<p>Seismic data are frequently contaminated by random noise, which masks or distorts weak reflection signals and reduces the reliability of seismic interpretation. The Cadzow filtering method, based on singular value decomposition (SVD), is a powerful technique for random noise attenuation; however, its effectiveness strongly depends on the correct selection of the number of effective singular values. Conventional approaches typically rely on empirical thresholds or trial-and-error strategies, which are subjective and may either retain excessive noise or suppress useful signal components. To address this limitation, we propose an adaptive Cadzow filtering method that incorporates mutual information theory to determine the number of effective singular values objectively. In the proposed workflow, seismic data are decomposed into multiple sub-gathers through short-time windowing and transformed into the frequency domain. For each frequency slice, a high-dimensional Hankel matrix is constructed and decomposed using SVD. Instead of manually selecting singular values, we calculate the mutual information difference spectrum between the reconstructed components and the original signal. Abrupt changes in this spectrum provide a reliable indicator for separating effective signal components from noise. Synthetic experiments demonstrate that the adaptive method not only achieves superior random noise suppression compared with the conventional Cadzow approach but also significantly improves denoising fidelity. Application to field seismic data from Sichuan, China further verifies that the proposed algorithm maintains the continuity of reflection axes in structurally complex regions while significantly improving the overall signal-to-noise ratio. These results confirm that adaptive SVD-Cadzow filtering offers a robust, data-driven solution for seismic noise attenuation.</p>