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Purpose  To develop an ESPIRiT‐based method to estimate coil sensitivities with image phase as a building block for efficient and robust image reconstruction with phase constraints.    Theory and Methods  ESPIRiT is a new framework for calibration of the coil sensitivities and reconstruction in parallel magnetic resonance imaging. Applying ESPIRiT to a combined set of physical and virtual conjugate coils (VCC‐ESPIRiT) implicitly exploits conjugate symmetry in k‐space similar to VCC‐GRAPPA. Based on this method, a new post‐processing step is proposed for the explicit computation of coil sensitivities that include the absolute phase of the image. The accuracy of the computed maps is directly validated using a test based on projection onto fully sampled coil images and also indirectly in phase‐constrained parallel‐imaging reconstructions.    Results  The proposed method can estimate accurate sensitivities which include low‐resolution image phase. In case of high‐frequency phase variations VCC‐ESPIRiT yields an additional set of maps that indicates the existence of a high‐frequency phase component. Taking this additional set of maps into account can improve the robustness of phase‐constrained parallel imaging.    Conclusion  The extended VCC‐ESPIRiT is a useful tool for phase‐constrained imaging. Magn Reson Med 77:1201–1207, 2017. © 2016 International Society for Magnetic Resonance in Medicine

Estimating absolute‐phase maps using ESPIRiT and virtual conjugate coils