PMC

Qualitative reconstruction results from the human in vivo multi-shell diffusion imaging experiment. Each column corresponds to an image acquired with a different b-value. The images in the top row were generated using the standard reconstruction, while the images in the bottom row were generated using the proposed method.

Correlation matrix for the edge magnitudes in different simulated DW mouse brain images. The correlation matrix includes DW images with b-values of 0, 1000, 2000, and 3000 s/mm². The diagonal of the correlation matrix has been color-coded to depict the orientation of the diffusion encoding vectors, using the same standard coding scheme used in previous figures.

Results of applying the proposed method to DSI data. Tractograms are shown that were generated from (a) standard image reconstruction and from (b) the proposed method, visualizing the white matter fibers that were identified as connecting to the mesial temporal lobe. (c) Whole-brain histograms of the differences between symmetric pairs of q-space samples for (blue) standard reconstruction and (green) the proposed reconstruction. The proposed reconstruction displays more q-space symmetry than the standard reconstruction.

Qualitative DTI results from the human in vivo multi-shell diffusion imaging experiment. Tensors were estimated separately for data acquired at different b-values, and each column shows results for a different b-value. The top row of images shows DTI parameter estimates based on the standard reconstructions, while the bottom row shows parameter estimates based on the proposed reconstructions. The images show FA, color-coded based on the orientation of the principal eigenvector of the estimated diffusion tensor: red corresponds to right-left, green corresponds to anterior-posterior, and blue corresponds to superior-inferior.

Representative simulation results for the Q=7 dataset. The columns, from left to right, show the gold standard images, the simulated noisy images, images denoised with RMNLM, and the proposed reconstructions, respectively. The top row shows one of the DW images, while the middle row shows the corresponding FA map. The bottom row shows the FA map, color-coded based on the orientation of the principal eigenvector of the estimated diffusion tensor: red corresponds to right-left, green corresponds to anterior-posterior, and blue corresponds to dorso-ventral.

Representative simulation results for the Q=48 dataset. The columns, from left to right, show the gold standard images, the simulated noisy images, images denoised with RMNLM, and the proposed reconstructions, respectively. The top row shows one of the DW images, while the middle row shows the corresponding FA map. The bottom row shows the FA map, color-coded based on the orientation of the principal eigenvector of the estimated diffusion tensor: red corresponds to right-left, green corresponds to anterior-posterior, and blue corresponds to dorso-ventral.

Quantitative simulation results for the Q = 48 dataset. The columns, from left to right, show the results for the original noisy data, the RMNLM denoised images, the OMNLM denoised images, and the images reconstructed using the proposed method. The top row shows scatter plots of the FA error (true FA - estimated FA) as a function of the true FA value. Also shown is the mean FA error ± two standard deviations. The bottom row shows histograms of the estimated tensor error, as measured with the log-Euclidean distance metric.

Quantitative simulation results for the Q = 7 dataset. The columns, from left to right, show the results for the original noisy data, the RMNLM denoised images, the OMNLM denoised images, and the images reconstructed using the proposed method. The top row shows scatter plots of the FA error (true FA - estimated FA) as a function of the true FA value. Also shown is the mean FA error ± two standard deviations. The bottom row shows histograms of the estimated tensor error, as measured with the log-Euclidean distance metric.

Simulation results for the Q=7 dataset, where the parameters of the proposed method are adjusted to reduce the noise variance by factors of (from left to right) 2, 4, 8, 16, and 32. The top row shows the color-coded FA maps estimated from a DTI fit to the images, while the bottom row shows the difference between the noisy color-coded FA and the gold standard color-coded FA (shown in ). The difference images are scaled by a factor of two for improved visualization.

Resolution and noise analysis for the simulated data. Top left: estimated edge-map for the set of jointly-reconstructed images using the proposed method. Top right: normalized point-spread functions for the (green) standard reconstruction and (blue) proposed reconstruction methods, extracted from one of the smooth regions of the image. The proposed method leads to a slight broadening of the point-spread function, as expected. Bottom left: spatial map of SNR improvement, as predicted by the linear noise analysis. Bottom right: Monte Carlo verification that the predicted noise variance using linear noise analysis corresponds well with the actual variance measured by reconstructing the same dataset with different Gaussian noise realizations. The prediction error is calculated for each pixel by subtracting the empirical variance of the pixel over 100 reconstructions of the dataset (with different noise realizations) from the predicted noise variance based only on the estimated edge map.