<p>Accurate discrimination and identification of underwater magnetic targets rely heavily on high-fidelity magnetic anomaly data. However, in practical geophysical surveys, magnetic signals are often corrupted by low signal-to-noise ratios (SNR) and complex background interference, which limits the performance of conventional end-to-end deep learning denoising methods. This paper proposes an Iterative U-Net framework designed for progressive magnetic data denoising and signal recovery. Unlike traditional one-step mapping, the proposed architecture decomposes the complex denoising task into multiple successive sub-tasks through a weight-sharing iterative structure. By incorporating residual learning, the model predicts and attenuates the remaining noise at each stage, achieving a coarse-to-fine refinement of the magnetic anomalies. Furthermore, to balance denoising performance with computational efficiency, a dynamic early-stopping strategy based on residual energy is introduced. This mechanism allows the model to adaptively determine the optimal iteration depth according to the convergence state of the data, ensuring stable and detail-preserving results across varying noise levels. Experimental results on both synthetic and field-measured magnetic datasets demonstrate that the Iterative U-Net significantly outperforms state-of-the-art methods in suppressing non-stationary noise while preserving the subtle features of small-scale magnetic targets.</p>