Using eigen-decomposition of a modified k-t SPIRiT operator, computationally optimized reconstruction formally translating into auto-calibrated SENSE-like reconstruction of a coil-combined x-f image (k-t ESPIRiT) is proposed. 2D and 3D in-vivo experiments show equivalence of k-t SPIRiT and k-t ESPIRiT, and significant reconstruction time speed-up's of the proposed relative to the standard technique.