Image denoising using a tight frame

Lixin Shen; Manos Papadakis; Ioannis A. Kakadiaris; Ioannis Konstantinidis; Donald Kouri; David Hoffman

doi:10.1109/TIP.2005.864240

Image denoising using a tight frame

Lixin Shen, Manos Papadakis, Ioannis A. Kakadiaris, Ioannis Konstantinidis, Donald Kouri, David Hoffman

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

61 Scopus citations

Abstract

We present a general mathematical theory for lifting frames that allows us to modify existing filters to construct new ones that form Parseval frames. We apply our theory to design nonseparable Parseval frames from separable (tensor) products of a piecewise linear spline tight frame. These new frame systems incorporate the weighted average operator, the Sobel operator, and the Laplacian operator in directions that are integer multiples of 45°. A new image denoising algorithm is then proposed, tailored to the specific properties of these new frame filters. We demonstrate the performance of our algorithm on a diverse set of images with very encouraging results.

Original language	English (US)
Pages (from-to)	1254-1263
Number of pages	10
Journal	IEEE Transactions on Image Processing
Volume	15
Issue number	5
DOIs	https://doi.org/10.1109/TIP.2005.864240
State	Published - May 2006
Externally published	Yes

Keywords

Image denoising
Tight frame
Wavelets

ASJC Scopus subject areas

Software
Computer Graphics and Computer-Aided Design

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10.1109/TIP.2005.864240

Cite this

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title = "Image denoising using a tight frame",

abstract = "We present a general mathematical theory for lifting frames that allows us to modify existing filters to construct new ones that form Parseval frames. We apply our theory to design nonseparable Parseval frames from separable (tensor) products of a piecewise linear spline tight frame. These new frame systems incorporate the weighted average operator, the Sobel operator, and the Laplacian operator in directions that are integer multiples of 45°. A new image denoising algorithm is then proposed, tailored to the specific properties of these new frame filters. We demonstrate the performance of our algorithm on a diverse set of images with very encouraging results.",

keywords = "Image denoising, Tight frame, Wavelets",

author = "Lixin Shen and Manos Papadakis and Kakadiaris, {Ioannis A.} and Ioannis Konstantinidis and Donald Kouri and David Hoffman",

note = "Funding Information: Manuscript received June 26, 2003; revised February 22, 2005. This work was supported in part by Grants NSF IIS-0431144, NSF IIS-0335578, NSF DMS-1041539, NSF CHE-0074311, ARP 003652-0071-2001, NSF DMS-0406748, the Welch Foundation E-0608, and the University of Houston{\textquoteright}s TLCC funds. The associate editor coordinating the review of this manuscript and approving it for publication Dr. Ivan W. Selesnick.",

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month = may,

doi = "10.1109/TIP.2005.864240",

language = "English (US)",

volume = "15",

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journal = "IEEE Transactions on Image Processing",

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publisher = "Institute of Electrical and Electronics Engineers Inc.",

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AU - Shen, Lixin

AU - Papadakis, Manos

AU - Kakadiaris, Ioannis A.

AU - Konstantinidis, Ioannis

AU - Kouri, Donald

AU - Hoffman, David

N1 - Funding Information: Manuscript received June 26, 2003; revised February 22, 2005. This work was supported in part by Grants NSF IIS-0431144, NSF IIS-0335578, NSF DMS-1041539, NSF CHE-0074311, ARP 003652-0071-2001, NSF DMS-0406748, the Welch Foundation E-0608, and the University of Houston’s TLCC funds. The associate editor coordinating the review of this manuscript and approving it for publication Dr. Ivan W. Selesnick.

PY - 2006/5

Y1 - 2006/5

N2 - We present a general mathematical theory for lifting frames that allows us to modify existing filters to construct new ones that form Parseval frames. We apply our theory to design nonseparable Parseval frames from separable (tensor) products of a piecewise linear spline tight frame. These new frame systems incorporate the weighted average operator, the Sobel operator, and the Laplacian operator in directions that are integer multiples of 45°. A new image denoising algorithm is then proposed, tailored to the specific properties of these new frame filters. We demonstrate the performance of our algorithm on a diverse set of images with very encouraging results.

AB - We present a general mathematical theory for lifting frames that allows us to modify existing filters to construct new ones that form Parseval frames. We apply our theory to design nonseparable Parseval frames from separable (tensor) products of a piecewise linear spline tight frame. These new frame systems incorporate the weighted average operator, the Sobel operator, and the Laplacian operator in directions that are integer multiples of 45°. A new image denoising algorithm is then proposed, tailored to the specific properties of these new frame filters. We demonstrate the performance of our algorithm on a diverse set of images with very encouraging results.

KW - Image denoising

KW - Tight frame

KW - Wavelets

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JO - IEEE Transactions on Image Processing

JF - IEEE Transactions on Image Processing

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Image denoising using a tight frame

Abstract

Keywords

ASJC Scopus subject areas

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