Adaptive Volterra Filter for Parallel MRI Reconstruction

Parallel magnetic resonance imaging (MRI) technique is able to accelerate MRI speed for reducing costs and enhancing patient’s comfortability. Parallel MRI can be categorized into two types: image-based and k-space-based methods. For k-space-based parallel MRI, missing k-space data is reconstructed by interpolating existing acquired k-space data with appropriate coefficients, which is generally considered as a linear process. However, noise cannot be suppressed or removed during the linear reconstruction process and therefore reconstructed image often suffers serious noise, especially when the acceleration factor is high. Non-linear filters are known to remove non-linear noise better. Based on the Volterra series that discovers and removes the second-order non-linear noise, we proposed a non-linear reconstruction strategy called adaptive Volterra generalized autocalibrating partial parallel acquisition (AV-GRAPPA) to reconstruct the unacquired k -space signals. For the proposed AV-GRAPPA, optimal selection of the second-order Volterra series terms is adjusted and determined for optimizing reconstruction quality. Experimental results show that the proposed method is able to better remove the reconstruction noise and suppress aliasing artifacts.