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A vectorial total variation model for denoising high angular resolution diffusion images corrupted by Rician noise. (English) Zbl 1293.49030

Summary: 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.

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
65K10 Numerical optimization and variational techniques
68U10 Computing methodologies for image processing
92C55 Biomedical imaging and signal processing
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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