Study On Multifactor Audio Signal Modeling And Applications Based On Tensor Analysis

With the increasing developments of Internet technology and multimedia technology, the analysis and processing of audio signal, which is as an important part of multimedia signal, has attracted more and more attention from the researchers. Tensor analysis, as a multilateral or multiple linear analysis tool, is widely used in recent years. Tensor analysis can handle the signals of multifactor, which include the signals norm of higher-order extension or the signals itself being multi-dimensional. In this paper, the tensor analysis method, as a multifactor analysis method, is introduced into modeling the multifactor audio signal and related application field. The three application problems are solved by using tensor analysis which can keep the structure information of audio data. The problems include higher-order features of audio signal modeling, audio classification of higher-order subspace analysis and recovering the missing data of multichannel audio signal. The author’s major contributions are outlined as follows:1. For modeling features of the audio signal, the traditional one and or dimensional modeling ways are extended. Higher-order features of audio are represented by tensors, which can reflect the physical meaning of the audio signal in different attribute subspace, and ensure the relationships between each subspace. Moreover, the underlying latent and distinguishable information of the structure can be excavated by tensor factorization. In the speech command recognition system of driverless Car, a 3-order tensor is constructed by frames, scales and feature parameters. In the audio classification system, a 3-order tensor is constructed by different attribute spaces including the acoustic feature space, the perceptual feature space and the psychological acoustic feature space. The audio feature set obtained from modeling and factorization by using tensor is advantageous to improve the accuracy of audio recognition and classification.2. For audio classification, a pattern recognition problem, non-negative tensor factorization technique, as a higher-order subspace analysis method, is creatively used for classifying audio signal. In supervised training, a non-negative tensor is represented audio signal. For ensuring the uniqueness of the factorization results, the non-negative tensor factorization is used to learn each type of audio signal, and the non-negative core tensor and factor matrix are obtained. In tests of audio classification, the test audio signals are mapped to each type of audio space by the non-negative factor matrix, and the similarity between the different types of audio core tensor and mapped results are obtained by the Frobenius norm. At last, Audio signals are classed. Compared with the traditional classifier, the nonlinear relationships in the structure of audio signal is not destroyed when non-negative tensor is factorizated, so our classifier outperforms traditional classifiers, and can perform classification with a higher accuracy in audio database.3. For recovering the missing data of multichannel audio signal, tensor factorization and tensor completion are used first time as methods of reconstructing data. In tensor factorization method, missing entries of audio signal is modeled by a third-order tensor and factorized, and the objective function of formulating missing data is minimized by weighed technique and alternative iteration. In tensor completion method, rank function minimization problem is transformed into the trace norm minimization problem by the definition of tensor trace norm and using convex relaxation technique; that is to say, the completion of nonconvex optimization problem is transformed into a convex optimization problem. The NP-hard problem will be solved. The missing data of multichannel audio signal will be completely recovered by simple completion based on the block coordinate descent algorithm and accurate completion based on alternating direction method of multipliers.