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

<b>Background/Objectives:</b> 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. <b>Methods:</b> In this work, we propose a logarithmic scaled scheme for conventional loss functions (e.g., ℓ1, ℓ2) to enhance self-supervised MRI reconstruction. Standard self-supervised methods typically compute loss in the <i>k</i>-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. <b>Results:</b> Experiments on public datasets demonstrate consistent quantitative improvements when the proposed log-scaled loss is applied within a self-supervised MRI reconstruction framework. <b>Conclusions:</b> The proposed approach improves reconstruction fidelity and perceptual quality while remaining lightweight, architecture-agnostic, and readily integrable into existing self-supervised MRI reconstruction pipelines.