Noise Level Estimation for Overcomplete Dictionary Learning Based on Tight Asymptotic Bounds

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In this letter, we address the problem of estimating Gaussian noise level from the trained dictionaries in update stage. We first provide rigorous statistical analysis on the eigenvalue distributions of a sample covariance matrix. Then we propose an interval-bounded estimator for noise variance in high dimensional setting. To this end, an effective estimation method for noise level is devised based on the boundness and asymptotic behavior of noise eigenvalue spectrum. The estimation performance of our method has been guaranteed both theoretically and empirically. The analysis and experiment results have demonstrated that the proposed algorithm can reliably infer true noise levels, and outperforms the relevant existing methods.