Bregman Wave Distribution Function Method

This study proposes a wave distribution function (WDF) estimation method based on minimizing the Bregman divergence in the function space. The proposed method is entirely data‐driven and requires no hyperparameter tuning during the estimation process. It can be regarded as an extension of the maximum entropy method. Whitening the spectral matrix was found to significantly enhance the estimation accuracy. By replacing the likelihood or loss function of the spectral matrix with its whitened counterpart, the estimated solutions were significantly improved. This method enables the precise estimation of WDFs from electromagnetic field observations, establishing a technical foundation for diagnosing space plasma environments and forecasting space weather. To address the uncertainty arising from the limited snapshots, we derive the posterior distribution of the spectral matrix. The Bregman divergence‐based framework ensures stable and interpretable estimation under both physical and statistical constraints. Numerical experiments confirmed that whitening markedly improved both accuracy and robustness in realistic random wave scenarios.