Methods and Applications of Analysis

Volume 21 (2014)

Number 1

A vectorial total variation model for denoising high angular resolution diffusion images corrupted by Rician noise

Pages: 151 – 176

DOI: http://dx.doi.org/10.4310/MAA.2014.v21.n1.a7

Authors

M. Tong (Department of Mathematics, University of California at Los Angeles)

Y. Kim (Department of Diagnostic Radiology, Yale University, New Haven, Connecticut, U.S.A.)

L. Zhan (Laboratory of Neuro Imaging, University of Southern California at Los Angeles)

G. Sapiro (Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina, U.S.A.)

C. Lenglet (Center for Magnetic Resonance Research, University of Minnesota, Minneapolis, Minn., U.S.A.)

B. A. Mueller (Department of Psychiatry, University of Minnesota, Minneapolis, Minn., U.S.A.)

P. M. Thompson (Laboratory of Neuro Imaging, University of Southern California at Los Angeles)

L. A. Vese (Department of Mathematics, University of California at Los Angeles)

Abstract

The presence of noise in High Angular Resolution Diffusion Imaging (HARDI) data of the brain can limit the accuracy with which fiber pathways of the brain can be extracted. In this work, we present a variational model to denoise HARDI data corrupted by Rician noise. We formulate a minimization model composed of a data fidelity term incorporating the Rician noise assumption and a regularization term given by the vectorial total variation. Although the proposed minimization model is non-convex, we are able to establish existence of minimizers. Numerical experiments are performed on three types of data: 2D synthetic data, 3D diffusion-weighted Magnetic Resonance Imaging (DW-MRI) data of a hardware phantom containing synthetic fibers, and 3D real HARDI brain data. Experiments show that our model is effective for denoising HARDI-type data while preserving important aspects of the fiber pathways such as fractional anisotropy and the orientation distribution functions.

Keywords

total variation, Rician noise, denoising, diffusion imaging

2010 Mathematics Subject Classification

35-xx, 49-xx, 65-xx, 68U10

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