Diffusion tensor regularization with constraints preservation

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Diffusion tensor regularization with constraints preservation

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by David Tschumperlé , Rachid Deriche

Venue:	IN IEEE COMPUTER SOCIETY CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION, KAUAI MARRIOTT
Citations:	43 - 12 self

BibTeX

@INPROCEEDINGS{Tschumperlé_diffusiontensor,
    author = {David Tschumperlé and Rachid Deriche},
    title = {Diffusion tensor regularization with constraints preservation},
    booktitle = {IN IEEE COMPUTER SOCIETY CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION, KAUAI MARRIOTT},
    year = {},
    publisher = {}
}

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Abstract

This paper deals with the problem of regularizing noisy fields of diffusion tensors, considered as symmetric and semi-positive definite n n matrices (as for instance 2D structure tensors or DT-MRI medical images). We first propose a simple anisotropic PDE-based scheme that acts directly on the matrix coefficients and preserve the semi-positive constraint thanks to a specific reprojection step. The limitations of this algorithm lead us to introduce a more effective approach based on constrained spectral regularizations acting on the tensor orientations (eigenvectors) and diffusivities (eigenvalues), while explicitely taking the tensor constraints into account. The regularization of the orientation part uses orthogonal matrices diffusion PDE’s and local vector alignment procedures and will be particularly developed. For the interesting 3D case, a special implementation scheme designed to numerically fit the tensor constraints is also proposed. Experimental results on synthetic and real DT-MRI data sets finally illustrates the proposed tensor regularization framework.

Keyphrases

diffusion tensor regularization constraint preservation tensor con-straints orthogonal matrix diffusion pde algorithm lead semi-positive definite matrix ori-entation part real dt-mri data set effective approach specific reprojection step semi-positive constraint thanks structure tensor constrained spectral regular-izations matrix coefficient local vector alignment procedure special implemen-tation scheme simple anisotropic pde-based scheme dt-mri medical image ten-sor constraint tensor regularization framework diffusion tensor noisy field tensor orientation experimental result

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