Channel combination without acquiring coil sensitivity maps can be challenging for phase images. Since different coils are subject to different sensitivities, the phase images acquired by different channels vary a lot. A direct Weighted Mean (WM) combination ¹ ($$$\theta_{combined}=\sum_kM_k^2exp(i\theta_k)/\sum_kM_k^2$$$, $$$k$$$ represents channel index, $$$M_k$$$ and $$$\theta_k$$$ are magnitude and phase of channel $$$k$$$) may lead to signal cancellation and decrease the SNRs of combined images. Adaptive reconstruction ² (AR) can improve SNR, but it is sensitive to patterns and variations of sensitivity maps, which may lead to open-ended fringe artifacts (Fig. 1f). In this study, we demonstrate a two-step way to estimate and eliminate the phase terms introduced by coil sensitivities and improve the robustness of traditional AR method.

Signals acquired from different channels can be modeled as $$$C_k=M\cdot S_k\cdot exp(i(\theta+\phi_k+\eta_k))$$$, $$$k$$$ represents the $$$k^{th}$$$ channel, $$$C_k$$$: acquired complex images, $$$S_k$$$ and $$$\phi_k$$$: magnitude and phase of coil sensitivity, $$$M$$$ and $$$\theta$$$: magnitude and phase of underlying signals, $$$\eta_k$$$: noise term. The huge variations of $$$\phi_k$$$ and the singularities contained in $$$\phi_k$$$ can both influence the combined phase image potentially. So $$$\phi_k$$$ should be removed before AR.

We combine the different channel data in two steps:

Step 1: Estimate $$$\phi_k$$$. a) The phase images from the original data are high-pass filtered to remove $$$\phi_k$$$ ($$$\phi_k$$$ is supposed to be a low-frequency component) and combined using the WM method to generate a rough combined phase map $$$\widehat{\theta}$$$ ³. b) The original multichannel phase images are subtracted by $$$\widehat{\theta}$$$ to generate rough $$$\phi_k$$$ maps. c) $$$\phi_k$$$ maps are smoothed to suppress noise.

Step 2: Remove $$$\phi_k$$$ from the original data, and then perform an AR operation.

Phantom and in-vivo studies were conducted on a Philips 3.0T Achieva TX MRI scanner (Philips Healthcare, Best, The Netherlands). A 32-channel head coil was used, with smart selection on. Human studies were performed under IRB approval from our institution. Phantom study: 2D multiecho gradient echo, 4 echoes with TR/TE₁/△TE = 447/3.6/5.0ms, flip angle = 18°， FOV = 230×230mm², Matrix = 256×256, slice thickness = 2mm, slice number = 20; coil elements used = 28. In-vivo study: 2D multiecho gradient echo, 4 echoes with TR/TE₁/△TE = 895/3.6/5.0ms, flip angle = 18°， FOV = 230×230mm², Matrix = 256×256, slice thickness = 2mm, slice number = 40, coil elements used = 30.

These two datasets were processed using three methods: WM, the traditional AR and our proposed method, to test the robustness and SNR performance of these algorithms.

Fig. 1 shows the results for the phantom study. The singularities shown in Fig. 1a exist in all the phase images acquired by this channel, indicate that these singularities are introduced by coil-dependent phase term $$$\phi_k$$$. $$$\phi_k$$$ maps (Fig. 1c) are estimated from the original phase maps (Fig. 1b) and removed away (Fig. 1d). It is obvious that there is open-ended fringe artifact in the result of AR (circle in Fig. 1f). It has been eliminated by our method (Fig. 1g). The standard deviations of the same regions (yellow boxes) from e to g are 0.147, 0.064 and 0.044, respectively, indicate the high SNR performance of the traditional and our proposed methods. The different standard deviations between f and g may arise from the elimination of low-frequency components in Step 1.

Fig. 2 shows the results for the in-vivo study. The WM method provides results with low SNR (Fig. 2a). AR can get a relative high SNR compared with the WM method. Both the WM and AR methods generate a phase singularity shown in the circled areas. These singularities lead to the errors in the unwrapped phase and high-pass filtered phase images (Figs. 2d, 2e, 2g and 2h). In comparison, our proposed method can eliminate this singularity and maintain the high SNR (Figs. 2c, 2f and 2i).

AR processing of phase images may suffer from the variations and singularities of sensitivity phase maps and lead to open-ended fringe artifacts. These artifacts may hinder the subsequent phase unwrapping and phase usage. Our two-step way estimates the phase maps of coil sensitivities firstly and eliminates these phase terms thereafter. Then a repeated AR can combine phase images with a high SNR and free of singularity.The two-step way can improve the robustness of traditional AR method to combine phased-array signals while maintaining high SNRs of the combined results.