© 2020 Lippincott Williams and Wilkins. All rights reserved. Different types of noise from the surrounding always interfere with speech and produce annoying signals for the human auditory system. To exchange speech information in a noisy environment, speech quality and intelligibility must be maintained, which is a challenging task. In most speech enhancement algorithms, the speech signal is characterized by Gaussian or super-Gaussian models, and noise is characterized by a Gaussian prior. However, these assumptions do not always hold in real-life situations, thereby negatively affecting the estimation, and eventually, the performance of the enhancement algorithm. Accordingly, this paper focuses on deriving an optimum low-distortion estimator with models that fit well with speech and noise data signals. This estimator provides minimum levels of speech distortion and residual noise with additional improvements in speech perceptual aspects via four key steps. First, a recent transform based on an orthogonal polynomial is used to transform the observation signal into a transform domain. Second, the noise classification based on feature extraction is adopted to find accurate and mutable models for noise signals. Third, two stages of nonlinear and linear estimators based on the minimum mean square error (MMSE) and new models for speech and noise are derived to estimate a clean speech signal. Finally, the estimated speech signal in the time domain is determined by considering the inverse of the orthogonal transform. The results show that the average classification accuracy of the proposed approach is 99.43%. In addition, the proposed algorithm significantly outperforms existing speech estimators in terms of quality and intelligibility measures.