  Federated learning enables multiple hospitals to cooperatively learn a shared
model without privacy disclosure. Existing methods often take a common
assumption that the data from different hospitals have the same modalities.
However, such a setting is difficult to fully satisfy in practical
applications, since the imaging guidelines may be different between hospitals,
which makes the number of individuals with the same set of modalities limited.
To this end, we formulate this practical-yet-challenging cross-modal vertical
federated learning task, in which shape data from multiple hospitals have
different modalities with a small amount of multi-modality data collected from
the same individuals. To tackle such a situation, we develop a novel framework,
namely Federated Consistent Regularization constrained Feature Disentanglement
(Fed-CRFD), for boosting MRI reconstruction by effectively exploring the
overlapping samples (individuals with multi-modalities) and solving the domain
shift problem caused by different modalities. Particularly, our Fed-CRFD
involves an intra-client feature disentangle scheme to decouple data into
modality-invariant and modality-specific features, where the modality-invariant
features are leveraged to mitigate the domain shift problem. In addition, a
cross-client latent representation consistency constraint is proposed
specifically for the overlapping samples to further align the
modality-invariant features extracted from different modalities. Hence, our
method can fully exploit the multi-source data from hospitals while alleviating
the domain shift problem. Extensive experiments on two typical MRI datasets
demonstrate that our network clearly outperforms state-of-the-art MRI
reconstruction methods. The source code will be publicly released upon the
publication of this work.
