Synopsis

Phased-array coils are used in MRI to improve signal-to-noise ratio (SNR) or to accelerate data acquisition speed through parallel imaging. It is beneficial to have a phased-array imagery reconstruction method that extracts the complex magnetization information from the multichannel data. In this work, we adopt the fusion frame theory to estimate the magnitude of the underlying magnetization and further employ the matched-filter method to estimate the magnetization phase, thereby reconstructing a complex image that does not have coil sensitivity weightings.

Introduction

Methods

Complex image estimation from multichannel data was done through the following. First, multichannel data were structured into a data matrix (A) as shown in Figure 1. Then the matrix A was decomposed into A=UΣV^H using the singular-value decomposition (SVD). The dominant singular vectors in U were used to generate the spatial matched filters and to estimate the phase as described in Uecker et al.⁵ The dominant singular vectors in V were used to generate a fusion frame and its associated fusion frame operator (S). It can be shown that the impulse response of S is the weighted Fourier transform of the squared magnitude of the magnetization. Therefore, the desired magnitude image can be estimated from $$\mid I \mid =\sqrt{F^{-1}W^{-1}S(\delta)},$$ where F is the Fourier transform, W is the weighting matrix and I is the image.

To demonstrate the capability of the proposed method, we performed the following experiments. First, we used a T₁-weighted, IR-SPGR 8-channel brain data and reconstructed final images using SSOS and the proposed method. To show the removal of coil weighting, plots of the magnitude values along a line in the images were also calculated. Next, using the same data, we removed three coil data (channels 6,7, and 8 placed at the upper-left corner of the brain) and again reconstructed using SSOS and the proposed method. Finally, we performed the same experiment using a T₂-weighted, fat-suppressed 8-channel knee data. After noticing a singularity in the phase image, we removed a coupled coil data and reconstructed again to compare the results.

Results

Figure 2 shows the results from the SSOS and the proposed reconstruction with the phase image. Note the bright subcutaneous fat signal surrounding the cranium, which is a characteristic of the used T₁-weighted IR-SPGR sequence. The magnitude image acquired from the proposed method shows evenly distributed fat signals, whereas the SSOS image clearly shows the effect of coil weighting.

Figure 3 shows reconstructed results from using only a subset of coils. The SSOS image shows severe darkening in the area where the removed three coils were originally placed. As opposed to that, the proposed method is able to reconstruct all the structures in that area with slightly decreased SNR.

Figure 4 shows the same set of experiment performed with the knee data. The magnitude image from the proposed method again shows flat magnetization profile compared to the SSOS image. However, the phase image contained a singularity. This phenomenon has been observed consistently in works that adopted adaptive coil combination method⁶.

After noticing the singularity, we looked through individual coil images and identified a channel that suffered from coupling. We then removed the coil data and reconstructed again with the proposed method. Figure 5 shows the coupled coil and the reconstructed magnitude and phase images. Once the coupled coil data was removed, we were able to estimate the phase better with minimally decreased SNR in the magnitude image.

Discussion

Conclusion

We have presented a phased-array reconstruction method that extracts complex magnetization images that does not contain coil weightings as in SSOS. The proposed method can be valuable in applications where magnetization quantification is crucial.

Acknowledgements

We gratefully acknowledge National Institutes of Health (P41-EB013598) for their financial support.

References

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