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In a highly noisy environment, bone-conducted speech seems to be more advantageous than normal noisy speech because of its stability against surrounding noise. The sound quality of bone-conducted speech, however, is very low and restoring bone-conducted speech is a challenging new topic in speech signal processing field. In this paper, we propose a restoration model based on linear prediction (LP). To evaluate the ability of the LP-based model to improve the voice quality, we compared it with existing models using one subjective and three objective measurements. The experiments showed that the LP-based model yields restored signals that are better for both human hearing and for the front-ends of automatic speech recognition systems. As the restoration ability of the LP-based model depended on a few parameters related to the LP coefficients of air-conducted speech, we applied a multi-layer perceptron neural network to blindly predict them with reasonable results.