LAPNet: Non-rigid Registration derived in k-space for Magnetic Resonance Imaging

Physiological motion, such as cardiac and respiratory motion, during Magnetic Resonance (MR) image acquisition can cause image artifacts. Motion correction techniques have been proposed to compensate for these types of motion during thoracic scans, relying on accurate motion estimation from undersampled motion-resolved reconstruction. A particular interest and challenge lie in the derivation of reliable non-rigid motion fields from the undersampled motion-resolved data. Motion estimation is usually formulated in image space via diffusion, parametric-spline, or optical flow methods. However, image-based registration can be impaired by remaining aliasing artifacts due to the undersampled motion-resolved reconstruction. In this work, we describe a formalism to perform non-rigid registration directly in the sampled Fourier space, i.e. k-space. We propose a deep-learning based approach to perform fast and accurate non-rigid registration from the undersampled k-space data. The basic working principle originates from the Local All-Pass (LAP) technique, a recently introduced optical flow-based registration. The proposed LAPNet is compared against traditional and deep learning image-based registrations and tested on fully-sampled and highly-accelerated (with two undersampling strategies) 3D respiratory motion-resolved MR images in a cohort of 40 patients with suspected liver or lung metastases and 25 healthy subjects. The proposed LAPNet provided consistent and superior performance to image-based approaches throughout different sampling trajectories and acceleration factors.