Anatomically and biochemically guided deep image prior for sodium MRI denoising

Sodium (²³Na) magnetic resonance imaging (MRI) provides valuable metabolic information but is fundamentally limited by low signal-to-noise ratio (SNR) and long acquisition times. While classical and learning-based denoising methods such as NLM, BM3D, TV, and RD-DIP can produce visually plausible results, they may alter the underlying sodium signal distribution, potentially affecting structural fidelity and quantitative consistency. To address these challenges, we propose DIP-Fusion, a Deep Image Prior (DIP)-based framework for sodium MRI denoising that exploits complementary anatomical information from proton (¹H) MRI and biochemical information from ²³Na MRI via a novel fused proton-sodium prior within a directional total variation (dTV) regularization scheme. The framework optimizes a variational loss combining data fidelity, fused dTV regularization, gradient consistency, and bias-field correction to ensure stable denoising. We evaluate DIP-Fusion on healthy volunteers and breast cancer patients under multiple acquisition settings, comparing against classical denoising methods (NLM, BM3D, TV) and a recent deep learning-based Rician denoising approach (RD-DIP). Results demonstrate consistent improvements over all baselines. In healthy subjects, DIP-Fusion achieves PSNR gains of up to +2.36 dB and SSIM improvements of approximately 5%, with reduced perceptual error. In patient datasets, it further improves image quality, achieving PSNR gains of up to +3.35 dB while preserving sodium-specific signal characteristics. Under varying Rician noise levels, DIP-Fusion shows improved robustness compared to RD-DIP, maintaining higher denoising accuracy and structural fidelity, particularly in high-noise regimes. Overall, the proposed fusion-based prior stabilizes DIP optimization and enables more reliable sodium MRI denoising under challenging noise conditions.