Multi-Channel Audio Completion Algorithm Based on Tensor Nuclear Norm

Multi-channel audio signals provide a better auditory sensation to the audience. However, missing data may occur in the collection, transmission, compression, or other processes of audio signals, resulting in audio quality degradation and affecting the auditory experience. As a result, the completeness of the audio signal has become a popular research topic in the field of signal processing. In this paper, the tensor nuclear norm is introduced into the audio signal completion algorithm, and the multi-channel audio signals with missing data are restored by using the completion algorithm based on the tensor nuclear norm. First of all, the multi-channel audio signals are preprocessed and are then transformed from the time domain to the frequency domain. Afterwards, the multi-channel audio with missing data is modeled to construct a third-order multi-channel audio tensor. In the next part, the tensor completion algorithm is used to complete the third-order tensor. The optimal solution of the convex optimization model of the tensor completion is obtained by using the convex relaxation technique and, ultimately, the data recovery of the multi-channel audio with data loss is accomplished. The experimental results of the tensor completion algorithm and the traditional matrix completion algorithm are compared using both objective and subjective indicators. The final result shows that the high-order tensor completion algorithm has a better completion ability and can restore the audio signal better.