Receive array magnetic resonance spectroscopy: Whitened singular value decomposition (WSVD) gives optimal Bayesian solution.
Rodgers CT., Robson MD.
Receive array coils play a pivotal role in modern MRI. MR spectroscopy can also benefit from the enhanced signal-to-noise 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.