Adaptive self-calibrating parallel magnetic resonanceimaging using Kalman filter

Abstract

Parallel magnetic resonance imaging (pMRI) in k-space typically employs variable density sampling and estimates spatial correlation (convolution kernel) among neighboring signals in calibration to reconstruct missing signals. However, it is often challenging to obtain accurate calibration information due to data corruption with noises and spatially varying convolution kernels. Thus, we develop a novel, adaptive self-calibrating pMRI using the Kalman filter, wherein during calibration the variance of estimation errors for convolution kernels is minimized using discrete linear state space models with two distinct phases: predict and update. In the predict phase, convolution kernels and corresponding error covariance at each step are recursively estimated employing an identity state transition model and including process noises (a priori estimate). In the update phase, the a priori estimates are adaptively estimated between ideal and measured information employing measurement models, which consist of measured signals sliding group-wise with increasing steps to consider spatially varying convolution kernels, and incorporating pre-scanned noises (a posteriori estimate). The effect of calibration parameters on the level of artifacts and noises is investigated. Accelerated brain data are reconstructed using both conventional and proposed k-space pMRI for comparison, demonstrating that the proposed method not only produces highly accurate convolution kernels but also reduces artifacts and noises.