Revisiting MRI Reconstruction Using a Combination of Complex and Magnitude Measurements with Learned Priors

MR image reconstruction techniques, from parallel imaging to compressed sensing to deep learning (DL), have been critical for reducing scan time with sub-sampled acquisitions. These methods have naturally all focused on complex-valued k -space measurements. On the other hand, theoretical results for sparse recovery have established that two random magnitude-only measurements, as in phase retrieval tasks, provide as much information as a single complex-valued measurement. However, these results have not translated into MRI reconstruction, as scenarios with magnitude-only measurements without access to corresponding complex data is unclear. In this work, with the advent of large-scale databases of raw data and physics-driven DL (PD-DL) tools, we revisit the idea of combining image reconstruction and phase retrieval for MRI. We first investigate the k -space magnitude similarity across cardiac phases in cine MRI over a database, and establish this as a potential application. Subsequently, we propose a magnitude-informed PD-DL framework (C+ Mag PD-DL), which jointly leverages complex-valued and auxiliary magnitude information with a novel data-fidelity (DF) term. Experiments demonstrate that the proposed approach improves image sharpness and reduced artifacts compared to conventional PD-DL methods, highlighting the potential of integrating magnitude of k -space measurements as auxiliary information for improving MRI reconstruction.