An effective way to increase noise robustness in automatic speech recognition (ASR) systems is feature enhancement based on an analytical distortion model that describes the effects of noise on the speech features. One of such distortion models that has been reported to achieve a good trade-off between accuracy and simplicity is the masking model. Under this model, speech distortion caused by environmental noise is seen as a spectral mask and, as a result, noisy speech features can be either reliable (speech is not masked by noise) or unreliable (speech is masked). In this paper, we present a detailed overview of this model and its applications to noise robust ASR. Firstly, using the masking model, we derive a spectral reconstruction technique aimed at enhancing the noisy speech features. Two problems must be solved in order to perform spectral reconstruction using the masking model: (1) mask estimation, i.e. determining the reliability of the noisy features, and (2) feature imputation, i.e. estimating speech for the unreliable features. Unlike missing data imputation techniques where the two problems are considered as independent, our technique jointly addresses them by exploiting a priori knowledge of the speech and noise sources in the form of a statistical model. Secondly, we propose an algorithm for estimating the noise model required by the feature enhancement technique. The proposed algorithm fits a Gaussian mixture model to the noise by iteratively maximising the likelihood of the noisy speech signal so that noise can be estimated even during speech-dominating frames. A comprehensive set of experiments carried out on the Aurora-2 and Aurora-4 databases shows that the proposed method achieves significant improvements over the baseline system and other similar missing data imputation techniques.