Research On Robust Reconstruction Technology For Speech Compressed Sensing

Compressed sensing is a new signal processing technology,which can compress signal while sampled signal,breaking the constraints of the traditional Nyquist sampling theorem.Its sampling frequency is much lower than the Nyquist sampling frequency,at the same time to achieve the signal compression,which greatly saves the sampling resources,transmission bandwidth and storage space.Compressed sensing mainly consists of three parts: the sparse representation of the signal,the construction of the observation matrix,and the design of reconstruction algorithm.The prerequisite of compressed sensing is that the signal is sparse,and because the speech signal is approximately sparse,so speech signal processing can employ compressed sensing.This thesis studies the combination of speech signal and compressed sensing,and focuses on the design of the robust reconstruction algorithm of speech compressed sensing.Because the robustness of the reconstruction algorithm is the key to whether compressed sensing technology can be applied.The main contents and innovations of this thesis are as follows:Firstly,this thesis introduces the theory of compressed sensing and the combination of speech signal and compressed sensing,and verifies the sparsity of the speech signal,and discusses the performance of the existing speech observation matrix and reconstruction algorithm.Then the effect of noise on each part of speech compressed sensing system is analyzed.Secondly,a new kind of fast reconstruction algorithm is presented,which is different from other algorithms.It makes the complexity of the reconstruction algorithm greatly reduce with the help of the characteristics of discrete cosine transform and deterministic observation matrix.However,it is found that the fast reconstruction algorithm has a poor anti-noise ability.Therefore,this thesis proposes an adaptive fast reconstruction algorithm,which adaptively selects the optimal reconstruction parameters based on the signal-to-noise ratio of the input speech signal.The simulation results show that the adaptive fast reconstruction algorithm has better anti-noise ability,improves the signal-to-noise ratio of the reconstructed speech signal and improves the reconstruction speed.Finally,the forward-backward pursuit algorithm is put forward and it is found that the forward and backward steps are fixed,which leads to the low reconstruction speed.Because in the process of reconstruction,the residual contains fewer and fewer signal components,so the iterative steps should be increased to speed up the reconstruction of the algorithm.Therefore,this thesis proposes a fast forward-backward pursuit algorithm,which dynamic adjusts the forward step according to the rate of change of residual,thus improves the reconstruction speed of the algorithm.The simulation results show that the FFBP algorithm has the same reconstructed signal-to-noise ratio as the FBP algorithm.However,the reconstruction speed of the FFBP algorithm is much faster than the FBP algorithm.