Considering the highly complex structure of quantum chaos and the nonstationary characteristics of speech signals, this paper proposes a quantum chaotic encryption and quantum particle swarm extraction method based on an underdetermined model. The proposed method first uses quantum chaos to encrypt the speech signal and then uses the local mean decomposition (LMD) method to construct a virtual receiving array and convert the underdetermined model to a positive definite model. Finally, the signal is extracted using the Levi flight strategy based on kurtosis and the quantum particle swarm optimization optimized by the greedy algorithm (KLG-QPSO). The bit error rate and similarity coefficient of the voice signal are extracted by testing the source voice signal SA1, SA2, and SI943 under different SNR, and the similarity coefficient, uncertainty, and disorder of the observed signal and the source voice signal SA1, SA2, and SI943 verify the effectiveness of the proposed speech signal extraction method and the security of quantum chaos used in speech signal encryption.
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