Introduction

Many techniques have been designed to compensate for pseudo-periodic^1-4 and rigid-body motion⁵. Some of these techniques need to oversample the K-space data to estimate motion, such as PROPELLER^4,5. Another kind of retrospective techniques compensate the motion in K-space, such as COCOA⁶ and PANDA⁷. Empirical thresholds are used in these techniques to identify the corrupted data, which are hard to be optimized for different clinical cases. Moreover, although these techniques are effective against random or sudden movement, they are ineffective when there is strong coherence of the ghost (Eg: rigid translation). Here a novel, sensitivity constrained phase update method, is proposed for the reduction of different kinds of ghost artifacts. Compared with magnitude value, phase of MRI signal is more prone to be influenced by motion. So once the phase error is corrected, the ghost artifacts can be largely suppressed.

Method

For each individual coil image at position $$$y$$$, ghost artifacts were modulated by sensitivities, it could be written as $$m_i(y)=S_i(y)m_i(y)+\sum_{p=1}^{P}\omega_pS_i(y+\Delta y_p)m_k(y+\Delta y_p)\qquad(1)$$Here $$$S_i$$$ is the sensitivity, $$$y+∆y_p$$$ represents where the folded artifacts is come from and totally $$$P$$$ folded positions. $$$ω_p$$$ is the ghost level.Using sensitivities as a constraint, a synthetic image can be generated via equation (2) $$synm_i(y)=S_i(y)\frac{\sum_{j,k}S_{j}^{*}(y)\psi_{j,k}m_k(y)}{\sum_{j,k}S_{j}^{*}(y)\psi_{j,k}S_k(y)} \qquad(2)$$ $$$ψ_(j,k)$$$is the noise correlation, combining equations (1) and (2),$$synm_i(y)=S_i(y)m_i(y)+S_i(y)\frac{\sum_{j,k}S_{j}^{*}(y)\psi_{j,k}[\sum_{p=1}^{P}\omega_pS_k(y+\Delta y_p)m_k(y+\Delta y_p)]}{\sum_{j,k}S_{j}^{*}(y)\psi_{j,k}S_k(y)} $$
$$=S_i(y)m_i(y)+S_i(y)\sum_{p=1}^{P}\omega_p{\chi} m_{k}(y+\Delta y_p) \qquad(3)$$
where$$\chi=\frac{\sum_{j,k}S_{j}^{*}(y)\psi_{j,k}S_k(y+\Delta y_p)}{\sum_{j,k}S_{j}^{*}(y)\psi_{j,k}S_k(y)}$$
For phase array coils, sensitivity is spatially varied that means $$$S_j (y)$$$ and $$$S_k (y+∆y_p )$$$ have different phase and magnitude. $$$\chi$$$ is much less than 1 due to high probability of phase cancellation. So, the ghost component in synthetic image is smaller while the true image component remains unchanged, as in Fig 1.
Fourier Transform of the difference of raw and synthetic image into frequency domain, we can get the phase error$$\Delta \varphi_i=\phi (F(m_i-synm_i)) \qquad(4)$$Where $$$F$$$ is the Fourier Transform operator and $$$ϕ$$$ is a phase operator. To control the noise amplification during the phase update, a magnitude weighted phase combination of all coils was performed. $$\Delta \varphi=\sum_{i}^{N}\lambda_i\Delta \varphi_i \qquad(5)$$Finally, phase error $$$\Delta \varphi$$$ can be subtracted from the raw k-space to reduce the ghost artifact, the iterative update approach could be written as$$ K_{n+1}=K_ne^{-i\Delta \varphi}\qquad(6)$$
Simulated and in-vivo data was used to validate the proposed method. A standard head image and 8ch sensitivities (http://hansenms.github.io/sunrise/sunrise2013/) were used for simulation, with both linear and random phase error to simulate motion induced artifacts. Also Gaussian noise was simulated to verify the degradation due to noise.

Two in-vivo datasets, head T2 FSE images and abdominal triggered T2 FSE images, were acquired on a 1.5T whole-body scanner (Centauri, Alltech Medical Systems). For head imaging, acquisition parameters were ETL 16, FOV 230mmx230mm, TR/TE 5000/90ms, matrix size 256*256 and 8 channel head coil. There were two intentional slight head shakes during the scan. For abdominal imaging, acquisition parameters were ETL 16, FOV 300mmx350mm, TR/TE 3672/90ms, matrix size 240*256, 15 channel torso coil. Since the volunteer’s breathing was very bad, there were obvious ghost artifacts. The sensitivity maps were calibrated via ESPIRiT⁸ with 6x6 kernel from 24 calibration lines.

Results

Fig. 2 shows the ghost reduction results with simulated data. Fig.2a & Fig.2d are the simulated ghost images with linear and random phase error respectively. Fig.2b & Fig.2e are the correction results and Fig.2c & Fig.2f are the ghost map. The ghost artifact had almost been cleared in 10 iterations, but a little noise amplification is seen.

Fig. 3 shows convergence performance and noise amplification during the iterations. The algorithm converges very fast that the residual ghost is very small after 5~10 iterations while the noise amplification increases slowly with iteration. From this simulation, 5~10 iteration is a good compromise between ghost reduction and noise amplification.

Fig.4&Fig.5 are the in-vivo application of the proposed method. The results show that the ghost due to head shake or irregular breathing had been dramatically reduced.

The computing time per 256x256 image for 10 iteration is about 500ms, using MATLAB on a PC with Intel i7@3.6GHz and 16G RAM.

Disscussion

Advantages: First of all, the proposed method does not require extra hardware or additional data. Second, both Cartesian and non-Cartesian acquisition are applicable. Third, this method is fast and robust, ghost due to periodic or random motion can be efficiently reduced.

Sensitivity map: Accurate and fast varying receiver sensitivity map is the critical factor for estimating the phase error. Since phase array coils were optimized for parallel imaging, the sensitivity often varies fast. From our test results, sensitivity map via ESPIRiT calibration is accurate enough in most cases.

Noise amplification: There was a bit more noise amplification for large number iteration. From the simulation, 5~10 iteration is a good compromise between ghost reduction and noise amplification. Filtering or fitting the phase error can be implemented as a further work to control the noise amplification.

Conclusion

A novel method, named sCPU, was proposed for robust and efficent ghost reduction. Motion induced error was estimated from the raw image and a sensitivity constrained synthetic image, then it was subtracted from the raw k-space to iteratively reduce ghost artifact. The results with simulated and in-vivo datasets show that the ghost artifacts can be efficiently reduced after several iterations.

(Code: https://github.com/concher009/MRI/tree/master/sCPU )

Acknowledgements

No acknowledgement found.