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This paper presents a framework for efficient HMM-based estimation of unreliable spectrographic speech data. It discusses the role of hidden Markov models (HMMs) during minimum mean-square error (MMSE) spectral reconstruction. We develop novel HMM-based reconstruction algorithms which exploit intra-channel (across-time) correlation and/or inter-channel (across-frequency) correlation. For the sake of computational efficiency, this paper utilizes approximations to HMM-based decoding methods by developing models constructed from lower resolution quantizers. State configurations for lower resolution models are obtained through a tree-structured mapping of quantizer centroids, and model parameters are adapted accordingly. HMM downsampling avoids expensive retraining of models, and eliminates unnecessary memory requirements. Explicit general formulae are presented for the adaptation of steady-state and transitional statistics. Adaptation of observation statistics are derived from stochastic models of noise spectral magnitude estimation accuracies. The proposed estimation methods are applied in combination with oracle masks, which provide an upper performance bound, as well as masks derived from speech presence probability, which represent a more realistic scenario. Both methods are shown to boost noise robust recognition accuracies significantly relative to the Mel-frequency cepstral coefficient (MFCC) baseline system. Furthermore, HMM downsampling greatly reduces the complexity of the HMM-based reconstruction method while negligibly affecting results.