An algorithm for the optimum combination of data from arbitrary magnetic resonance phased array probes

Abstract

When summing the spectra acquired with phased array coils, signals with low signal-to-noise ratio or wrongly corrected phase may degrade the overall signal-to-noise ratio (SNR). Here we present a mathematical expression predicting the dependence of combined SNR on the signal-to-noise ratios and errors in phase correction of composite signals. Based on this equation, signals that do not lead to an overall increase in signal-to-noise ratio can be identified and excluded from the weighted sum of signals. This tool is particularly useful for the combination of large numbers of signals. Additionally, a simple and robust algorithm for calculating the complex weighting factors necessary for the signal-to-noise weighted combination of spectroscopic data is presented. Errors in the calculation and correction of relative phase differences between composite spectra are analysed. The errors have a negligible effect on the overall spectral SNR for typical clinical magnetic resonance spectroscopy (MRS). The signal combination routine developed here has been applied to the first in vivo MRS study of human rectal adenocarcinomas at 1.5 T (Dzik-Jurasz A S K, Murphy P S, George M, Prock T, Collins D J, Swift I and Leach M O 2001 Magn. Reson. Med. at press), showing improvements of combined spectral SNR of up to 34% over the maximum SNR from a single element.

The rapid and automatic combination of proton MRSI data using multi-channel coils without water suppression

“…Improvement in SNR was attributable to the much greater strength of the water signal compared with either noise or baseline distortion. Use of SNR of water as a reference also contributed to the improvement of SNR because it accounted both for the amplitudes of the water signals and for the differences in noise levels across coil elements [2,3,5].…”

“…This approach in essence disregards the correlations of noise across coil elements, which seems reasonable, given that noise correlations are minimal for decoupled multi-channel coils [18]. A common procedure to determine SNR is to measure the signal and noise in the same voxel [5]. In this case, however, water components must be removed from the signal before measuring residual noise in each voxel for each coil element, which can be time-consuming.…”

“…A multi-channel coil consists of an array of mutually decoupled, geometrically optimized surface coils, which receive MR signal from the brain simultaneously [1][2][3][4][5][6][7]. These multiple signals are then combined mathematically to yield a single spectroscopic signal at each voxel.…”

“…Another approach used spectral fitting software to identify in the frequency domain phase differences in metabolite signals that originated in different coil elements [3]. To calculate the WFs required for signal summation, some approaches have employed background noise as a reference to optimize SNR [2,4], whereas others have used as a reference the SNR of a spectrum [5] or the peak area of a particular metabolite [3,6] to calculate the optimal WFs. Each of these approaches used water suppression (WS) during signal acquisition to reduce the dynamic range of the signal, thereby avoiding introduction of noise from the analog-to-digital conversion, and simplifying the postprocessing of the MR signal.…”

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

“…This can be automated by fitting or integrating over a reference peak, using this to phase the spectra (3). The reference peak amplitudes can then be used to disregard low SNR array elements (6). Better results are obtained by weighting the spectra according to the reference peak amplitudes (3) or SNRs (7), which approximate a matched filter.…”