Autofocusing-Based Phase Correction

System instabilities and physiological motion such as breathing and cardiac pulsation can cause signal fluctuations in gradient-echo scans. In spin-warp imaging (standard Cartesian acquisition), different phase offsets for each line of k-space can lead to severe ghosting in the image domain. The severity of the phase fluctuation depends on the magnitude of the underlying magnetic fluctuation as well as on the time the phase has to evolve, that is, the echo time. Thus, this problem is more severe for higher field systems as well as for strongly T2*-weighted (long TE) scans.
In this work, we attempt to correct for constant phase errors in spin-warp imaging as well as for constant and linear phase errors in EPI by estimating the phase offsets directly from the raw image data using an autofocusing approach. Autofocusing (AF) methods belong to the class of retrospective reconstruction techniques, and are well-studied in the context of motion correction. Compared to the existing work on navigator-less phase error correction outlined above, our approach can be applied to a general case of phase distortions in each k-space line/partition. We tackle the phase correction problem with an optimization-based search of phase correction factors. Such search relies on an objective function with differentiable terms that is sensitive to the phase-related ghosting artifacts. We seek the latent phase offsets that are associated with an optimal value of the image quality measure that is evaluated in the spatial domain. This way we avoid the need for extra navigator scans and the related increase in sequence complexity and scan time. Furthermore, we propose and explore two distinct objective functions that can be used to correct for phase artifacts in the scans acquired with parallel imaging and acceleration. The experimental results demonstrate that our method is capable of minimizing the ghosting artifacts and that the quality of the output images is similar to navigator-based reconstructions.