Main peaks from the fiber ODFs estimated in the “HARDI Reconstruction Challenge 2013” phantom.

<p>Visualization of the main peaks extracted from the fiber ODFs reconstructed from the SMF-based data generated with SNR = 20 in a complex region of the “HARDI Reconstruction Challenge 2013” phantom. Results are based on reconstructions using 400 iterations. Peaks are visualized as thin cylinders.</p

Reconstruction accuracy of RUMBA-SD and dRL-SD measured in phantoms with different volume fractions.

<p>Reconstruction accuracy of RUMBA-SD (blue color) and dRL-SD (red color) is shown in terms of the volume fraction of the smaller fiber bundle (upper panel) and the success rate (middle panel) in the 41 synthetic phantoms with inter-fiber angle equal to 70 degrees, using different volume fractions. The lower panel shows results similar to those depicted in the upper panel but considering only voxels where the two fiber bundles were detected. The discontinuous diagonal black line in the upper and lower panels represents the ideal result as a reference. The continuous coloured lines in each plot denote the mean values for each method. The semi-transparent coloured bands represent the values within one standard deviation to both sides of the mean. Results refer to the datasets with SNR = 15 and dictionary created with the true diffusivities.</p

Main peaks in the 45-degrees phantom data.

<p>Main peaks extracted from the fiber ODFs estimated in the phantom data with inter-fiber angle equal to 45 degrees and Rician noise with a SNR = 15 are shown. Results are based on reconstructions using 200 iterations. Peaks are visualized as thin cylinders.</p

Main peaks in the 33-degrees phantom data.

<p>Main peaks extracted from the fiber ODFs estimated in the phantom data with inter-fiber angle equal to 33 degrees and Rician noise with a SNR = 15 are shown. Results are based on reconstructions using 200 iterations. Peaks are visualized as thin cylinders.</p

Fiber ODF profiles estimated from real data.

<p>Visualization of the fiber ODFs estimated in a region of interest on the right brain hemisphere. Results from both SMF- and SoS-based multichannel diffusion datasets (i.e., with Rician and Noncentral Chi noise, respectively) are depicted. The background images are the generalized fractional anisotropy images computed from each reconstruction.</p

Reconstruction accuracy for RUMBA-SD and dRL-SD using a dictionary based on original diffusivities.

<p>Reconstruction accuracy of RUMBA-SD (blue color) and dRL-SD (red color) are shown in terms of the angular error (θ) (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0138910#pone.0138910.e041" target="_blank">Eq (17)</a>) and the volume fraction error (Δ<i>f</i>) (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0138910#pone.0138910.e042" target="_blank">Eq (18)</a>), as a function of the inter-fiber angle in the 90 synthetic phantoms. Continuous lines in each plot represent the mean values for each method. The semi-transparent coloured bands symbolize values within one standard deviation from both sides of the mean. Analyses are based on a dictionary created with the same diffusivities used to generate the data and with a SNR = 15.</p

Reconstruction accuracy levels of RUMBA-SD+TV and dRL-SD+TV.

<p>Reconstruction accuracy of RUMBA-SD+TV (blue color) and dRL-SD+TV (red color) is shown in terms of the angular error (θ) (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0138910#pone.0138910.e041" target="_blank">Eq (17)</a>) and the volume fraction error (Δ<i>f</i>) (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0138910#pone.0138910.e042" target="_blank">Eq (18)</a>) as a function of the inter-fiber angle in the 90 synthetic phantoms. Continuous lines are the mean values for each method, and semi-transparent coloured bands contain values within one standard deviation on both sides of the mean. This analysis is based on a dictionary created with the same diffusivities used to generate the data with a SNR = 15.</p

Scatter plots of inter-fiber angles estimated in real data.

<p>Scatter plots of the inter-fiber angles estimated by dRL-SD and RUMBA-SD (panel A) and by dRL-SD+TV and RUMBA-SD+TV (panel B) in the same voxels. Results are based on reconstructions in the 64-direction SMF dataset. Only voxels in white matter where both methods detected one or two fibers are included. The inter-fiber angle in voxels with a single fiber was assumed to be equal to zero. Points on the main diagonal line are those voxels where the inter-fiber angle estimated from both methods was identical, whereas points above and below the main diagonal correspond to voxels where the two methods detected two fibers but with different inter-fiber angle. Points located on the X and Y axes are voxels where one method detected two fibers whereas the other detected a single fiber.</p

General pseudocode MAP algorithm.

<p>⁽*⁾ Optionally, the ODF vector may be scaled to unity, thus preserving the physical definition of the <i>j</i> th element in <b>f</b> as the volume fraction of the <i>j</i> th compartment of the voxel (see Eqs (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0138910#pone.0138910.e001" target="_blank">1</a>)–(<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0138910#pone.0138910.e004" target="_blank">3</a>)). This step would make sense when the fiber response signal used to create the dictionary matches the real signal from the compartments, whereas it may be omitted when the latter cannot be guaranteed. Notice that the original implementation of dRL-SD did not include this step.</p><p>General pseudocode MAP algorithm.</p