Magnetic resonance images are often acquired as several 2D slices and stacked into a 3D volume, yielding a lower through-plane resolution than in-plane resolution. Many super-resolution (SR) methods have been proposed to address this, including those that use the inherent high-resolution (HR) in-plane signal as HR data to train deep neural networks. Techniques with this approach are generally both self-supervised and internally trained, so no external training data is required. However, in such a training paradigm limited data are present for training machine learning models and the frequency content of the in-plane data may be insufficient to capture the true HR image. In particular, the recovery of high frequency information is usually lacking. In this work, we show this shortcoming with Fourier analysis; we subsequently propose and compare several approaches to address the recovery of high frequency information. We test a particular internally trained self-supervised method named SMORE on ten subjects at three common clinical resolutions with three types of modification: frequency-type losses (Fourier and wavelet), feature-type losses, and low-resolution re-gridding strategies for estimating the residual. We find a particular combination to balance between signal recovery in both spatial and frequency domains qualitatively and quantitatively, yet none of the modifications alone or in tandem yield a vastly superior result. We postulate that there may either be limits on internally trained techniques that such modifications cannot address, or limits on modeling SR as finding a map from low-resolution to HR, or both.
Keywords: MRI; anisotropic; deep learning; self-supervised; super-resolution.