Super-resolution in diffusion-weighted imaging

Abstract

Diffusion-weighted imaging (DWI) enables non-invasive investigation and characterization of the white-matter but suffers from a relatively poor resolution. In this work we propose a super-resolution reconstruction (SRR) technique based on the acquisition of multiple anisotropic orthogonal DWI scans. We address the problem of patient motions by aligning the volumes both in space and in q-space. The SRR is formulated as a maximum a posteriori (MAP) problem. It relies on a volume acquisition model which describes the generation of the acquired scans from the unknown high-resolution image. It enables the introduction of image priors that exploit spatial homogeneity and enables regularized solutions. We detail our resulting SRR optimization procedure and report various experiments including numerical simulations, synthetic SRR scenario and real world SRR scenario. Super-resolution reconstruction in DWI may enable DWI to be performed with unprecedented resolution.

Fig. 1

(a) Scheme illustrating the super-resolution reconstruction from the acquisition of two orthogonal thick slices. (b) Alignment in q-space: the gradient images of each acquisition k > 1 are resampled so that its gradient directions g^k (red dots arrows) correspond to the reference gradient directions of the first acquisition g̃ (grey plain arrows). At each voxel, we compute novel intensities corresponding to the gradients g̃ by interpolation in q-space from the observed intensities corresponding to g^k.

Fig. 2

Numerical simulations from the tensors of Fig.a. Fig.b-d: Tensors estimated resp. from a single LR acquisition, from the mean of the LR acquisitions and from the SRR. Fig.e-g: Corresponding tensor fractional anisotropy. It shows the tensor directions to be well estimated from the mean (Fig.c). However, the SRR provides a much more accurate reconstruction of the complete tensor (see the better FA uniformity in Fig.g).

Fig. 3

Fig.a: Synthetic SRR scenario from a real acquisition. a.a: b=0 image. a.b: Axial down-sampled b=0 image with a factor of 4. a.c: Mean of the b=0 images of the LR acquisitions. a.d: SRR of the b=0 image. The SRR is better contrasted and is less blurry than the mean. Fig.b and Fig.c: Quantitative evaluation of the reconstruction accuracy in term of PSNR for the /2 and /4 down-sampling, for each gradient direction.

Fig. 4

3-Dimensional angular reconstructions of the diffusion signal at four voxels whose position is shown on the b=0s/mm² image (left image). The voxels were chosen to have a high FA (FA > 0.9). The obtained 3-D shapes are proportional to the apparent diffusion coefficient (ADC). Comparison between the 3-D reconstruction performed from the mean image (first line) and from the SRR estimate (second line). The stick indicates the major fiber direction estimated by a single-tensor model. The color encodes for the error with the ground-truth (difference in image intensity). It shows the SRR estimate to provide a much better reconstruction for each gradient image.

Fig. 5

Real SRR scenario. Fig.a-b: FA computed from the mean of the LR acquisition (a) and from the SRR (b). Fig.c-d: idem for MD. It shows that the SRR leads to more contrasted and less blurry FA and MD estimates.