Non-Linear Inversion in Parallel MRI: Considerations on Noise Amplification in the Joint Estimation of Image and Coil Sensitivities

Julien Sngas¹, Martin Uecker²

Recently, iterative joint estimation algorithms have been proposed to reconstruct aliasing free images and coil sensitivities in a single step from self-calibrating sampling trajectories such as Cartesian with variable density. Due to the non-linearity of the reconstruction method, their behavior with respect to noise amplification is more difficult to predict. In this work, we extend the non-linear inversion algorithm (NLINV) by incorporating the noise covariance of the coil array in the minimization function and by applying additional regularization for the coil sensitivities, both with the aim of improving the SNR of the reconstructed image. We present detailed results on the noise amplification properties of this joint reconstruction scheme and evaluate the proposed algorithm in vivo.