Nonlinear image restoration using FFT-based conjugate gradient methods

Michael K. Ng

doi:10.1109/ICIP.1995.537410

Nonlinear image restoration using FFT-based conjugate gradient methods

Michael K. Ng^*

^*Corresponding author for this work

Department of Mathematics

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

2 Citations (Scopus)

Abstract

Nonlinear image restoration finds applications in a wide variety of research areas. In this paper, we consider nonlinear space-invariant imaging system with additive noise. The restored images can be found by solving weighted Toeplitz least squares problems. Since the normal equations matrices are non-Toeplitz in general, the fast Fourier transforms (FFTs) cannot be utilized in the evaluation of their inverses. We employ the preconditioned conjugate gradient method (PCG) with the FFT-based preconditioners to solve regularized linear systems arising from nonlinear image restoration problems. Thus we precondition these linear systems in the Fourier domain, while iterating in the spatial domain. Numerical examples are reported on a ground-based atmospheric imaging problem to demonstrate the fast convergence of the FFT-based PCG method.

Original language	English
Title of host publication	Proceedings - 1995 IEEE International Conference on Image Processing, ICIP 1995
Publisher	IEEE
Pages	41-44
Number of pages	4
ISBN (Print)	0818673109
DOIs	https://doi.org/10.1109/ICIP.1995.537410
Publication status	Published - Oct 1995
Event	1995 IEEE International Conference on Image Processing, ICIP 1995 - , United States Duration: 23 Oct 1995 → 26 Oct 1995 https://ieeexplore.ieee.org/xpl/conhome/4052/proceeding (Conference Proceedings)

Conference

Conference	1995 IEEE International Conference on Image Processing, ICIP 1995
Country/Territory	United States
Period	23/10/95 → 26/10/95
Internet address	https://ieeexplore.ieee.org/xpl/conhome/4052/proceeding (Conference Proceedings)

Scopus Subject Areas

Hardware and Architecture
Computer Vision and Pattern Recognition
Electrical and Electronic Engineering

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10.1109/ICIP.1995.537410

Cite this

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title = "Nonlinear image restoration using FFT-based conjugate gradient methods",

abstract = "Nonlinear image restoration finds applications in a wide variety of research areas. In this paper, we consider nonlinear space-invariant imaging system with additive noise. The restored images can be found by solving weighted Toeplitz least squares problems. Since the normal equations matrices are non-Toeplitz in general, the fast Fourier transforms (FFTs) cannot be utilized in the evaluation of their inverses. We employ the preconditioned conjugate gradient method (PCG) with the FFT-based preconditioners to solve regularized linear systems arising from nonlinear image restoration problems. Thus we precondition these linear systems in the Fourier domain, while iterating in the spatial domain. Numerical examples are reported on a ground-based atmospheric imaging problem to demonstrate the fast convergence of the FFT-based PCG method.",

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AB - Nonlinear image restoration finds applications in a wide variety of research areas. In this paper, we consider nonlinear space-invariant imaging system with additive noise. The restored images can be found by solving weighted Toeplitz least squares problems. Since the normal equations matrices are non-Toeplitz in general, the fast Fourier transforms (FFTs) cannot be utilized in the evaluation of their inverses. We employ the preconditioned conjugate gradient method (PCG) with the FFT-based preconditioners to solve regularized linear systems arising from nonlinear image restoration problems. Thus we precondition these linear systems in the Fourier domain, while iterating in the spatial domain. Numerical examples are reported on a ground-based atmospheric imaging problem to demonstrate the fast convergence of the FFT-based PCG method.

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BT - Proceedings - 1995 IEEE International Conference on Image Processing, ICIP 1995

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T2 - 1995 IEEE International Conference on Image Processing, ICIP 1995

Y2 - 23 October 1995 through 26 October 1995

ER -

Nonlinear image restoration using FFT-based conjugate gradient methods

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