Logarithmic Scaling of Loss Functions for Enhanced Self-Supervised Accelerated MRI Reconstruction

Background/Objectives: Magnetic resonance imaging (MRI) is a widely used non-invasive imaging modality that provides high-fidelity soft-tissue contrast without ionizing radiation. However, acquiring high-resolution MRI scans is time-consuming, necessitating accelerated acquisition and reconstruction methods. Recently, self-supervised learning approaches have been introduced for reconstructing undersampled MRI data without external fully sampled ground truth. Methods: In this work, we propose a logarithmic scaled scheme for conventional loss functions (e.g., ${\ell }_1$, ${\ell }_2$) to enhance self-supervised MRI reconstruction. Standard self-supervised methods typically compute loss in the k-space domain, which tends to overemphasize low spatial frequencies while under-representing high-frequency information. Our method introduces a logarithmic scaling to adaptively rescale residuals, emphasizing high-frequency contributions and improving perceptual quality. Results: Experiments on public datasets demonstrate consistent quantitative improvements when the proposed log-scaled loss is applied within a self-supervised MRI reconstruction framework. Conclusions: The proposed approach improves reconstruction fidelity and perceptual quality while remaining lightweight, architecture-agnostic, and readily integrable into existing self-supervised MRI reconstruction pipelines.