Deep-learning based motion-corrected image reconstruction in 4D magnetic resonance imaging of the body trunk

Respiratory and cardiac motion can cause artifacts in magnetic resonance imaging of the body trunk if patients cannot hold their breath or triggered acquisitions are not practical. Retrospective correction strategies usually cope with motion by fast imaging sequences with integrated motion tracking under free-movement conditions. These acquisitions perform sub-Nyquist sampling and retrospectively bin the data into the respective motion states, yielding subsampled and motionresolved k-space data. The motion-resolved k-spaces are linked to each other by non-rigid deformation fields. The accurate estimation of such motion is thus an important task in the successful correction of respiratory and cardiac motion. Usually this problem is formulated in image space via diffusion, parametric-spline or optical flow methods. Image-based registration can be however impaired by aliasing artifacts or by estimation from low-resolution images. Subsequently, any motion-corrected reconstruction can be biased by errors in the deformation fields. In this work, we propose a novel deep-learning based motion-corrected 4D (3D spatial + time) image reconstruction which combines a non-rigid registration network and a(3+1)D reconstruction network. Non-rigid motion is estimated directly in k-space based on an optical flow idea and incorporated into the reconstruction network. The proposed method is evaluated on in-vivo 4D motionresolved magnetic resonance images of patients with suspected liver or lung metastases and healthy subjects.