PhaseNet: Phase-Encode Denoising Network for Compressed Sensing MRI

Sparse reconstruction is an important aspect of modern medical imaging, reducing the acquisition time of relatively slow modalities such as magnetic resonance imaging (MRI). Popular methods are based mostly on compressed sensing (CS), which relies on the random sampling of Fourier coefficients ($k$-space) to produce incoherent (noise-like) artefacts that can be removed via convex optimisation. Hardware constraints currently limit Cartesian CS to one dimensional (1D) phase-encode undersampling schemes, leading to coherent and structured artefacts. Reconstruction algorithms typically deploy an idealised and limited 2D regularisation for artefact removal, which increases the difficulty of image recovery. Recognising that phase-encode artefacts can be separated into contiguous 1D signals, we develop two decoupling techniques that enable explicit 1D regularisation. We thereby leverage the excellent incoherence characteristics in the phase-encode direction. We also derive a combined 1D + 2D reconstruction technique that further takes advantage of spatial relationships within the image, leading to an improvement of existing 2D deep-learned (DL) recovery techniques. Performance is evaluated on a brain and knee dataset. We find the proposed 1D CNN modules significantly improve PSNR and SSIM scores compared to the base 2D models, demonstrating a superior scaling of performance compared to increasing the size of 2D network layers.