Recurrent Variational Network: A Deep Learning Inverse Problem Solver applied to the task of Accelerated MRI Reconstruction

Magnetic Resonance Imaging can produce detailed images of the anatomy and physiology of the human body that can assist doctors in diagnosing and treating pathologies such as tumours. However, MRI suffers from very long acquisition times that make it susceptible to patient motion artifacts and limit its potential to deliver dynamic treatments. Conventional approaches such as Parallel Imaging and Compressed Sensing allow for an increase in MRI acquisition speed by reconstructing MR images by acquiring less MRI data using multiple receiver coils. Recent advancements in Deep Learning combined with Parallel Imaging and Compressed Sensing techniques have the potential to produce high-fidelity reconstructions from highly accelerated MRI data. In this work we present a novel Deep Learning-based Inverse Problem solver applied to the task of accelerated MRI reconstruction, called Recurrent Variational Network (RecurrentVarNet) by exploiting the properties of Convolution Recurrent Networks and unrolled algorithms for solving Inverse Problems. The RecurrentVarNet consists of multiple blocks, each responsible for one unrolled iteration of the gradient descent optimization algorithm for solving inverse problems. Contrary to traditional approaches, the optimization steps are performed in the observation domain ($k$-space) instead of the image domain. Each recurrent block of RecurrentVarNet refines the observed $k$-space and is comprised of a data consistency term and a recurrent unit which takes as input a learned hidden state and the prediction of the previous block. Our proposed method achieves new state of the art qualitative and quantitative reconstruction results on 5-fold and 10-fold accelerated data from a public multi-channel brain dataset, outperforming previous conventional and deep learning-based approaches. We will release all models code and baselines on our public repository.