# Reconstruction by Calibration over Tensors for Multi-Coil Multi-Acquisition Balanced SSFP Imaging

## TL;DR

This paper introduces ReCat, a tensor-based reconstruction method for multi-coil, multi-acquisition bSSFP imaging that improves image quality and computational efficiency over existing methods.

## Contribution

The paper proposes a novel reconstruction framework called ReCat and a multi-acquisition coil compression technique using MLCC, advancing rapid, high-quality bSSFP imaging.

## Key findings

- ReCat outperforms SPIRiT and PE-SSFP in SNR and image detail.
- MLCC improves computational efficiency over GCC.
- ReCat achieves high-quality, artifact-free images at higher acceleration factors.

## Abstract

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.