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Windowed whitened singular value decomposition (wWSVD): An improved data-driven strategy for combining MR spectra from multi-channel phased array coils
Ren Geryak1, Kelsey Li2, Maame Owusu-Ansah1, Xiaodong Zhong3, Hui Mao1, and Candace C Fleischer1

1Department of Radiology & Imaging Sciences, Emory University School of Medicine, Atlanta, GA, United States, 2Department of Biomedical Engineering, Duke University, Durham, NC, United States, 3MR R&D Collaborations, Siemens Healthineers, Los Angeles, CA, United States

Synopsis

Data driven methods to combine multi-channel phased array data such as singular value decomposition (SVD) can greatly improve SNR in MR spectra. Current SVD implementation has two primary limitations: 1) the assumption that noise is independent between coil channels; and 2) utilization of the entire spectrum to calculate the optimized coil combination. Here, we present a method using a whitened SVD (WSVD) matrix to decorrelate noise from individual coil elements, followed by an optimized and iterative windowing approach termed windowed whitened SVD (wWSVD) to determine the optimal subset of the spectrum for SVD analysis that is then used to combine multi-channel spectral data. We report a significant in vivo improvement in spectral SNR using wWSVD over WSVD.

Introduction

A major limitation of magnetic resonance spectroscopy (MRS) is the long acquisition time needed to acquire spectra with adequate signal-to-noise ratio (SNR). Signal collection from multi-channel phased array coils is becoming increasingly common to improve SNR for faster acquisition, but the final combined SNR is largely determined by the method used to combine these signals.1 Data driven methods to combine multi-channel array data such as singular value decomposition (SVD) can greatly improve SNR. SVD uses the entire spectrum to identify the primary components of the signal for optimal coil combination and often relies on the assumption that spectral noise is independent between coils. Rodgers and Robson demonstrated improvements in SVD-based spectral combination by first decorrelating the noise between coils via a whitening transformation in a method referred to as whitened SVD (WSVD).2 While SVD is typically applied across the entire collected spectrum,3 the signal from WSVD combination can be enhanced by narrowing the spectral region to which the method is applied. Here, we present a windowed whitened SVD (wWSVD) approach that iteratively determines the optimal subset of the original spectrum for SVD that is then used to combine multi-channel MRS data.

Methods

Single voxel MRS data was collected from 5 healthy subjects (all male, mean ± standard deviation age = 21 ± 2 years old) who provided informed consent. Data was acquired on a 3 T Prisma Fit whole-body MR scanner (Siemens, Erlangen, Germany) using a 32-channel head coil. MR spectra were collected from the posterior cingulate cortex (PCC) and left and right frontal white matter (LFWM and RFWM, respectively) using the point-resolved spectroscopy (PRESS) sequence (TR/TE= 1700/35 ms;1200 Hz bandwidth; CHESS water suppression; 128 averages; nominal voxel size of 2x2x2 cm3­). Raw Siemens TWIX data from all coils was analyzed with Gannet (version 3.0)4 and Matlab (Mathworks, 2018a).

WSVD was performed as previously described.2 A noise covariance matrix (N = CDC†) was calculated from the last 200 data points in the spectrum using all averages from all coils (819,200 points). A noise decorrelation or ‘whitening’ matrix calculated from N was applied to the data matrix containing individual coils and spectral data points (M) to generate a whitened matrix (W0 = MCD-1/2). SVD was then applied to the whitened matrix (W0 = UΣV†), where the first left singular vector (U) represents the combined spectral data. For wWSVD, the spectral bandwidth was iteratively truncated by 1 data point and WSVD was then applied to each truncated spectrum (Wt). Validation was performed on 8-acquisition summed spectra using a moving sum. The first right singular vector represents the coil combination that is used to combine the full (whitened, untruncated) spectrum (W0Vi,1 = Ui,1 Σ1,1). SNR was calculated from the maximum value of the NAA peak divided by the standard deviation of the first 200 spectral data points. Combined spectral SNR using WSVD and wWSVD were compared using a paired one-tailed t-test (p<.05 was significant). Voxels in different regions acquired in the same subject were treated as independent signals due to asymmetries in coil geometry (12 anterior and 20 posterior coils) and voxel positions relative to each coil element.

Results and Discussion

SNR comparisons between WSVD and wWSVD are shown in Table 1. The wWSVD produced a significant increase in SNR over the WSVD (p=.0004). Improvements in SNR occur in a relatively narrow region near the metabolites of interest and truncation eventually leads to a large decrease in the signal (Figure 2A). The wWSVD approach identifies the spectral region used to calculate the coil combination that produces the highest SNR (Figure 2B). This trend in SNR with the windowing approach indicates that the wWSVD-derived combination can be optimized for a narrow region of the spectrum when larger signals (i.e. water) are not included in the data. Further truncation of the spectrum to exclude all detectable metabolites results in lower SNR as the SVD method relies on spectral peaks to determine the coil combination.

To determine whether this approach generates consistent improvement over the WSVD approach, the wWSVD algorithm was applied to subsets of the voxel data for each subject. Summed subsets of the spectra (n=8) for all 128 acquisitions were analyzed with wWSVD. Consistent SNR improvement using wWSVD over WSVD is shown in Figure 3.

Conclusion

wWSVD is an improved data-driven approach for combining data from multi-channel phased array coils that leads to significant improvements in SNR compared to WSVD. This method may be beneficial for improving SNR in spectral regions with reduced metabolite concentrations, low numbers of spectral acquisitions, and distorted peak line shapes.

Acknowledgements

This work was supported in part by NIH 5R01CA203388. MR experiments were facilitated by the Emory Center for Systems Imaging Core (CSIC).
5R01CA203388-02

References

  1. Abdoli A and Maudsley AA. Phased-array combination for MR spectroscopic imaging using a water reference. Magn Reson Med., 2015;76(3):733-41.
  2. Rodgers CT and Robson MD. Coil combination for receive array spectroscopy: Are data‐driven methods superior to methods using computed field maps? Magn. Reson. Med., 2016; 75:473-487.
  3. Bydder M, Hamilton G, Yokoo T, and Sirlin CB. Optimal phased array combination for spectroscopy. Magn Reson Imaging., 2008; 26(6):847-850.
  4. gabamrs.blogspot.com

Figures

Figure 1. Combination of MR spectra acquired from multi-channel phased arrays using whitened singular value decomposition (WSVD) and windowed WSVD (wWSVD). Increased in vivo SNR was observed with wWSVD. See Methods for full details.

Table 1. In vivo spectral SNR after combining individual spectra acquired from a 32-channel phased array head coil using WSVD and wWSVD methods.

Figure 2. wWSVD applied to a LFWM spectrum. (A) Percent change in SNR as a function of spectral data points used for windowing in wWSVD. Left arrow is the spectral point corresponding to the center of the NAA peak. Right arrow corresponds to the center of the residual water peak. (B) Spectra following combination with WSVD (blue) and wWSVD (orange). Spectral noise was normalized to facilitate comparison of the NAA peak intensity (inset).

Figure 3. Box and whisker plots demonstrate consistent in vivo SNR improvements across multiple spectra from 3 voxel positions. For each subject, WSVD and wWSVD was applied on 121 summed spectra (8 acquisitions each). Plots are grouped by voxel location: (A) PCC, (B) LFWM, and (C) RFWM.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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