Robust Nyquist Ghost Correction by Incorporating Phase Errors Correction in SENSE
Victor B. Xie1,2, Mengye Lyu1,2, Yilong Liu1,2, Yangqiu Feng1,2, and Ed X. Wu1,2

1Laboratory of Biomedical Imaging and Signal Processing, The University of Hong Kong, Hong Kong SAR, China, People's Republic of, 2Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong SAR, China, People's Republic of

### Synopsis

In this abstract, we proposed a novel method that can fully and robustly correct EPI Nyquist ghost by incorporating high-order phase error correction into SENSE reconstruction. More importantly, this method does not induce SNR loss, greatly benefiting the final reconstructed images. Phantom and in vivo imaging results clearly demonstrated the efficacy of this method in ghost correct as well as its superior SNR performance, particularly in accelerated data set that can suffer from amplified noise problems. This novel method has great potentials to be applied in all kinds of EPI-based MRI studies, such as fMRI and DTI.

### Introduction

EPI is widely applied in various MRI applications because of its fast imaging capability. However, its image quality is intrinsically hindered by Nyquist ghost, which is induced by inconsistency between positive and negative echoes. Numerous methods have been proposed to correct Nyquist ghost, among which model-based correction methods are widely used. The phase inconsistency is usually modeled as 1D linear phase error [1, 2], 1D nonlinear phase error [3], or 2D phase errors [4]. Phase errors can be modeled from a reference scan [1, 3] or image based entropy optimization [2]. However, it is challenging for all these methods when high-order phase errors are introduced by eddy current or magnetic susceptibility effect, especially in oblique imaging where different physical gradients may have different eddy currents and time delays [5]. With the invention of phased array coils, several new methods have been proposed for Nyquist ghost correction. Briefly, an EPI k-space data set can be separated into two groups of positive or negative echoes. Each group can be treated as a data set that is equally undersampled by a factor of two, thus can be reconstructed into a Nyquist ghost free image using parallel imaging reconstruction methods [6-9]. However, these methods usually suffer from SNR loss during parallel imaging (PI) reconstruction. In this abstract, we propose a novel method that can fully correct EPI Nyquist ghost without sacrificing image SNR.

### Methods

Figure 1 illustrates the procedures for Nyquist ghost correction and image reconstruction. Multi-channel EPI data are grouped into positive and negative echoes. The aliased image from positive echoes in each coil is encoded as $C_{1,j}=\sum_{n=0}^{2R-1}S_{j}(x,y+\frac{nN_{y}}{2R})I_{p,j}(x,y+\frac{nN_{y}}{2R})$ (Eq.[1]), where Sj is the coil sensitivity matrix in the jth coil, R is acceleration factor, and Ny is the number of pixels in PE direction. Then a Nyquist ghost free image Ip can be reconstructed by SENSE, so is In from negative echoes $C_{2,j}=\sum_{n=0}^{2R-1}S_{j}(x,y+\frac{nN_{y}}{2R})I_{n,j}(x,y+\frac{nN_{y}}{2R})$ (Eq.[2]). But phase errors originating from inconsistency between different echo polarities still exist between In and Ip and are calculated from the their phase difference as $\triangle\phi=Arg(I_{p}I_{n}^{*})$. Then Eq.[1] can be formulated as $C_{1,j}=\sum_{n=0}^{2R-1}S_j^{'}(x,y+\frac{nN_{y}}{2R})I_{n,j}(x,y+\frac{nN_{y}}{2R})$, where $S^{'}=S\cdot{exp(i\triangle\phi)}$. So the number of equation for solving In is doubled together with Eq.[2], improving matrix inversion condition and benefiting image SNR.

To validate this proposed method, water phantom and in vivo rat brain spin-echo EPI data were acquired on a 7T Bruker MR scanner equipped with a 4-channel surface coil using the following parameters: TE/TR = 60/2000ms, matrix size = 128×128, no partial-Fourier. Human brain gradient-echo EPI data were also acquired on a Philips Achieva 3T MRI scanner equipped with an eight-channel SENSE head coil using TE/TR = 30/1000ms, matrix size = 96×96, no partial-Fourier. All scans were acquired first with full k-space coverage and then repeated with acceleration factor R = 2. Coil sensitivity maps were generated from a Nyquist ghost free EPI image acquired and reconstructed using PLACE [10]. Traditional Nyquist ghost correction methods, linear phase error correction (LPC) [2] and phased array ghost elimination (PAGE) [7] were also implemented for comparison.

### Results

Figure 2 shows the phantom images reconstructed using different methods. Parallel imaging based method PAGE performed better than LPC as it effectively eliminated the Nyquist ghost, although at the expense of increased noise, especially in accelerated data set. In contrast to this, our proposed method could fully eliminate the Nyquist ghost without deteriorating the image SNR.

Figure 3 and Figure 4 further show the rat and human brain images reconstructed using different correction methods. Again, the LPC method failed to fully eliminate the Nyquist ghost while the PAGE method dramatically enhanced the noise level in the accelerated data set. In contrast, our proposed method exhibited a superior performance by fully eliminating the Nyquist ghost without deteriorating imaging SNR.

### Discussion and Conclusion

This study demonstrated a novel method that can robustly eliminate EPI Nyquist ghost without degrading image SNR. This method first uses SENSE to reconstruct two separate images from positive and negative echoes. High order (not only first and second order) phase error information can be well obtained from these two images. Therefore, feeding this phase error information into SENSE during reconstruction of the final image can provide the highest SNR efficiency, similar to MUSE [11] in multi-shot DWI. Our phantom and in vivo imaging results clearly demonstrated that our proposed method performs well not only in non-accelerated data set, but also in accelerated data set, the use of which is often limited by amplified noise level. Undoubtedly, this novel method has great potentials to be applied in all kinds of EPI-based MRI studies, such as fMRI and DTI.

### Acknowledgements

No acknowledgement found.

### References

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### Figures

Figure 1. Reconstruction procedures for Nyquist ghost correction

Figure 2. Spin-echo EPI phantom images with Nyquist ghost corrected by LPC, PAGE and the proposed method.

Figure 3. Spin-echo EPI rat brain images with Nyquist ghost corrected by LPC, PAGE and the proposed method.

Figure 4. Gradient-echo EPI human brain images at 3T with Nyquist ghost corrected by LPC, PAGE and the proposed method.

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