Chia-Chu Chou^{1}, Frank Q Ye^{2}, Cecil Chern-Chyi Yen^{3}, Behtash Babadi^{1}, Rao P Gullapalli^{4}, David A Leopold^{2}, and JiaChen Zhuo^{4}

3D-DTI are often used in ex vivo imaging to achieve superior spatial resolution and to map fine white matter structure. However, image acquisition time is long especially when many diffusion directions are used to better define orientation profiles and resolve crossing fibers. In this study we apply a new imaging acceleration technique – Partial Fourier Compressed Sensing (PFCS) on DTI acceleration. We demonstrated PFCS provide satisfactory reconstruction with only half of the raw data while retaining fine anatomical details on DTI parameter maps.

Experiments

Methods

PFCS is an image acceleration technique which apply conjugate symmetry property of k-space with compressed sensing reconstruction ^{5}. To test the efficacy of the PFCS reconstruction on 3D-DTI dataset, we further under-sampled the k-space in the slice direction. We divided the data into two partitions: a large fully-sampled area in the center (30% of matrix size) with the rest sparsely sampled with Poisson disc random sampling in a manner that resulted in 50% under sampling (see Fig 1). Furthermore, to eliminate erroneous phase map estimation for each DWI, we use POCS ^{5,6} (Projection Onto Convex Sets) method to estimate the phase map from the data after down sampling on slice dimension. Performance of PFCS reconstruction and compressed sensing (CS) reconstruction were compared with the original partial Fourier reconstructed images (Ground Truth) and comparisons were made regarding image quality and normalized mean square error (nMSE), which is defined by $$$\sqrt{\frac{||ReconstructedImage - Ground Truth||^2}{||Ground Truth||^2}}$$$.We also compared parameter maps from fitting data to the diffusion tensor mode.

**Discussion**

We demonstrated that PFCS can double the acceleration rate in 3D DTI scans by acquiring only 50% of data on the slice dimension. The missing data are well compensated in PFCS by deriving them from the conjugate symmetry of the k-space. PFCS reconstructed FA maps is less noisy than Ground Truth because of the natural smoothing property of compressed sensing reconstruction. Although denoising usually accompanies with loss of resolution, this is shown to be tolerable in FA and principle direction map estimation where fine structure details are well kept. Future work will continue to optimize this technique to obtain better spatial resolution and acceleration rate.

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4. Reveley C et al., "Superficial white matter fiber systems impede detection of longrange cortical connections in diffusion MR tractography," PNAS, vol. 112, no. 21, pp. 2820-2828.

5. C.C Chou, C. Cadisetti, T. Shin, N. Devasahayam, A. McMillan, B. Babadi, R. Gullapalli, M. Cherukuri, J. Zhuo, "Accelerated electron paramagnetic resonance imaging using partial Fourier compressed sensing reconstruction," Magnetic Resonance Imaging (In Press), 2016.

6. J. Pauly, "Partial K-space reconstruction".Stanford University.

Figure 1: The sampling mask specified for DTI. For the frequency
encoding direction (shown in orange dash arrow), the data are fully acquired.
For the phase encoding dimension, raw data have included Partial Fourier down sampling
(~60% of matrix size). For the slice dimension, the data points are divided into
fully acquired center and Poisson disc sparsely sampling peripheral. In total only
30% of k-space points are used in PFCS reconstruction. (60% on phase encoding
dimension, and 50% on slice dimension)

Figure 2: The comparison of conventional CS and PFCS on DWIs. The image magnitude of several DWIs is displayed in (a). The PFCS images
are less blurring and able to preserve more details than CS. The difference
maps are given in (b). From (b) we can easily observe the improvement of PFCS
reconstructed images, especially in some boundary areas (blue arrow).

Figure 3: The nMSE of DWIs of all the 26
diffusion gradient directions as well as 3 b0 images (The first three points). Obviously,
PFCS outperforms CS in every DWIs.

Figure 4: The FA
and the Principal Diffusion Direction Map from Ground Truth and PFCS-DWIs. It
is clear that PFCS preserved almost all the details of the Ground Truth FA map,
including tiny fibers. Meanwhile, it accurately captured the principle
diffusion direction. However, PFCS FA map is smoother due to the natural smoothing
property of reconstruction.