Recurrence formula-based automatic gradient eddy current compensation method for a 0.255 T MRI system

Gradient coils play a critical role in magnetic resonance imaging (MRI) systems by enabling spatial encoding through generating rapidly switching magnetic fields. However, these time-varying fields induce eddy currents in surrounding conductive structures, leading to gradient field distortions and imaging artifacts. In this study, we propose an automatic eddy current compensation method implemented on a field-programmable gate array (FPGA) platform. The approach employs iterative correction formulas for both linear gradient and $B_0$ eddy fields, enabling real-time compensation. To enhance computational efficiency, a novel layout for the pre-emphasis (PE) unit is also introduced. Compared to conventional compensation techniques, the proposed FPGA-based solution offers significant improvements in implementation simplicity and system stability. Experimental results demonstrate that the residual direct- and cross-term eddy current fields are reduced to below 0.02%, equivalent to 4 $\mathrm{\mu T}/m$, for a test gradient of 20 mT/m. Furthermore, the $B_0$ eddy field is suppressed to below 0.1 $\mathrm{\mu T}$ when a $B_0$ compensation coil is employed. These improvements effectively reduce ghosting artifacts in multi-slice gradient-echo (GRE) phantom images. The robustness of the method is further validated across various imaging sequences, including T1-weighted (T1w) and T2-weighted (T2w) protocols.