least Squares Estimate
Formulation
Smooth Solution
Linear Operator
Least Squares
Regularization
Correspondence
Perturbation
Minimise
Simulation

Keywords

  • Image reconstruction
  • Image recovery
  • Image restoration
  • Inverse problems
  • Optical tomography
  • Regularization
  • Tomographic imaging

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Vision and Pattern Recognition

Cite this

Regularized total least squares approach for nonconvolutional linear inverse problems. / Zhu, Wenwu; Wang, Yao; Galatsanos, Nikolas P.; Zhang, Jun.

In: IEEE Transactions on Image Processing, Vol. 8, No. 11, 1999, p. 1657-1661.

Research output: Contribution to journalArticle

Zhu, Wenwu ; Wang, Yao ; Galatsanos, Nikolas P. ; Zhang, Jun. / Regularized total least squares approach for nonconvolutional linear inverse problems. In: IEEE Transactions on Image Processing. 1999 ; Vol. 8, No. 11. pp. 1657-1661.
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