  Multi-modal Magnetic Resonance Imaging (MRI) offers complementary diagnostic
information, but some modalities are limited by the long scanning time. To
accelerate the whole acquisition process, MRI reconstruction of one modality
from highly undersampled k-space data with another fully-sampled reference
modality is an efficient solution. However, the misalignment between
modalities, which is common in clinic practice, can negatively affect
reconstruction quality. Existing deep learning-based methods that account for
inter-modality misalignment perform better, but still share two main common
limitations: (1) The spatial alignment task is not adaptively integrated with
the reconstruction process, resulting in insufficient complementarity between
the two tasks; (2) the entire framework has weak interpretability. In this
paper, we construct a novel Deep Unfolding Network with Spatial Alignment,
termed DUN-SA, to appropriately embed the spatial alignment task into the
reconstruction process. Concretely, we derive a novel joint
alignment-reconstruction model with a specially designed cross-modal spatial
alignment term. By relaxing the model into cross-modal spatial alignment and
multi-modal reconstruction tasks, we propose an effective algorithm to solve
this model alternatively. Then, we unfold the iterative steps of the proposed
algorithm and design corresponding network modules to build DUN-SA with
interpretability. Through end-to-end training, we effectively compensate for
spatial misalignment using only reconstruction loss, and utilize the
progressively aligned reference modality to provide inter-modality prior to
improve the reconstruction of the target modality. Comprehensive experiments on
three real datasets demonstrate that our method exhibits superior
reconstruction performance compared to state-of-the-art methods.
