Rodrigo A. Lobos^{1}, Tae Hyung Kim^{1}, Kawin Setsompop^{2}, and Justin P. Haldar^{1}

^{1}Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, United States, ^{2}Martinos Center for Biomedical Imaging, Charlestown, MA, United States

Many autocalibrated parallel imaging reconstruction methods are based on linear-predictive/autoregressive principles, including noniterative GRAPPA-type interpolation methods, iterative SPIRiT-type annihilation methods, and structured low-rank matrix methods like PRUNO and Autocalibrated LORAKS. In principle, all of these approaches could be adapted for simultaneous multislice (SMS) reconstruction. However, in practice, GRAPPA-type SMS methods are popular, but there has been limited exploration of more advanced annihilation-based or structured low-rank matrix SMS methods. In this work, we adapt and evaluate these advanced approaches for SMS reconstruction. Results demonstrate that these advanced approaches can offer substantial improvements over simpler GRAPPA-type methods when applied to SMS.

Although these ALP methods can easily be generalized to simultaneous multislice (SMS) reconstruction problems

We undertake such a task in this work, by adapting and evaluating annihilation-based and structured low-rank ALP methods for SMS, with comparisons against GRAPPA-type SMS ALP methods.

We implemented and compared two existing SMS ALP methods and two new ones. The existing methods included a GRAPPA-type method (Split Slice-GRAPPA

The second new method follows the same basic principles described above, except that we are inspired by the modified Autocalibrated LORAKS approach of Ref. 11 to add an additional nonconvex structured low-rank regularization term that automatically identifies and imposes support, phase, and parallel imaging constraints. This new approach, which we call Regularized SMS AC-LORAKS, solves $$\hat{\mathbf{k}} = \arg\min_{\mathbf{k}} \sum_{\ell=1}^{L}\|\mathcal{P}_C(\mathbf{k}_\ell)\mathbf{N}_\ell\|_F^2 + \lambda \sum_{\ell=1}^{L}J(\mathcal{P}_S(\mathbf{k}_\ell)) \mathrm{\,\,\,\,\, subject\, to\,\,\,\,\, } \mathcal{A}(\mathbf{k})=\mathbf{d},$$ where $$$J(\cdot)$$$ is a nonconvex penalty that promotes low rank; and $$$\mathcal{P}_S(\cdot)$$$ is an operator that constructs an alternative convolution-structured matrix that can take advantage of the relationships between k-space samples on opposite sides of k-space (i.e., the LORAKS “S-matrix”

The SMS ALP methods were evaluated using in vivo 16-channel spin-echo brain data

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Gold standard and ACS datasets used for evaluation. For visualization, the multichannel data for
each slice was combined using a sum-of-squares procedure.

Reconstruction results for multiband factor=4
with different levels of uniformly-subsampled in-plane acceleration. Due to space constraints, we only show
results for one slice, with multichannel data combined using a sum-of-squares
procedure.

Error images (masked to the support of the gold
standard image) corresponding to the reconstructions in Fig. 2.

Average normalized root-mean-squared error
metrics (over all slices) for each method. Error calculations were performed only for voxels within the mask
defined by the support of the gold standard image.