The distortion-free diffusion and relaxometry images provided by echo-planar time resolved imaging (EPTI) ) represent a valuable acquisition strategy for mapping brain tissue microstructure. However, given the large under-sampling factor of EPTI acquisition and the intrinsically low SNR of diffusion MRI, an SNR-efficient reconstruction is vital. Subspace reconstruction can improve SNR efficiency by reducing the number of unknowns. In subspace reconstruction, the selection of bases strongly affects the reconstruction image fidelity, SNR, and computational efficiency. Here, we explore a new subspace-based EPTI reconstruction with magnitude-only bases and synergistic phase bias updating and demonstrate its performance for microstructural mapping.