  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.
