In clinical practice, magnetic resonance imaging (MRI) with multiple contrasts is usually acquired in a single study to assess different properties of the same region of interest in human body. The whole acquisition process can be accelerated by having one or more modalities under-sampled in the $k$-space. Recent researches demonstrate that, considering the redundancy between different contrasts or modalities, a target MRI modality under-sampled in the $k$-space can be more efficiently reconstructed with a fully-sampled MRI contrast as the reference modality. However, we find that the performance of the above multi-modal reconstruction can be negatively affected by subtle spatial misalignment between different contrasts, which is actually common in clinical practice. In this paper, to compensate for such spatial misalignment, we integrate the spatial alignment network with multi-modal reconstruction towards better reconstruction quality of the target modality. First, the spatial alignment network estimates the spatial misalignment between the fully-sampled reference and the under-sampled target images, and warps the reference image accordingly. Then, the aligned fully-sampled reference image joins the multi-modal reconstruction of the under-sampled target image. Also, considering the contrast difference between the target and the reference images, we particularly design the cross-modality-synthesis-based registration loss, in combination with the reconstruction loss, to jointly train the spatial alignment network and the reconstruction network. Experiments on both clinical MRI and multi-coil $k$-space raw data demonstrate the superiority and robustness of multi-modal MRI reconstruction empowered with our spatial alignment network. Our code is publicly available at url{https://github.com/woxuankai/SpatialAlignmentNetwork}.
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