Volterra series modelling and compensation of non-linear distortions caused by susceptibility difference artefacts related to the presence of ferromagnetic implants in magnetic resonance imaging

Magnetic resonance imaging is popular in medical settings due to its unique technical characteristics. However, its full potential has been limited by imaging artefacts caused by various phenomena. Previously, a methodology was proposed to characterize and reduce artefacts caused specifically by magnetic susceptibility differences. In the present work, the Volterra series approach is suggested as an alternative method for describing non-linear distortions induced by susceptibility artefacts. A second-order Volterra series is utilized for characterizing the image non-linearities using a block-by-block processing approach. Subsequently, a corresponding second-order inverse Volterra series is applied to compensate for the quantified distortions. In addition, a technique for automatic demarcation of recoverable and non-recoverable regions in magnetic resonance images is proposed to ameliorate the developed methodology. Experimental results indicate that this approach offers improved accuracy and flexibility in reducing non-linear distortions caused by magnetic susceptibility artefacts.