SENSE-LORAKS: Phase-Constrained Parallel MRI without Phase Calibration

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

SENSE [1,2] and phase-constrained partial Fourier [3,4] reconstruction are two powerful approaches to accelerated MRI, that are even more successful when combined together [5-7]. However, previous phase-constrained SENSE approaches require an estimate of the image phase. As a result, specialized k-space trajectories are often used that densley sample the center of k-space to enable phase calibration. This can lead to non-uniform k-space sampling, which may introduce undesirable artifacts when used with sequences like EPI and balanced SSFP [8-9]. In addition, measuring a densely-sampled calibration region can also place restrictions on trajectory design and limit potential acceleration factors.

In this work, we introduce a novel image reconstruction approach, called SENSE-LORAKS, that enables phase-constrained parallel MRI reconstruction without prior phase estimation. SENSE-LORAKS uses the implicit regularization-based phase, support, and parallel imaging constraints of LORAKS [10,11] to regularize conventional SENSE reconstruction. LORAKS regularization is based on the observation that it is possible to embed k-space data into higher-dimensional low-rank matrices for images that possess limited image support, slowly-varying phase, and/or correlations between different parallel imaging receiver channels. This low-rank matrix embedding is powerful, because low-rank matrices have relatively few degrees of freedom and can be recovered from limited data using regularization techniques. Additionally, LORAKS is compatible with a wider range of sampling trajectories than conventional sparsity-based reconstruction [10,11].

Compared to previous fully-calibrationless LORAKS-based methods [10,11], SENSE-LORAKS has access to additional information about the coil sensitivity profiles. As a result, the SENSE-LORAKS inverse problem is better posed, and SENSE-LORAKS is compatible with a wider range of k-space trajectories that are less appropriate for fully calibrationless reconstruction (e.g., the uniform undersampling trajectories that are most appropriate for EPI and balanced SSFP).

A fully sampled brain dataset was acquired using a T2-weighted turbo spin echo (TSE) sequence with a 12 channel headcoil on a 3T scanner. The data was retrospectively undersampled using uniform 1D k-space trajectories that are not well-suited to conventional phase-constrained reconstruction. Conventional uniform sampling was simulated with sample spacing 5$$$\times$$$ larger than Nyquist, leading to a total of 5.1$$$\times$$$ acceleration (noninteger because the image matrix is not divisible by the undersampling factor). We also applied uniform partial Fourier sampling to achieve the same total 5.1$$$\times$$$ acceleration but with higher sampling density. Results are shown in Fig. 1. Conventional Tikhonov-SENSE reconstruction has large error due to the poor g-factor at this level of acceleration, and SENSE with total variation (TV) [13] has limited capabilities to address the coherent aliasing artifacts. P-LORAKS [11] is unable to reconstruct this data successfully, because it lacks prior sensitivity map information and cannot successfully estimate the intracoil correlations without more nonuniformity in the sampling pattern. In contrast, the proposed SENSE-LORAKS reconstruction yields much more accurate reconstruction results using both full and partial Fourier k-space trajectories. Importantly, the partial Fourier SENSE-LORAKS reconstruction leads to the best results, which may be explained by the fact that it achieves higher sampling density than the other trajectories with the same acceleration factors.

Fig. 3 shows a similar comparison with 64-channel uniformly undersampled EPI data at 3T. Notably, SENSE-LORAKS reconstruction with a partial Fourier trajectory can achieve a similar artifact level at 7.7$$$\times$$$ acceleration as compared to conventional Tikhonov-SENSE [12] reconstruction at 5$$$\times$$$ acceleration without partial Fourier acquisition. Moreover, the use of partial Fourier trajectories with EPI enables shorter minimum echo time [14].

[1] Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: sensitivity encoding for fast MRI. Magn Reson Med 1999;42:952-962.

[2] Pruessmann KP, Weiger M, Börnert P, Boesiger P. Advances in sensitivity encoding with arbitrary k-space trajectories. Magn Reson Med 2001;46:638-651.

[3] Margosian P, Schmitt F, Purdy D. Faster MR imaging: imaging with half the data. Health Care Instrum 1986;1:195-197.

[4] Noll DC, Nishimura DG, Macovski A. Homodyne detection in magnetic resonance imaging. IEEE Trans Med Imag 1991;10:154-163.

[5] Bydder M, Robson MD. Partial Fourier partially parallel imaging. Magn Reson Med 2005;53:1393-1401.

[6] Lew C, Pineda AR, Clayton D, Spielman D, Chan F, Bammer R. SENSE phase-constrained magnitude reconstruction with iterative phase refinement. Magn Reson Med 2007;58:910-921.

[7] Blaimer M, Heim M, Neumann D, Jakob PM, Kannengiesser S, Breuer F. Comparison of phase-constrained parallel MRI approaches: Analogies and differences. Magn Reson Med 2015;In Press.

[8] Bernstein MA, King KF, Zhou XJ. Handbook of MRI Pulse Sequences. Burlington: Elsevier Academic Press. 2004.

[9] Bieri O, Markl M, Scheffler K. Analysis and compensation of eddy currents in balanced SSFP. Magn Reson Med 2005;54:129–137.

[10] Haldar JP. Low-rank modeling of local k-space neighborhoods (LORAKS) for constrained MRI. IEEE Trans Med Imag 2014;33:668–681.

[11] Haldar JP, Zhuo J. P-LORAKS: Low-rank modeling of local k-space neighborhoods with parallel imaging data. Magn Reson Med 2015;In Press.

[12] Liang ZP, Bammer R, Ji J, Pelc NJ, Glover GH. Making better SENSE: Wavelet denoising, Tikhonov regularization, and total least squares. In: Proc. Int. Soc. Magn. Reson. Med.. 2002;p. 2388.

[13] Liang D, Liu B, Wang JJ, Ying L. Accelerating SENSE using compressed sensing. Magn Reson Med 2009;62:1574–1584.

[14] Hyde JS, Biswal BB, Jesmanowicz A. High-resolution fMRI using multislice partial k-space GR-EPI with cubic voxels. Magn Reson Med 2001;46:114–125.

Figure 1: Reconstruction
results with 5.1× acceleration. Numbers below the results are normalized
root-mean-square error (NRMSE). Error
images are also shown in color. (a) Gold Standard images (magnitude and phase).
With uniform sampling, (b) SENSE, (c) SENSE+TV, (d) SENSE-LORAKS, and (e)
P-LORAKS. With partial Fourier uniform
undersampling, (f) P-LORAKS, and (g) SENSE-LORAKS.

Figure 2: Reconstruction results with 64-channel EPI data. (a) Gold Standard images. (b)
5.0× SENSE with uniform sampling, (c) 5.0× SENSE-LORAKS with uniform sampling.
(d) 7.7× SENSE-LORAKS with partial Fourier uniform undersampling.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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