The nonlinear relationship between missing and acquired data in k-space has been proved in nonlinear GRAPPA. In this work, we propose nonlinear SPIRiT which integrates the polynomial kernel method into SPIRiT via a simple second-order virtual coil approach. The proposed method represents the relationship between missing and acquired data in k-space of SPIRiT using a more accurate nonlinear model. In vivo results demonstrated that nonlinear SPIRiT could suppress aliasing artifact or noise better than SPIRiT, and was applicable to more acceleration scenarios than nonlinear GRAPPA.
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