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Home arrow Computer Science arrow Computational Diffusion MRI: MICCAI Workshop, Athens, Greece, October 2016

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Simulation and Diffusion Signal Reconstruction

The complex DWIs have in all cases been created by generating a synthetic phase image, Ф^,, associated with a magnitude image, M^. The phase images are created in order to mimic the outcome of subject movements. We assume a bi-dimensional sinusoidal wave oriented along the direction v = (vx, vy) with frequencies fx, fy and initial shifts фх, фу

where wx, wy are scale parameters: in this case they correspond to the width of the image along the corresponding direction (wx = card.X), wy = card(Y)). Eventually, constant phase patches are added. Assuming to have the ground-truth images of magnitude Mxy and phase Фху, the latter resulting from Eq. (4), then

where prxy,p[1]xy 2 N.0, a2). The noise is added with a value of a calculated according to the DW-MRI convention a = (^card[p(X x Y)]_1 Pxy p(x, y/M^f^ /SNR0,

where SNR0 is defined on the magnitude image without diffusion weighting Мъ=°, and p 2{0,1} is a mask defined on the pairs (x, y), e.g., a mask of the tissue-related signal like the brain mask. The Rician magnitude |DWI|xy and the phase /DWIxy are calculated from the real and imaginary parts in Eq. (5).

The data used for the experiments is a HCP brain dataset corrected for eddy currents where we selected DWIs of interest for b 2 [0,1000, 3000] s/mm2. Other experiments use Phantomas [ 15] to obtain the ground-truth magnitude images, Mxy. This software requires input with a geometrical description of tissue structures and fiber bundles. We used the well known geometry produced for the HARDI reconstruction challenge 2013.[1] We generated DWIs for a 3-shells scheme with b 2 {1000,2000,3000}s/mm2, 51 samples per shell, with samples uniformly distributed within and among shells [16].

The phase-corrected real DWIs can contain negative values: the noise is zero- mean Gaussian and the noise floor is absent. Therefore, the DTI reconstruction is performed by non-linearly en forcing signal positivity, and MAP is performed with Laplacian regularization imposing positivity on the recovered Ensemble Average Propagator [17].

  • [1] http://hardi.epfl.ch/static/events/2013_ISBI/,https://github.com/ecaruyer/phantomas/blob/master/ examples/isbi_challenge_2013.txt.
  • [2] http://hardi.epfl.ch/static/events/2013_ISBI/,https://github.com/ecaruyer/phantomas/blob/master/ examples/isbi_challenge_2013.txt.
 
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