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

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. (author)