Selective combination of MRI phase images
Viktor Vegh1, Kieran O'Brien2, David C Reutens1, Steffen Bollmann1, and Markus Barth1

1Centre for Advanced Imaging, University of Queensland, Brisbane, Australia, 2Magnetic Resonance, Siemens Healthcare Pty. Ltd., Brisbane, Australia


Signal phase acquired via gradient recalled echo MRI sequences provides and an important source of tissue contrast. The use of phased array coils results in multiple-channel images that have to be combined to form a single image. A robust method of computing phase images has been challenging to develop, primarily due to the distribution of noise in phase images. We propose a new approach of combining phase images by exploiting the inherent noise in signal phase. Our selectively combined signal phase results show an improvement in the quality of the combined phase image in comparison to existing methods.


The so-called “optimal” method of combining multiple channel data overcomes the inability of computing combined phase images by working with the complex signal and by using information about relative complex sensitivity profiles of individual coils.1 An adaptive technique to combine multiple channel data has also been proposed,2 the drawback of which can be phase image singularities. More recently, a body coil scan was used to aid reconstruction of combined phase images.3 However, a pre-scan is required making the scan sessions longer and the signal phase is highly sensitive to motion which may affect the processing as two data sets are used. As an outcome of existing work, coil profiles have been shown to be important in phase combine reconstructions, as it has been indicated that information from individual coils should be weighted by the signal-to-noise ratio. In fact, an averaging operation does not make sense when signal-to-noise ratio in phase images is less than three due to violation of the Gaussian distribution assumption.4 The problem of obtaining high quality combined phase images remains a challenge, and certain approaches as shown by Liu et al. improve phase images via multiple echo time data and by applying a weighting factor to each channel based on the temporal variance of the signals.5 Existing approaches focus on the notion that all channels should contribute to the final outcome and the amount of contribution scales with the image signal-to-noise ratio. We propose a selective channel combination method (i.e. different voxels have different channels contributing to them) wherein noisy channels are not used in the reconstruction process.


32-channel MRI data was collected using a Magnetom 7T scanner (Siemens Healthcare, Erlangen, Germany). A gradient recalled echo sequence with the following parameter settings was used: TE = 20.4 ms, TR = 765 ms, resolution of 0.5 by 0.5 by 3 mm3, field-of-view = 224 by 154mm2, slices 30, iPAT = 2, partial Fourier = 75% and bandwidth = 257 Hz/pixel. Magnitude and phase images were saved for each channel. We applied a homodyne filter with ¼ window size with respect to the matrix size.6 Relative phase noise maps were then reconstructed by conjugating complex image data of all channels individually. That is, for any two different channels m and n, we computed ɛm,n = arg(Imconj(In)), where Im and In are complex valued (see Fig 1). The standard deviation of the spatial variation in ɛm,n was computed by applying a moving window of size 3 by 3 voxels across the entire range of ɛm,n. Following on, Gaussian smoothing with a window size of 11 by 11 voxels was applied, and then thresholded resulting in a mask for coil combination m and n (examples are shown in Fig 2). Phase signals were averaged in masked regions (Gudbjartsson and Patz provide justification for averaging phase signals in high signal-to-noise regions7).


In Fig 2, the combination of channels 6 and 2 (top row) lead to the classical outcome wherein we expect regions of high signal-to-noise ratio to be used in phase combine. For channels 12 and 1 (third row), however, the spatial variation maps of ɛm,n at location of the arrow show that even though a high signal-to-noise ratio is expected in this area, the noise in the phase is very high. Our mask shows that information from this region was not used to combine individual phase from these two channels. Furthermore, the combination of channels 1 and 4 (fourth row) shows that not all regions with high signal-to-noise ratio provide information that is useful in combining phase data. Fig 3 shows the results of optimal, adaptive and selective combine of phase images. An appreciable level of improvement in the phase image using selective phase combine is present in comparison to the adaptive method. Our findings also suggest that the method used to combine phase images can bias results.


Additional work is needed to examine other combinations of filter sizes for both the standard deviation calculation and Gaussian smoothing for the evaluation of image improvements. Nevertheless, we have been able to show that selective combination of individual phase images results in combined phase images with clear qualitative improvements. These findings are timely in view of the increased use of frequency shift and quantitative susceptibility mapping relying on accurate processing of ultra-high field signal phase.


Our results imply that selective channel combination of phase images can improve the quality of combined phase images.


Markus Barth acknowledges funding from ARC Future Fellowship grant FT140100865. The authors acknowledge the facilities of the National Imaging Facility at the Centre for Advanced Imaging, University of Queensland.


1. Roemer PB, Edelstein WA, Hayes CE, et al. The NMR phased array, 1990; MRM 16(2): 192-225.

2. Walsh DO, Gmitro AF and Marcellin MW. Adaptive reconstruction of phased array MR imagery, 2000; MRM 43(5): 682-690.

3. Jellus V and Kannengiesser AR. Adaptive coil combination using a body coil scan as phase reference, 2014; ISMRM: 4406.

4. Lathi BP. Modern Digital and Analog Communication Systems. Hault-Saunders International Edition; Japan: 1983.

5. Liu J, Rudko DA, Gati JS, et al. Inter-echo variance as a weighting factor for multi-channel combination in multi-echo acquisitior for local frequency shift mapping, 2015; MRM 73(4): 1654-1661.

6. Rauscher A, Barth M, Reichenback JR, et al. Automated unwrapping of MR phase images applied to BOLD MR-venography at 3 Tesla, 2003; JMRI 18(2): 175-180.

7.Gudbjartsson H and Patz S. The Rician distribution of noisy MRI data, 1995; MRM 34(6): 910-914.


Fig 1. Steps involved in selectively combining multiple channel phase images. Numbers 1 and 3 define channel numbers, and ϕ is phase and ɛ is an estimate of noise.

Fig 2. Rows correspond to different channel combinations and the number identifies the channels used in the example. The ‘+’ symbol denotes combined images using the sum-of-squares method. Signal phase noise maps showing spatial distribution of noise and masks used to combine phase images are also shown.

Fig 3. Comparison of (a) optimal, (b) adaptive and (c) selective combination of phase images. In the insets the numbers correspond to mean (standard deviation) and ‘*’ denotes a significant difference with respect to the colour. Notably, the method used to combine phase images can bias the result.

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