Operator decomposition using the wavelet transform: Fundamental properties and image restoration applications

M. E. Zervakis; Taek M Kwon; A. E. Savakis

doi:10.1109/ICIP.1994.413274

Operator decomposition using the wavelet transform: Fundamental properties and image restoration applications

M. E. Zervakis, Taek M Kwon, A. E. Savakis

Electrical Engineering

Research output: Contribution to journal › Conference article › peer-review

Abstract

A novel formulation of image processing operations in the wavelet domain is presented which directly associates multiresolution with multichannel image processing. The formation of the multiresolution image is expressed as an operator on the image domain that transforms block-circulant structures into partially-block-circulant structures. The proposed implementation relaxes the stationarity and space-invariance assumptions in the image domain and introduces new operator structures for the implementation of single-channel algorithms which take advantage of the correlation structure in the wavelet domain. Based on this structure, the authors discuss the estimation of the power spectrum in the wavelet domain. Image restoration examples using the linear minimum mean square error filter show significant improvement achieved by the proposed approach over the conventional discrete Fourier transform (DFT) implementation.

Original language	English (US)
Article number	413274
Pages (from-to)	56-60
Number of pages	5
Journal	Proceedings - International Conference on Image Processing, ICIP
Volume	1
DOIs	https://doi.org/10.1109/ICIP.1994.413274
State	Published - 1994
Event	The 1994 1st IEEE International Conference on Image Processing - Austin, TX, USA Duration: Nov 13 1994 → Nov 16 1994

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© 1994 IEEE.

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title = "Operator decomposition using the wavelet transform: Fundamental properties and image restoration applications",

abstract = "A novel formulation of image processing operations in the wavelet domain is presented which directly associates multiresolution with multichannel image processing. The formation of the multiresolution image is expressed as an operator on the image domain that transforms block-circulant structures into partially-block-circulant structures. The proposed implementation relaxes the stationarity and space-invariance assumptions in the image domain and introduces new operator structures for the implementation of single-channel algorithms which take advantage of the correlation structure in the wavelet domain. Based on this structure, the authors discuss the estimation of the power spectrum in the wavelet domain. Image restoration examples using the linear minimum mean square error filter show significant improvement achieved by the proposed approach over the conventional discrete Fourier transform (DFT) implementation.",

author = "Zervakis, {M. E.} and Kwon, {Taek M} and Savakis, {A. E.}",

note = "Publisher Copyright: {\textcopyright} 1994 IEEE.; The 1994 1st IEEE International Conference on Image Processing ; Conference date: 13-11-1994 Through 16-11-1994",

year = "1994",

doi = "10.1109/ICIP.1994.413274",

language = "English (US)",

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T1 - Operator decomposition using the wavelet transform

T2 - The 1994 1st IEEE International Conference on Image Processing

AU - Zervakis, M. E.

AU - Kwon, Taek M

AU - Savakis, A. E.

PY - 1994

Y1 - 1994

N2 - A novel formulation of image processing operations in the wavelet domain is presented which directly associates multiresolution with multichannel image processing. The formation of the multiresolution image is expressed as an operator on the image domain that transforms block-circulant structures into partially-block-circulant structures. The proposed implementation relaxes the stationarity and space-invariance assumptions in the image domain and introduces new operator structures for the implementation of single-channel algorithms which take advantage of the correlation structure in the wavelet domain. Based on this structure, the authors discuss the estimation of the power spectrum in the wavelet domain. Image restoration examples using the linear minimum mean square error filter show significant improvement achieved by the proposed approach over the conventional discrete Fourier transform (DFT) implementation.

AB - A novel formulation of image processing operations in the wavelet domain is presented which directly associates multiresolution with multichannel image processing. The formation of the multiresolution image is expressed as an operator on the image domain that transforms block-circulant structures into partially-block-circulant structures. The proposed implementation relaxes the stationarity and space-invariance assumptions in the image domain and introduces new operator structures for the implementation of single-channel algorithms which take advantage of the correlation structure in the wavelet domain. Based on this structure, the authors discuss the estimation of the power spectrum in the wavelet domain. Image restoration examples using the linear minimum mean square error filter show significant improvement achieved by the proposed approach over the conventional discrete Fourier transform (DFT) implementation.

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ER -

Operator decomposition using the wavelet transform: Fundamental properties and image restoration applications

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