Motion‐robust reconstruction of multishot diffusion‐weighted images without phase estimation through locally low‐rank regularization

Purpose The goal of this work is to propose a motion robust reconstruction method for diffusion‐weighted MRI that resolves shot‐to‐shot phase mismatches without using phase estimation. Methods Assuming that shot‐to‐shot phase variations are slowly varying, spatial‐shot matrices can be formed using a local group of pixels to form columns, in which each column is from a different shot (excitation). A convex model with a locally low‐rank constraint on the spatial‐shot matrices is proposed. In vivo brain and breast experiments were performed to evaluate the performance of the proposed method. Results The proposed method shows significant benefits when the motion is severe, such as for breast imaging. Furthermore, the resulting images can be used for reliable phase estimation in the context of phase‐estimation‐based methods to achieve even higher image quality. Conclusion We introduced the shot–locally low‐rank method, a reconstruction technique for multishot diffusion‐weighted MRI without explicit phase estimation. In addition, its motion robustness can be beneficial to neuroimaging and body imaging.