Introducing diffusion tensor to high order variational model for image reconstruction

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Introducing diffusion tensor to high order variational model for image reconstruction. / Duan, Jinming; Ward, Wil O.C.; Sibbett, Luke; Pan, Zhenkuan; Bai, Li.

In: Digital Signal Processing, Vol. 69, 01.10.2017, p. 323-336.

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Duan, Jinming ; Ward, Wil O.C. ; Sibbett, Luke ; Pan, Zhenkuan ; Bai, Li. / Introducing diffusion tensor to high order variational model for image reconstruction. In: Digital Signal Processing. 2017 ; Vol. 69. pp. 323-336.

Bibtex

@article{b6211026bf174d78aa0738ed8bfb6ada,
title = "Introducing diffusion tensor to high order variational model for image reconstruction",
abstract = "Second order total variation (SOTV) models have advantages for image reconstruction over their first order counterparts including their ability to remove the staircase artefact in the reconstructed image. However, such models tend to blur the recovered image when discretised for a numerical solution [1–5]. To overcome this drawback, we introduce a novel tensor weighted second order (TWSO) variational model for image reconstruction. Specifically, we develop a new regulariser for the original SOTV model that uses the Frobenius norm of the product of the Hessian matrix and a diffusion tensor, which has the duel effects of sharpening edges and introducing anisotropy to the model. We then efficiently solve the proposed model by breaking the original problem into several closed-form subproblems using the alternating direction method of multipliers. The proposed method is compared with state-of-the-art approaches such as the tensor-based anisotropic diffusions, total generalised variation, and Euler's elastica. We validate the TWSO model using extensive experiments on numerous images from the Berkeley BSDS500. We also show that our method effectively reduces both the staircase and blurring effects and outperforms existing approaches for image inpainting and denoising applications.",
keywords = "ADMM, Diffusion tensor, Fast Fourier transform, Frobenius norm, Hessian, Total variation",
author = "Jinming Duan and Ward, {Wil O.C.} and Luke Sibbett and Zhenkuan Pan and Li Bai",
year = "2017",
month = oct,
day = "1",
doi = "10.1016/j.dsp.2017.07.001",
language = "English",
volume = "69",
pages = "323--336",
journal = "Digital Signal Processing",
issn = "1051-2004",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Introducing diffusion tensor to high order variational model for image reconstruction

AU - Duan, Jinming

AU - Ward, Wil O.C.

AU - Sibbett, Luke

AU - Pan, Zhenkuan

AU - Bai, Li

PY - 2017/10/1

Y1 - 2017/10/1

N2 - Second order total variation (SOTV) models have advantages for image reconstruction over their first order counterparts including their ability to remove the staircase artefact in the reconstructed image. However, such models tend to blur the recovered image when discretised for a numerical solution [1–5]. To overcome this drawback, we introduce a novel tensor weighted second order (TWSO) variational model for image reconstruction. Specifically, we develop a new regulariser for the original SOTV model that uses the Frobenius norm of the product of the Hessian matrix and a diffusion tensor, which has the duel effects of sharpening edges and introducing anisotropy to the model. We then efficiently solve the proposed model by breaking the original problem into several closed-form subproblems using the alternating direction method of multipliers. The proposed method is compared with state-of-the-art approaches such as the tensor-based anisotropic diffusions, total generalised variation, and Euler's elastica. We validate the TWSO model using extensive experiments on numerous images from the Berkeley BSDS500. We also show that our method effectively reduces both the staircase and blurring effects and outperforms existing approaches for image inpainting and denoising applications.

AB - Second order total variation (SOTV) models have advantages for image reconstruction over their first order counterparts including their ability to remove the staircase artefact in the reconstructed image. However, such models tend to blur the recovered image when discretised for a numerical solution [1–5]. To overcome this drawback, we introduce a novel tensor weighted second order (TWSO) variational model for image reconstruction. Specifically, we develop a new regulariser for the original SOTV model that uses the Frobenius norm of the product of the Hessian matrix and a diffusion tensor, which has the duel effects of sharpening edges and introducing anisotropy to the model. We then efficiently solve the proposed model by breaking the original problem into several closed-form subproblems using the alternating direction method of multipliers. The proposed method is compared with state-of-the-art approaches such as the tensor-based anisotropic diffusions, total generalised variation, and Euler's elastica. We validate the TWSO model using extensive experiments on numerous images from the Berkeley BSDS500. We also show that our method effectively reduces both the staircase and blurring effects and outperforms existing approaches for image inpainting and denoising applications.

KW - ADMM

KW - Diffusion tensor

KW - Fast Fourier transform

KW - Frobenius norm

KW - Hessian

KW - Total variation

UR - http://www.scopus.com/inward/record.url?scp=85026736962&partnerID=8YFLogxK

U2 - 10.1016/j.dsp.2017.07.001

DO - 10.1016/j.dsp.2017.07.001

M3 - Article

AN - SCOPUS:85026736962

VL - 69

SP - 323

EP - 336

JO - Digital Signal Processing

JF - Digital Signal Processing

SN - 1051-2004

ER -