Fast high-resolution image reconstruction using tikhonov regularization based total least squares

Geunseop Lee, Haoying Fu, Jesse Louis Barlow

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The solution of an ill-conditioned total least squares (TLS) problem from highresolution imaging by the regularization approach of Golub, Hansen, and O'Leary [SIAM J. Matrix Anal. Appl., 21 (2000), pp. 185-194] is considered. This work solves the regularized TLS problem as a system of nonlinear equations in the two regularization parameters. Since the Jacobian of the system can be computed inexpensively, the approach is based upon Newton's method. From experimental results, the algorithm produces a fast computation of the solution of the high-resolution image reconstruction problem.

Original languageEnglish (US)
JournalSIAM Journal on Scientific Computing
Volume35
Issue number1
DOIs
StatePublished - Apr 22 2013

Fingerprint

Total Least Squares
Tikhonov Regularization
Least Squares Problem
Image Reconstruction
Newton-Raphson method
Image reconstruction
Nonlinear equations
High Resolution
Imaging techniques
System of Nonlinear Equations
Regularization Parameter
Newton Methods
Two Parameters
Regularization
Imaging
Experimental Results

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

@article{91c7236efa9c4474b9a81b57e5fc94d0,
title = "Fast high-resolution image reconstruction using tikhonov regularization based total least squares",
abstract = "The solution of an ill-conditioned total least squares (TLS) problem from highresolution imaging by the regularization approach of Golub, Hansen, and O'Leary [SIAM J. Matrix Anal. Appl., 21 (2000), pp. 185-194] is considered. This work solves the regularized TLS problem as a system of nonlinear equations in the two regularization parameters. Since the Jacobian of the system can be computed inexpensively, the approach is based upon Newton's method. From experimental results, the algorithm produces a fast computation of the solution of the high-resolution image reconstruction problem.",
author = "Geunseop Lee and Haoying Fu and Barlow, {Jesse Louis}",
year = "2013",
month = "4",
day = "22",
doi = "10.1137/110850591",
language = "English (US)",
volume = "35",
journal = "SIAM Journal of Scientific Computing",
issn = "1064-8275",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",

}

Fast high-resolution image reconstruction using tikhonov regularization based total least squares. / Lee, Geunseop; Fu, Haoying; Barlow, Jesse Louis.

In: SIAM Journal on Scientific Computing, Vol. 35, No. 1, 22.04.2013.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Fast high-resolution image reconstruction using tikhonov regularization based total least squares

AU - Lee, Geunseop

AU - Fu, Haoying

AU - Barlow, Jesse Louis

PY - 2013/4/22

Y1 - 2013/4/22

N2 - The solution of an ill-conditioned total least squares (TLS) problem from highresolution imaging by the regularization approach of Golub, Hansen, and O'Leary [SIAM J. Matrix Anal. Appl., 21 (2000), pp. 185-194] is considered. This work solves the regularized TLS problem as a system of nonlinear equations in the two regularization parameters. Since the Jacobian of the system can be computed inexpensively, the approach is based upon Newton's method. From experimental results, the algorithm produces a fast computation of the solution of the high-resolution image reconstruction problem.

AB - The solution of an ill-conditioned total least squares (TLS) problem from highresolution imaging by the regularization approach of Golub, Hansen, and O'Leary [SIAM J. Matrix Anal. Appl., 21 (2000), pp. 185-194] is considered. This work solves the regularized TLS problem as a system of nonlinear equations in the two regularization parameters. Since the Jacobian of the system can be computed inexpensively, the approach is based upon Newton's method. From experimental results, the algorithm produces a fast computation of the solution of the high-resolution image reconstruction problem.

UR - http://www.scopus.com/inward/record.url?scp=84876219934&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84876219934&partnerID=8YFLogxK

U2 - 10.1137/110850591

DO - 10.1137/110850591

M3 - Article

AN - SCOPUS:84876219934

VL - 35

JO - SIAM Journal of Scientific Computing

JF - SIAM Journal of Scientific Computing

SN - 1064-8275

IS - 1

ER -