This paper considers the problem of undersampled MRI reconstruction. We propose a novel Transformer-based framework for directly processing signal in k-space, going beyond the limitation of regular grids as ConvNets do. As shown in the following figure, we adopt an implicit representation of k-sapce spectrogram, treating spatial coordinates as inputs, and dynamically query the sparsely sampled points to reconstruct the spectrogram, i.e. learning the inductive bias in k-space. To strike a balance between computational cost and reconstruction quality, we build the decoder with hierarchical structure to generate low-resolution and high-resolution outputs respectively. To validate the effectiveness of our proposed method, we have conducted extensive experiments on two public datasets, and demonstrate superior or comparable performance to state-of-the-art approaches.

Illustration of the proposed K-Space-Transformer. (a) The structure of Encoder. The goal of the Encoder is to compute a compact feature representation for the sampled frequency bins in k-space. (b) The structure of Decoder. The Decoder aims to reconstruct MRI by alternating completion in k-space and refinement in image domain. (c) The overall framework of the K-space Transformer. In practice, we adopt a hierarchical decoder to strive a balance between the computational cost and performance trade-off.

R1: Compared with baselines

Quantitative comparison with baselines on 1D sampling pattern

Quantitative comparison with baselines on 2D sampling pattern

Qualitative comparison of 5× acceleration on different sampling patterns. Brighter means higher error.

R2: Ablation Study

We remove the image domain refinement module (RM), and the LR decoder(LRD) sequentially on OASIS dataset to investigate the effectiveness of hybrid learning and the hierarchical structure.

R3: Analysis on intermedia results

We visualize some intermedia results of K-Space Transformer: LR denotes the reconstruction output of LR decoder; Upsampled denotes the up-sampled result of that; HR and HR(woRM) refer the output of HR decoder and that without refinement module

Based on a template by Phillip Isola and Richard Zhang.