Blind estimation of spatially variant noise in GRAPPA MRI

The reconstruction process in multiple coil MRI scanners makes the noise features in the final magnitude image become non-stationary, i.e. the variance of noise becomes position-dependent. Therefore, most noise estimators proposed in the literature cannot be used in multiple-coil acquisitions. This effect is augmented when parallel imaging methods, such as GRAPPA, are used to increase the acquisition rate. In this work we propose a new technique that allows the estimation of the spatially variant maps of noise from the GRAPPA reconstructed signal when only one single image is available and no additional information is provided. Other estimators in the literature need extra information that is not always available, which has supposed an important limitation in the usage of noise models for GRAPPA. The proposed approach uses a homomorphic separation of the spatially variant noise in two terms: a stationary noise term and one low frequency signal that correspond to the x-dependent variance of noise. The non-stationary variance of noise is estimated by a low pass filtering. The noise term is obtained via prior wavelet decomposition. Results in real and synthetic experiments evidence the suitability of the simplification used and the good performance of the proposed methodology.