K-Space Transformer for Fast MRIReconstruction with Implicit Representation

This paper considers the problem of fast MRI reconstruction. We propose a novel Transformer-based framework for directly processing the sparsely sampled signals in k-space, going beyond the limitation of regular grids as ConvNets do. We adopt an implicit representation of spectrogram, treating spatial coordinates as inputs, and dynamically query the partially observed measurements to complete the spectrogram, i.e. learning the inductive bias in k-space. To strive a balance between computational cost and reconstruction quality, we build an hierarchical structure with low-resolution and high-resolution decoders respectively. To validate the necessity of our proposed modules, we have conducted extensive experiments on two public datasets, and demonstrate superior or comparable performance over state-of-the-art approaches.