K-space Interpolation using Deep Koopman Autoencoders.

Motivation: Reconstruction of accelerated MRI acquisitions is crucial, particularly for parallel imaging, which is widely used in the clinic. Goal(s): To develop an interpretable neural network for the reconstruction of accelerated MRI data with reduced noise and improved image quality. Approach: A Deep Koopman autoencoder was developed with two non-linear layers for the encoder/decoder and a linear layer for interpolation in the latent space, and compared to GRAPPA and RAKI in two brain scans. Results: The approach results in improved qualitative and quantitative reconstruction results compared to GRAPPA. Compared to RAKI, visual inspection shows improved sharpness, albeit with a slightly higher residual noise. Impact: This work introduces an interpretable neural network for k-space interpolation, enabling good reconstruction quality and offering avenues for extensions to enable autoencoder-based scan-specific denoising.