Multi-parameter regularization methods for high-resolution image reconstruction with displacement errors

Yao Lu; Lixin Shen; Yuesheng Xu

doi:10.1109/TCSI.2007.902535

Multi-parameter regularization methods for high-resolution image reconstruction with displacement errors

Yao Lu, Lixin Shen, Yuesheng Xu

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

We propose multi-parameter regularization methods for high-resolution image reconstruction which is described by an ill-posed problem. The regularization operator for the ill-posed problem is decomposed in a multiscale manner by using bi-orthogonal wavelets or tight frames. In the multiscale framework, for different scales of the operator we introduce different regularization parameters. These methods are analyzed under certain reasonable hypotheses. Numerical examples are presented to demonstrate the efficiency and accuracy of these methods.

Original language	English (US)
Pages (from-to)	1788-1799
Number of pages	12
Journal	IEEE Transactions on Circuits and Systems I: Regular Papers
Volume	54
Issue number	8
DOIs	https://doi.org/10.1109/TCSI.2007.902535
State	Published - Aug 2007

Keywords

Framelets
High-resolution image reconstruction
Multi-parameter regularization
Wavelets

ASJC Scopus subject areas

Hardware and Architecture
Electrical and Electronic Engineering

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10.1109/TCSI.2007.902535

Cite this

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title = "Multi-parameter regularization methods for high-resolution image reconstruction with displacement errors",

abstract = "We propose multi-parameter regularization methods for high-resolution image reconstruction which is described by an ill-posed problem. The regularization operator for the ill-posed problem is decomposed in a multiscale manner by using bi-orthogonal wavelets or tight frames. In the multiscale framework, for different scales of the operator we introduce different regularization parameters. These methods are analyzed under certain reasonable hypotheses. Numerical examples are presented to demonstrate the efficiency and accuracy of these methods.",

keywords = "Framelets, High-resolution image reconstruction, Multi-parameter regularization, Wavelets",

author = "Yao Lu and Lixin Shen and Yuesheng Xu",

note = "Funding Information: Manuscript received August 31, 2006; revised February 22, 2007. This work was supported in part by the US National Science Foundation under Grant CCR-0407476, by National Aeronautics and Space Administration under Cooperative Agreement NNX07AC37A, by the Natural Science Foundation of China under Grant 10371122 and Grant 10631080, and by Ministry of Education, China, under the Changjiang Scholarship program through Zhongshan University, China. This paper was recommended by Associate Editor I. Yamada.",

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doi = "10.1109/TCSI.2007.902535",

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AU - Lu, Yao

AU - Shen, Lixin

AU - Xu, Yuesheng

N1 - Funding Information: Manuscript received August 31, 2006; revised February 22, 2007. This work was supported in part by the US National Science Foundation under Grant CCR-0407476, by National Aeronautics and Space Administration under Cooperative Agreement NNX07AC37A, by the Natural Science Foundation of China under Grant 10371122 and Grant 10631080, and by Ministry of Education, China, under the Changjiang Scholarship program through Zhongshan University, China. This paper was recommended by Associate Editor I. Yamada.

PY - 2007/8

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N2 - We propose multi-parameter regularization methods for high-resolution image reconstruction which is described by an ill-posed problem. The regularization operator for the ill-posed problem is decomposed in a multiscale manner by using bi-orthogonal wavelets or tight frames. In the multiscale framework, for different scales of the operator we introduce different regularization parameters. These methods are analyzed under certain reasonable hypotheses. Numerical examples are presented to demonstrate the efficiency and accuracy of these methods.

AB - We propose multi-parameter regularization methods for high-resolution image reconstruction which is described by an ill-posed problem. The regularization operator for the ill-posed problem is decomposed in a multiscale manner by using bi-orthogonal wavelets or tight frames. In the multiscale framework, for different scales of the operator we introduce different regularization parameters. These methods are analyzed under certain reasonable hypotheses. Numerical examples are presented to demonstrate the efficiency and accuracy of these methods.

KW - Framelets

KW - High-resolution image reconstruction

KW - Multi-parameter regularization

KW - Wavelets

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JF - IEEE Transactions on Circuits and Systems I: Regular Papers

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Multi-parameter regularization methods for high-resolution image reconstruction with displacement errors

Abstract

Keywords

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