Yamin Arefeen^{1}, Nick Arango^{1}, Siddharth Iyer^{1,2}, Borjan Gagoski^{3,4}, Kawin Setsompop^{2,4,5}, Jacob White^{1}, and Elfar Adalsteinsson^{1,5,6}

Half-Fourier-acquisition-single-shot-turbo-spin-echo (HASTE) serves as a valuable tool for fetal MRI as it is robust to fetal motion and produces images with T_{2}-weighted contrast. However, due to T_{2}-decay and T_{1}-recovery during the acquisition, clinically applied HASTE with sub-180° refocusing pulses and partial-fourier readouts, often yield images with compromised diagnostic quality compared to multi-shot T_{2}-weighted imaging. T_{2}-shuffling exploits a forward model of signal evolution to mitigate blurring and improve contrast in image reconstruction. We propose single-shot imaging with a refined-subspace, iterative application of T_{2}-shuffling, with demonstration in numerical models, that reduces blurring artifacts and improves image contrast in comparison to conventional HASTE.

Clinical fetal MRI utilizes 2D-single-shot imaging for T_{2} contrast, such as Half-Fourier-acquisition-single-shot-turbo-spin-echo (HASTE^{1}, SSFSE), in order to mitigate motion artifacts. However, weighting of k-space due to T_{2}-decay during a lengthy refocusing train results in an image with compromised diagnostic quality.

T_{2}-shuffling^{2} exploits a forward model of signal evolution to reconstruct multiple, sharp T_{2}-weighted images from a fast-spin-echo acquisition. We propose a two-iteration, refined-subspace T_{2}-shuffling method with dictionary matching^{3} for single-shot T_{2}-weighted acquisitions to produce images with reduced blurring and improved image contrast in comparison to conventional HASTE, with demonstrations in numerical simulations.

**T _{2}-Shufflng Forward Model:**

To fully incorporate signal evolution into the single-shot forward model, one can solve for a time series of images $$$x \in C^{M \times N \times T}$$$. Signal evolutions for HASTE, with realistic T_{1} and T_{2} values, when grouped into a dictionary, $$$X$$$, can be well approximated by a low dimensional subspace formed by the dictionary’s left two singular vectors^{2}, $$$\Phi$$$. By projecting $$$x$$$ onto $$$\Phi$$$, one can solve for coefficients, $$$\alpha \in C^{M \times N \times 2}$$$ with the T_{2}-shuffling forward model^{2},

$$y = R F S \Phi \alpha$$

where $$$R$$$ is the sampling mask, $$$F$$$ is the Fourier transform, and $$$S$$$ are the coil sensitivity operators.

**Second Iteration with Refined Basis: **

** **Due to the lengthy echo train and refocusing pulses in HASTE, two singular vectors poorly capture signal evolution from tissue with short T_{2} values. From an initial shuffling reconstruction, one can utilize dictionary matching^{3}, to compute an approximate T_{2} estimate for each voxel. Then, one can group voxels based on similar T_{2} values into $$$B$$$ bins and construct a tighter sub-dictionary, $$$X_i$$$, for each bin and construct a corresponding subspace $$$\Phi_i$$$ for each sub-dictionary. Now each $$$\Phi_i$$$ better represents $$$X_i$$$ since each subspace only needs to represent a smaller range of T_{2} values. Thus, the total range of T_{2} values in the total dictionary is much better represented, as illustrated by Figure 1, in both constant flip angle and variable flip angle acquisitions^{4}. On the second iteration of shuffling, the forward model remains unchanged, one just need to apply $$$\Phi_i$$$'s to the appropriate coefficients based on the voxel bin groupings.

**Dictionary Matching:**

Project $$$\alpha$$$ back into image space, with $$$x = \Phi \alpha$$$. Then, match the computed decay curve at each voxel to a signal evolution in the dictionary, using the l_{2}-norm distance metric. From this match, we estimate a T_{2} value, which can be used to either group voxels into $$$B$$$ bins or synthesize spin echo contrast.

**Numerical Comparison to HASTE:**

We obtained T_{1}, T_{2}, proton density, and coil sensitivity maps, from the Brainweb database^{5}. For the following numerical experiments , we used a constant 160° refocusing train and simulated the dictionary with a fixed T_{1} value of 1 second.

We performed a 2-mm resolution (128 x 128 matrix size) comparison. For single-shot T_{2} shuffling, we simulated randomly shuffled acquisition of 70 different phase encode lines over time (R= 128/70). For the standard HASTE comparison case, we simulated an R = 2 with 24 auto-calibration lines (ACS) acquisition with conventional linear phase ordering and 5/8, 6/7, and 15/16 partial fourier to achieve desired T_{2} contrast at central echo times of TE = 75 ms, 125 ms, and 175 ms respectively.

Similarly, we performed a 1-mm resolution comparison (256 x 256 matrix size). Again, we simulated random acquisition of 140 phase encode lines for T2 shuffling (R = 256/140). For the standard HASTE comparison, we maintained the same acceleration, ACS region, and echo times with 9/16, 5/8 , and 6/8 partial fourier.

All acquisitions maintained an echo-spacing of 5 ms, and the second iteration with refined subspaces grouped voxels into 10 different bins. Simulated coil sensitivity profiles and example sampling masks used for reconstruction can be seen in Figure 2.

We solved the T_{2}-shuffling problems with an l_{1}-regularized wavelet prior using BART^{6,7}, HASTE with GRAPPA and projection onto convex sets partial fourier, and the second iteration refined-basis problem with l_{1}-regularized wavelet using fast-iterative-threshold-shrinkage.

Figures 3 and 4 compare the 2-mm and 1-mm resolution single shot shuffling, refined subspace shuffling, HASTE, and spin-echo images at a variety of echo times, while Figure 5 illustrates the corresponding error maps. Both shuffling reconstructions reduce blurring artifacts in the corresponding HASTE images, while the refined subspace reconstruction more accurately represents spin-echo contrast in comparison to HASTE and single iteration shuffling.

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