  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$\pm$1.0 dB over
SPIRiT and by 0.9$\pm$0.3 dB over PE-SSFP (mean$\pm$std across subjects;
average for N=2-8, R=8-16). Furthermore, reconstructions based on MLCC achieve
0.8$\pm$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.
