Correcting the Side Effects of ADC Filtering in MR Image Reconstruction

This work investigates the role of the filters implemented on analog-to-digital converters for the reconstruction of magnetic resonance images. We analyze the effects of these filters both from a theoretical and an experimental point of view and demonstrate how it may lead to severe degradation of the reconstructed images when the distance between consecutive samples is larger than Shannon’s limit. Based on these findings, we propose a mathematical model and a numerical algorithm that allow to mitigate such filtering effects both for linear and nonlinear reconstructions. Experiments on simulated and real data on a 7 Tesla scanner show that the proposed ideas allow to significantly improve the overall image quality. These findings are particularly relevant for high resolution imaging and for recent sampling schemes saturating the maximum gradient amplitude. They also open new challenges in sampling theory.