This paper introduces the use of Wave atom transformation as an efficient speech noise filter with Gaussian mixture models (GMM) for robust text-independent speaker identification. The individual Gaussian components of a GMM are shown to represent some general speaker identity. The focus of this work is on applications which require high robustness of noise and high identification rates using short utterance from noisy (Natural Noise) numerical speech and alphabetical words speech. A Full experimental evaluation of the Gaussian mixture speaker model is conducted on a 10 speakers. The experiments examine algorithmic issues (Preprocessing (Denoising by Wave Atom), Feature Extraction (MFCC), Training using GMM, Pattern Matching (Maximum likelihood estimation ML), Decision Rule (Expectation Maximization EM)). The Proposed algorithm attains 95% identification accuracy using 5 seconds noisy speech utterances without Wave atom preprocessing it attains 90% identification accuracy using 5 seconds noisy speech utterances. Proposed denoisy algorithm increases the identification ratio by 5% for noisy speech signals, this ratio is interesting enough.