Compared with high sample-rate speeches, low sample-rate speeches lose all high frequency components that outrange the Nyquist
frequency, which might severely impair the speeches’ sound effects. To address this problem, this paper proposes a novel High-frequency
(HF) restoration method of low sample-rate speech based on Bayesian inference, which turns the restoration problem into a
maximizing a posteriori estimation. With this method, the relation between high frequency components and low frequency components
is first extracted from the training set. The compatibility between neighboring audio frames is also modelled by a one dimensional
Markov Random Field. Then the extracted knowledge is adopted in reconstructing the original high sample-rate signal for the
testing low sample-rate audio. Experiments prove the applicability and effectiveness of this method.