Intra-voxel incoherent motion (IVIM) magnetic resonance imaging (MRI) is a useful medical imaging tool for characterizing tissue type by deriving clinical markers associated with perfusion and diffusion of tissue (1). In practice, IVIM MRI utilizes diffusion-weighted echo-planar imaging (DW-EPI) technique to acquire a set of image data with multiple b-values (1). The major limitation of IVIM is due to long acquisition time for acquiring multiple b-values that lowers the feasibility of clinical use, especially it requires multiple averaging of high-b value to compensate low SNR. In addition, DW-EPI also suffers from geometric distortion and low resolution. To reduce the degraded image quality, parallel imaging such as SENSE reconstruction can be used to reduce the distortion (2). However, there is undesired noise amplification associated with SENSE reconstruction. Recently, a projection onto convex sets based multiplexed sensitivity encoding (POCSMUSE) reconstruction algorithm has been proposed to reconstruct interleaved DW-EPI data without undesired noise amplification (3). Even though interleaved DW-EPI with POCSMUSE reconstruction can simultaneously acquire high-resolution DWI data and address both geometric distortion and noise amplification issues, the much more prolonged scan time due to multi-shot acquisition substantially escalates the difficulty in clinical use. To further reduce the sub-total acquisition time for a set of high b-value DW images, we propose a joint reconstruction framework of POCSMUSE algorithm, to simultaneously reconstruct under-sampled multi-b interleaved DW-EPI data with reduced noise amplification compared to SENSE reconstruction.

I. POCSMUSE for joint reconstruction of under-sampled multi-b DW images: To simplifier the model for testing proposed algorithm, we assume that there is only mono-diffusion component across a set of high b-value DW images. Thus, the relationship between each pair of high b-value DW images is an exponential decay function with attenuation factor of apparent diffusion coefficient (ADC). The flowchart of iterative process of modified POCSMUSE framework for joint estimation of multi-b DW image is shown in Figure 1.

II. Data acquisition: A set of high-resolution brain multi-b DW data was acquired from one healthy volunteer at 3.0T MRI scanner (MR750, GE Healthcare) using an 8-channel phase-array head coil with a four-shot interleaved DW-EPI sequence. Four high b-value, 500, 800, 1200, and 1500 s/mm² were acquired to test proposed POCSMUSE framework. Other imaging parameters include: TE/TR = 65ms/5000ms, matrix size = 256 x 256, slice thickness = 4mm.

III. Hybrid simulation: The fully-sampled interleaved DW-EPI data was used to simulate an under-sampled data set by picking up different segments. For instance, 1^st segment from b=500 , 2^nd segment from b=800, 3^rd segment from b=1200, and 4^th segment from b=1500 DW images. To compare the performance of POCSMUSE framework, the under-sampled multi-b data set were also reconstructed by using SENSE. Moreover, the fully-sampled interleaved DW-EPI data was reconstructed by using original MUSE algorithm (4) as a gold standard of artifact-free multi-b DW images.

IV. Comparison: The L1-norm between fully-sampled and under-sampled multi-b DW images jointly reconstructed from proposed POCSMUSE framework was measured. The L1-norm between fully-sampled and SENSE reconstructed image was also measured.

Figure 2a shows four fully-sampled multi-b DW images reconstructed from MUSE algorithm. Figures 2b and 2c show four under-sampled multi-b DW image with reconstructed from proposed POCSMUSE framework and SENSE algorithm, respectively. Figure 3a and 3b show the L1-norm of four multi-b DW images between fully-sampled data and under-sampled data reconstructed from different method. Overall, propose POCSMUSE reconstructed images reveal a lower L1-nom than SENSE reconstructed images.The proposed POCSMUSE framework can produce high-quality high-resolution multi-b DW images with a joint estimation scheme. In hybrid simulation, the scan time of 4 b-values DW images is only one forth of fully-sampled acquisition (16 sec vs. 64 sec). Although SENSE reconstruction can produce aliasing-free multi-b DW image, the undesired noise amplification may affect the accuracy of ADC measurement. The POCSMUSE reconstructed multi-b DW images can be used as the input of IVIM MRI to further estimate the clinical markers. However, besides to lower L1-norm between POCSMUSE reconstructed image and gold standard, the major difference is laying on the voxels with partial volume of CSF. This also shows a limitation of proposed model with an assumption of mono-diffusion decay. We suppose that the incorporation of two component model or IVIM model into POCSMUSE framework may help to reduce this effect. In conclusion, POCSMUSE framework can help to reduce total acquisition time of IVIM MRI, thereby increasing feasibility of clinical use.