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Purpose  To develop a rapid imaging framework for balanced steady‐state free precession (bSSFP) that jointly reconstructs undersampled data (by a factor of  R ) across multiple coils ( D ) and multiple acquisitions ( N ). To devise a multi‐acquisition coil compression technique for improved computational efficiency.    Methods  The bSSFP image for a given coil and acquisition is modeled to be modulated by a coil sensitivity and a bSSFP profile. The proposed reconstruction by calibration over tensors (ReCat) recovers missing data by tensor interpolation over the coil and acquisition dimensions. Coil compression is achieved using a new method based on multilinear singular value decomposition (MLCC). ReCat is compared with iterative self‐consistent parallel imaging (SPIRiT) and profile encoding (PE‐SSFP) reconstructions.    Results  Compared to parallel imaging or profile‐encoding methods, ReCat attains sensitive depiction of high‐spatial‐frequency information even at higher R. In the brain, ReCat improves peak SNR (PSNR) by 1.1 ± 1.0 dB over SPIRiT and by 0.9 ± 0.3 dB over PE‐SSFP (mean ± SD across subjects; average for  N  = 2–8,  R  = 8–16). Furthermore, reconstructions based on MLCC achieve 0.8 ± 0.6 dB higher PSNR compared to those based on geometric coil compression (GCC) (average for  N  = 2–8,  R  = 4–16).    Conclusion  ReCat is a promising acceleration framework for banding‐artifact‐free bSSFP imaging with high image quality; and MLCC offers improved computational efficiency for tensor‐based reconstructions. Magn Reson Med 79:2542–2554, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Reconstruction by calibration over tensors for multi‐coil multi‐acquisition balanced SSFP imaging