Improved total sensitivity estimation for multiple receive coils in MRI using ratios of first-order statistics

Object Spatial variation in the sensitivity profiles of receive coils in MRI leads to spatially dependent scaling of the signal amplitude across an image. In practice, total sensitivity of the coil array is either calibrated or corrected directly by comparison to a uniform sensitivity image, fitting of coil profiles, or indirectly by constraining the reconstructed image or coil profiles. In the absence of these corrections, popular coil summation strategies are often designed to maximize the signal-to-noise ratio or optimize under-sampled encoding but not necessarily estimate the value of the signal unscaled by the coil spatial sensitivity. Materials and Methods We use ratios of first-order statistics to approach the unscaled value of the signal at any position. Motivated by the assumption that the coil array is a sample from much larger number of possible coils, we present two approaches to scale the mean signal in all coils: (1) an argument for use of the mode of the normalized signals, and (2) using a one-dimensional analog derive an approximate expression for scaling with the ratio of the square-of-the-mean to the mean-of-the-squares. We test these approaches with simulation where idealized coil elements are arrayed around an object, and on directly acquired data with an 8-channel coil array on a uniform 13C phantom, and on Hyperpolarized 13C pyruvate brain MRI. Results We show improved image uniformity using the ratios of first order statistics compared to a simple homomorphic filter, noting that these approaches are more sensitive to noise. Discussion We present simple methods for correcting the spatial variation in sensitivity profiles in the context of a coil array. These methods can be used as an initial or adjunct step in data post-processing.