# A joint linear reconstruction for multishot diffusion weighted non-Carr-Purcell-Meiboom-Gill fast spin echo with full signal

## Abstract

### Purpose

Diffusion weighted Fast Spin Echo (DW-FSE) is a promising approach for distortionless DW imaging that is robust to system imperfections such as eddy currents and off-resonance. Due to non-Carr-Purcell-Meiboom-Gill (CPMG) magnetization, most DW-FSE sequences discard a large fraction of the signal ($$\sqrt{2}-2\times$$), reducing signal-to-noise ratio (SNR) efficiency compared to DW-EPI. The full FSE signal can be preserved by quadratically incrementing the transmit phase of the refocusing pulses, but this method of resolving non-CPMG magnetization has only been applied to single-shot DW-FSE due to challenges associated with image reconstruction. We present a joint linear reconstruction for multishot quadratic phase increment data that addresses these challenges and corrects ghosting from both shot-to-shot phase and intrashot signal oscillations. Multishot imaging reduces T2 blur and joint reconstruction of shots improves g-factor performance. A thorough analysis on the condition number of the proposed linear system is described.

### Methods

A joint multishot reconstruction is derived from the non-CPMG signal model. Multishot quadratic phase increment DW-FSE was tested in a standardized diffusion phantom and compared to single-shot DW-FSE and DW-EPI in vivo in the brain, cervical spine, and prostate. The pseudo multiple replica technique was applied to generate g-factor and SNR maps.

### Results

The proposed joint shot reconstruction eliminates ghosting from shot-to-shot phase and intrashot oscillations. g-factor performance is improved compared to previously proposed reconstructions, permitting efficient multishot imaging. apparent diffusion coefficient estimates in phantom experiments and in vivo are comparable to those obtained with conventional methods.

### Conclusion

Multi-shot non-CPMG DW-FSE data with full signal can be jointly reconstructed using a linear model.