Complex-Valued Fourier Primal-Dual: Undersampled MRI Reconstruction in Hybrid-space

Iterative undersampled MRI reconstructions, such as compressed sensing, can reconstruct undersampled MRIs - but due to their slow execution speed, they are not suitable for real-time applications. Several deep learning approaches have been proposed, mostly working in image space. Some of the approaches, which work on the k-space or in a mix of spaces, employ real-valued convolutions splitting the complex k-space into real and imaginary parts for processing - destroying the geometric relationship within the data. This research proposes Fourier-PD and Fourier-PDUNet models using complex-valued convolutions, which attempt to predict missing k-space frequencies and also to reduce artefacts in the image space.