On the noise correlation matrix for multiple radio frequency coils

Noise correlation between multiple receiver coils is discussed using principles of statistical physics. Using the general fluctuation-dissipation theorem we derive the prototypic correlation formula originally determined by Redpath (Magn Res Med 1992; 24:85-89), which states that correlation of current spectral noise depends on the real part of the inverse impedance matrix at a given frequency. A distinct correlation formula is also derived using the canonical partition function, which states that correlation of total current noise over the entire frequency spectrum depends on the inverse inductance matrix. The Kramers-Kronig relation is used to equate the inverse inductance matrix to the spectral integral of the inverse impedance matrix, implying that the total noise is equal to the summation of the spectral noise over the entire frequency spectrum. Previous conflicting arguments on noise correlation may be reconciled by differentiating between spectral and total noise correlation. These theoretical derivations are verified experimentally using two-coil arrays.