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A speech enhancement algorithm that takes advantage of the time and frequency dependencies of speech signals is presented in this paper. The above dependencies are incorporated in the statistical model using concepts from the theory of Markov Random Fields. In particular, the speech short-time Fourier transform (STFT) amplitude samples are modeled with a novel Chi Markov Random Field prior, which is then used for the development of an estimator based on the Iterated Conditional Modes method. The novel prior is also coupled with a dasiaharmonicpsila neighborhood, which apart from the immediately adjacent samples on the time frequency plane, also considers samples which are one pitch frequency apart, so as to take advantage of the rich structure of the voiced speech time frames. Additionally, central to the development of the algorithm is the adaptive estimation of the weights that determine the interaction between neighboring samples, which allows the restoration of weak speech spectral components, while maintaining a low level of uniform residual noise. Results that illustrate the improvements achieved with the proposed algorithm, and a comparison with other established speech enhancement schemes are also given.