Synopsis

MRI can encode clinically important information in the image-phase, thus has great potentials to extend its capability for clinical applications. However, if phase references are not available, the multi-coil phase combination using the weighted average suffers from dominant signal losses coming from phase cancellations due to uncompensated coil-dependent phase offsets.

In this work, we developed a self-calibrating multi-coil phase combining method which does not require any additional scans for phase references. When applied to a single-point Dixon imaging, we verified the proposed method could successfully estimate the global phase-map with the minimal signal loss only using a single-scan image.

Introduction

Magnetic resonance imaging can encode clinically important information in the image phase, thus has great potentials to extend its capability for clinical applications. In multi-channel MR phase imaging, time consuming multiple image acquisitions are required to remove both spatially varying coil-independent phase errors and coil-dependent phase offsets added to the clinically useful information in the image-phase. However, if phase references are not available, the multi-coil phase combination using the weighted average suffers from dominant signal losses coming from global and local phase cancellations due to uncompensated coil-dependent phase offsets. Due to this limitation, their clinical use has been restricted only when phase references are available using multiple image acquisitions^1-2.

In this work, we developed a self-calibrating multi-coil phase combining method which does not require any additional scans for phase references. The proposed method uses the localized singular value decomposition (SVD) and rank-one approximation to estimate the initial global phase-map independently for each pixel, then the final multi-coil combined phase-map was composed after phase correction using a region-growing algorithm to estimate the unknown phase-signal polarity for each-pixel resulting from using localized SVD and rank-one approximation. The proposed method could successfully estimate the global phase-map with the minimal signal loss only using a single-scan image.

Methods

We developed a localized singular value decomposition (LSVD) method for multi-channel phase combination. Combining multi-coil phase-images using a single set of weighting coefficients calculated from the standard SVD is suboptimal especially when spatially varying coil-dependent phase offsets are uncompensated and inconsistent for multi-channel receivers. In our LSVD method, the initial global phase-map is estimated only using n x n surrounding neighboring pixels independently for each pixel. For each pixel, n x n neighboring pixels were rearranged in a [n² x c] matrix where c is the total number of coils. Then, the [n² x c] matrix of each pixel was decomposed using a standard SVD algorithm and the locally combined phase signals were estimated using the rank-one approximation (i.e. the largest singular value multiplied by the corresponding left singular vector)³. From the rearranged n x n image, only the central pixel was selected as the multi-coil combined signal for each pixel.

As the initial global phase map $$$e^{j\theta(\overrightarrow{r})}$$$ was estimated independently for each pixel using the localized SVD and rank-one approximation, the polarity of composed image-phase is unknown for each pixel and spatially inconsistent. Assuming that the image-phase is spatially smooth, the final phase-map was estimated by selecting a true solution between two candidates (i.e. $$$\pm e^{j\theta(\overrightarrow{r})}$$$) for each pixel using a region-growing algorithm⁴.

Results

The self-calibrating multi-coil image-phase combining algorithm was tested using a single-point Dixon images5. The total of 32 in vivo abdomen images were acquired within a single breath-hold using the fast spoiled 3D gradient-echo pulse sequence on a 1.5T whole body clinical scanner (GE Healthcare, Waukesha) with 4-channel torso-phased array coils. Scan parameters are scan-time = 14 secs, TR/TE=4.2/1.668 ms, flip angle=15°, acquisition matrix=384x110, receiver bandwidth=±83.3 kHz, FOV= 36x24.75 cm, slice-thickness = 5mm, and phase-difference of water and fat signals=116°. The proposed algorithm was implemented in MATLAB (MathWorks, Natick). Fig. 1 (a) and (b) are normalized four-channel phase vectors and their weighted average in a selected region from the acquired single-point Dixon images (yellow boxes). Signal losses coming from the phase cancellation are clearly observed in the suboptimally combined image phase (red arrows) due to uncompensated coil-dependent phase offsets. On the other hand, the proposed method could successfully estimate the global phase-map with the minimal signal loss as shown in Fig. 1 (c).

The initially estimated global phase map is shown in Fig. 2 (a). As the phase-map for each pixel was estimated independently for each pixel, the polarity of composed image-phase is unknown for each pixel and spatially inconsistent. Fig. 2 (b) is the final global phase-map estimated using simultaneously processed two phase-corrections using a single region growing algorithm⁴: (1) the phase correction to resolve the pixel-by-pixel polarity ambiguity resulting from using localized SVD and rank-one approximation, and (2) another phase correction required for Dixon imaging. After removing the estimated phase-map from the acquired single-point Dixon image, the uniformly separated water-only and fat-only images were reconstructed as shown in Fig. 2 (c) and (d).

Discussion

Acknowledgements

References

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5. Ma J. Breath-Hold Water and Fat Imaging Using a Dual-Echo Two-Point Dixon Technique With an Efficient and Robust Phase-Correction Algorithm. 2004;52:415-419.