This paper addresses the problem of feature compensation in the log-spectral domain by using the missing-data (MD) approach to noise robust speech recognition, that is, the log-spectral features can be either almost unaffected by noise or completely masked by it. First, a general MD framework based on minimum mean square error (MMSE) estimation is introduced which exploits the correlation across frequency bands to reconstruct the missing features. This framework allows the derivation of different MD imputation approaches and, in particular, a novel technique taking advantage of truncated Gaussian distributions is presented. While the proposed technique provides excellent results at high and medium signal-to-noise ratios (SNRs), its performance diminishes at low SNRs where very few reliable features are available. The reconstruction technique is therefore extended to exploit temporal constraints using two different approaches. In the first approach, time-frequency patches of speech containing a number of consecutive frames are modeled using a Gaussian mixture model (GMM). In the second one, the sequential structure of speech is alternatively modeled by a hidden Markov model (HMM). The proposed techniques are evaluated on Aurora-2 and Aurora-4 databases using both oracle and estimated masks. In both cases, the proposed techniques outperform the recognition performance obtained by the baseline system and other related techniques. Also, the introduction of a temporal modeling turns out to be very effective in reconstructing spectra at low SNRs. In particular, HMMs show the highest capability of accounting for time correlations and, therefore, achieve the best results.