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Echo Planar Imaging (EPI) is a fast MR imaging scheme for acquiring Fourier data in a single shot. EPI acquisitions are widely used to reduce scan time in applications including diffusion MRI and parameter mapping. The capability to provide high temporal resolution makes EPI a popular choice in many dynamic MR imaging studies, including perfusion MRI and imaging of the BOLD contrast in functional MRI (f-MRI).
The long read-out associated with EPI makes it particularly susceptible to off-resonance related geometric distortion artifacts, resulting from magnetic field (B0) inhomogeneities. B0 inhomogeneities arise primarily due to differences in magnetic susceptibility between air, tissue, and bone, which are particularly severe around the sinus and air canal regions.
In this work, we introduce a two-step structured low rank algorithm for the calibration-free compensation of field inhomogeneity artifacts in EPI data. By adopting a time segmentation approach, we transform the inhomogeneity compensation problem to the recovery of an image time series from undersampled Fourier measurements. See (a) in the figure below for an illustration of the time segmentation approach. We assume that the temporal signal at every pixel can be modeled using a single exponential, which is characterized by spatially smooth parameters; these parameters encode the distortion information. We exploit the spatial smoothness of the exponential parameters and the exponential behavior of the temporal signal at every pixel to derive a 3-D annihilation relation in the Fourier domain. This relation translates into a low rank property on a multi-fold Toeplitz matrix formed from the Fourier samples. The construction of the Toeplitz matrix is depicted below. We exploit the low rank property to estimate the null space in the first step, which is then used in the second step to recover the time series of images from the undersampled Fourier measurements. From the time series, the first image corresponds to the distortion-free image.
Construction of the Toeplitz matrix and the smaller sub-matrix
The direct implementation of the structured matrix recovery algorithm is associated with high costs. Hence, we introduce approximations that aid in the realization of a fast and memory efficient algorithm. The null space is estimated from the smaller sub-matrix.
We demonstrate the effectiveness of the proposed approach by applying it on phantom and human data. Reconstructions and field map corresponding to one slice of the phantom and human datasets are shown below.
References:
References:
A. Balachandrasekaran, M. Mani and M. Jacob. IEEE Transactions on Medical Imaging, 2018.
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