Receive array magnetic resonance spectroscopy: Whitened singular value decomposition (WSVD) gives optimal Bayesian solution

Abstract

Receive array coils play a pivotal role in modern MRI. MR spectroscopy can also benefit from the enhanced signal-tonoise ratio and field of view provided by a receive array. In any experiment using an n-element array, n different complex spectra will be recorded and each spectrum unavoidably contains an undesired noise contribution. Previous algorithms for combining spectra have ignored the fact that the noise detected by different array elements is correlated. We introduce here an algorithm for efficiently, robustly, and automatically combining these n spectra using noise whitening and the singular value decomposition to provide the single combined spectrum that has maximum likelihood in the presence of this correlated noise. Simulations are performed that demonstrate the superiority of this approach to previous methods. Experiments in phantoms and in vivo on the brain, heart, and liver of normal volunteers, at 1.5 T and 3 T, using array coils from eight to 32 elements and with 1 H and 31 P nuclei, validate our approach, which provides signal-to-noise ratio improvements of up to 60% in our tests. The whitening and the singular value decomposition algorithm become most advantageous for large arrays, when the noise is markedly correlated, and when the signal-to-noise ratio is low. Key words: MR spectroscopy; array; coil combination; WSVD; SVD; noise whitening MR spectroscopy provides unique insights into the chemical composition of a subject in a completely noninvasive manner. For example, chemical shift imaging (CSI) and single voxel spectroscopy allow measurement of the concentrations of metabolites containing nuclei such as 1 H and 31 P, offering a window into biochemical processes occurring in vivo. Nevertheless, constraints on the signalto-noise ratio (SNR) obtainable with current technology are one of the primary factors limiting clinical applications of MR spectroscopy. We report our recent work to alleviate this SNR limitation through an improved method for combining the data gathered from receive array coils.Receive array coils have a long history in the MRI community following the work of Hyde et al. (1) and Roemer et al. (2). By replacing the single radiofrequency receive coil in an MR scanner with an array of smaller coils (''array elements''), improvements in SNR are obtained. The smaller size of each of these elements makes them couple more strongly with the magnetization in the subject under examination, giving stronger signals and hence a larger SNR than with a single element coil. Furthermore, although each element has a smaller field of view, the field of view covered by at least one coil may be very large. Thus, when the signals from each element are combined appropriately, a receive array provides data of significantly enhanced SNR that cover a wider field of view. The Roemer et al. (2) founding paper on receive array MRI introduced a widely accepted model of the array detection process, which we use here to allow a unified description of existing methods for receive array combination in MR sp...

Quantitative Proton Magnetic Resonance Spectroscopy and Spectroscopic Imaging of the Brain

“…In general each coil in the parallel array has a different distance from the MRS volume element and produces a spectrum having its own unique signal strength and phase characteristics. It remains somewhat unclear how to optimally recombine the spectral information arriving from each of the coils in the array although several approaches have been proposed (7–9). …”

Dilated Cardiomyopathy: Phosphorus 31 MR Spectroscopy at 7 T

“…For this comparison, we chose to compare our most widely used 3-T coil (a heart-liver loop-butterfly coil with hardware quadrature combination, Siemens product for 1.5 T, retuned for 3 T) with our best available 7-T coil (a 16-element receive array used with a software combination and the whitened singular value decomposition algorithm [28]). The improvement seen here reflects real-world improvement at 7 T compared with 3 T. This is due both to the increase in field strength and to the optimized coil at 7 T. However, we note that when we previously attempted to introduce receive array coils at 3 T, we saw an increase in field of view for the coil, but with no statistically significant change in SNRsignal-to-noise ratio in the interventricular septum (actually a 6% loss in SNRsignal-to-noise ratio) compared with that with the use of the heart-liver coil (12).…”

Adaptively optimized combination (AOC) of magnetic resonance spectroscopy data from phased array coils

“…In this scenario, the aforementioned methods will have a risk of compromising the SNR of the combined spectrum. In order to alleviate this limitation, some schemes were proposed such as whitening the noise prior to the weighted combination (26,27). However, the method introduced by Martini et al (26) and the method proposed by Rodgers and Robson (27) underestimate those peaks with low SNRs.…”

“…In order to alleviate this limitation, some schemes were proposed such as whitening the noise prior to the weighted combination (26,27). However, the method introduced by Martini et al (26) and the method proposed by Rodgers and Robson (27) underestimate those peaks with low SNRs. Therefore, there is a need to develop an adaptively optimized MRS combination method that can perform the best in various scenarios of coil/channel noise.…”