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. 2012 Oct;16(7):1465-76.
doi: 10.1016/j.media.2012.05.003. Epub 2012 Jun 19.

Super-resolution Reconstruction to Increase the Spatial Resolution of Diffusion Weighted Images From Orthogonal Anisotropic Acquisitions

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Free PMC article

Super-resolution Reconstruction to Increase the Spatial Resolution of Diffusion Weighted Images From Orthogonal Anisotropic Acquisitions

Benoit Scherrer et al. Med Image Anal. .
Free PMC article

Abstract

Diffusion-weighted imaging (DWI) enables non-invasive investigation and characterization of the white matter but suffers from a relatively poor spatial resolution. Increasing the spatial resolution in DWI is challenging with a single-shot EPI acquisition due to the decreased signal-to-noise ratio and T2(∗) relaxation effect amplified with increased echo time. In this work we propose a super-resolution reconstruction (SRR) technique based on the acquisition of multiple anisotropic orthogonal DWI scans. DWI scans acquired in different planes are not typically closely aligned due to the geometric distortion introduced by magnetic susceptibility differences in each phase-encoding direction. We compensate each scan for geometric distortion by acquisition of a dual echo gradient echo field map, providing an estimate of the field inhomogeneity. We address the problem of patient motion by aligning the volumes in both space and q-space. The SRR is formulated as a maximum a posteriori problem. It relies on a volume acquisition model which describes how the acquired scans are observations of an unknown high-resolution image which we aim to recover. Our model enables the introduction of image priors that exploit spatial homogeneity and enables regularized solutions. We detail our SRR optimization procedure and report experiments including numerical simulations, synthetic SRR and real world SRR. In particular, we demonstrate that combining distortion compensation and SRR provides better results than acquisition of a single isotropic scan for the same acquisition duration time. Importantly, SRR enables DWI with resolution beyond the scanner hardware limitations. This work provides the first evidence that SRR, which employs conventional single shot EPI techniques, enables resolution enhancement in DWI, and may dramatically impact the role of DWI in both neuroscience and clinical applications.

Figures

Figure 1
Figure 1
Scheme illustrating the super-resolution reconstruction from the acquisition of two orthogonal thick slices.
Figure 2
Figure 2
In presence of motion, the DW-images for the same applied diffusion-sensitization gradient may represent different gradient directions in the patient coordinate system among the acquisitions.
Figure 3
Figure 3
Alignment in q-space. We consider the first acquisition (k = 1, in blue) as the reference (a), providing the reference gradient directions (in blue). The gradient images of an acquisition k > 1 are resampled so that its gradient directions gk (in red) correspond to the reference gradients . At each voxel, we compute the novel intensities corresponding to the gradients by interpolation in q-space from the observed intensities corresponding to gk (b).
Figure 4
Figure 4
Schematic describing the experimental setup to evaluate the SRR reconstruction from real acquisitions.
Figure 5
Figure 5
Numerical simulations. Fig.a. Original tensors used to simulate the DW signal. Fig.b–d: Tensors estimated resp. from a single LR acquisition, from the mean of the LR acquisitions and from the SRR. Fig.e–h: 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.h).
Figure 6
Figure 6
Fig.a: Synthetic SRR scenario from a real acquisition. a.i: b = 0 image. a.ii: Axial down-sampled b = 0 image with a factor of 4. a.iii: Mean of the b = 0 images of the LR acquisitions. a.iv: 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 two- and four- down-sampling factors, for each of the thirty gradient directions (x axis).
Figure 7
Figure 7
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). We compared 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 indicates difference between the reconstructed and ground truth intensities (difference in image intensity). It shows the SRR estimate provides a much better reconstruction for each gradient image.
Figure 8
Figure 8
Field-map based distortion correction. (a): Phase field-map generated from the dual-echo gradient echo sequence. The frontal lobe close to the sinuses is typically affected (region R1). (b): Axial acquisition with EPI distortion (b=0s/mm2, phase-encoding direction: anterior to posterior). (c): Corrected image. (d): Coronal acquisition with distortion (sagittal view, phase-encoding direction: head to foot). (e): Corrected image. The red circles highlight regions of high distortion.
Figure 9
Figure 9
Color-FA maps for (a):ISO, (b):d-ISO, (c):SRR and (d): FMC-SRR (axial view). R1 points out that fine structures are well conserved with FMC-SRR, despite the large slice thickness employed for each anisotropic acquisition. R2 highlights a region in which SRR (without distortion compensation) provides blurred results. Importantly, the structures in the region R2 are more detailed with FMC-SRR than with d-ISO.
Figure 10
Figure 10
Zoom on the color-FA maps in a region of the brain stem. (a): T1-weighted image showing the zoom location (axial view). Color-FA maps and estimated tensors for (b/f): ISO, (c/g): d-ISO, (d/h): SRR and (e/i): FMC-SRR. The color-FA for ISO is highly noisy, while the noise reduction technique employed in d-ISO makes the structures fuzzy (region R1) and produces artifacts (R3). In SRR some structures are missing due to the non-correction of distortion (R2). FMC-SRR provides the most detailed structures (R1).
Figure 11
Figure 11
Assessment of the estimation uncertainty by averaging the FA variance from the residual bootstrap in a 3-D region of interest. (a): region of interest considered, in the left external capsule. (b): average of the FA variance in the ROI.
Figure 12
Figure 12
Tractography results for the corpus callosum from (a): ISO, (b): d-ISO, (c): SRR and (d): FMC-SRR.
Figure 13
Figure 13
Tractography results for the pyramidal tracts (vertical streamlines) and the medial cerebellar peduncle, corresponding to a region close to the region in Fig.10, from (a): ISO, (b): d-ISO, (c): SRR and (d): FMC-SRR.
Figure 14
Figure 14
Employing anisotropic orthogonal acquisitions amounts to densely oversampling k-space along only two axes.
Figure 15
Figure 15
When using anisotropic acquisitions with the slice-thickness dimension twice the size of the in-plane resolution, the SRR problem is over-determined. It amounts to estimating each group of eight voxels of the high-resolution volume (right) from twelve measurements (left).

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