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Correcting the Side Effects of ADC Filtering in MR Image Reconstruction

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Abstract

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.

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Acknowledgements

C. Lazarus and P. Weiss wish to acknowledge P. Ciuciu and A. Vignaud for helping them to identify the filtering effect thanks to their strong engagement in the acquisition of Sparkling sampling patterns. M. März and P. Weiss wish to warmly thank G. Kutyniok for her support and enabling them to meet on a regular basis. The authors wish to thank David Brünner for sending them some references regarding the receive chain in MRI. We would like to express our gratitude to the donors involved in the body donation program of the Association des dons du corps du Centre Ouest, Tours, who made it possible to use an ex vivo human brain as phantom for our experiments, by generously donating their bodies for science. We also would like to acknowledge C. Destrieux and I. Zemmoura for the extraction and fixation of this anatomical piece. We also wish to thank M. Bottlaender for providing the baboon phantom. C. Lazarus wishes to thank the CEA Irtelis international PhD program for its financial support. She also acknowledges the France Life Imaging project Multi-CS-MRI, which supported her traveling expenses to ITAV. M. März is supported by the DFG Priority Program DFG-SPP 1798. P. Weiss thanks the ANR JCJC OMS for partial funding.

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Authors and Affiliations

  1. NeuroSpin, CEA Saclay, Gif-sur-Yvette, France

    Carole Lazarus

  2. Université Paris-Saclay, Paris, France

    Carole Lazarus

  3. Parietal, INRIA, Palaiseau, France

    Carole Lazarus

  4. Department of Mathematics, Technische Universität Berlin, 10623, Berlin, France

    Maximilian März

  5. IMT, CNRS & Université de Toulouse, Toulouse, France

    Pierre Weiss

  6. ITAV, CNRS & Université de Toulouse, Toulouse, France

    Pierre Weiss

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  1. Carole Lazarus
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Correspondence to Pierre Weiss.

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Lazarus, C., März, M. & Weiss, P. Correcting the Side Effects of ADC Filtering in MR Image Reconstruction. J Math Imaging Vis 62, 1034–1047 (2020). https://doi.org/10.1007/s10851-019-00940-w

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