NMF-based compositional models for audio source separation

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2017. 2. 김남수.Many classes of data can be represented by constructive combinations of parts. Most signal and data from nature have nonnegative values and can be explained and reconstructed by constructive models. By the constructive models, only the additive combination is allowed and it does not result in subtraction of parts. The compositional models include dictionary learning, exemplar-based approaches, and nonnegative matrix factorization (NMF). Compositional models are desirable in many areas including image or visual signal processing, text information processing, audio signal processing, and music information retrieval. In this dissertation, we choose NMF for compositional models and NMF-based target source separation is performed for the application. The target source separation is the extraction or reconstruction of the target signals in the mixture signals which consists with the target and interfering signals. The target source separation can be thought as blind source separation (BSS). BSS aims that the original unknown source signals are extracted without knowing or with very limited information. However, in these days, much of prior information is frequently utilized, and various approaches have been proposed for single channel source separation. NMF basically approximates a nonnegative data matrix V with a product of nonnegative basis and encoding matrices W and H, i.e., V WH. Since both W and H are nonnegative, NMF often leads to a part based representation of the data. The methods based on NMF have shown impressive results in single channel source separation The objective function of NMF is generally presented Euclidean distant, Kullback-Leibler divergence, and Itakura-saito divergence. Many optimization methods have been proposed and utilized, e.g., multiplicative update rule, projected gradient descent and NeNMF. However, NMF-based audio source separation has some issues as follows: non-uniqueness of the bases, a high dependence to the prior information, the overlapped subspace between target bases and interfering bases, a disregard of the encoding vectors from the training phase, and insucient analysis of sparse NMF. In this dissertation, we propose new approaches to resolve the above issues. In section 4, we propose a novel speech enhancement method that combines the statistical model-based enhancement scheme with the NMF-based gain function. For a better performance in time-varying noise environments, both the speech and noise bases of NMF are adapted simultaneously with the help of the estimated speech presence probability. In section 5, we propose a discriminative NMF (DNMF) algorithm which exploits the reconstruction error for the interfering signals as well as the target signal based on target bases. In section 6, we propose an approach to robust bases estimation in which an incremental strategy is adopted. Based on an analogy between clustering and NMF analysis, we incrementally estimate the NMF bases similar to the modied k-means and Linde-Buzo-Gray algorithms popular in the data clustering area. In Section 7, the distribution of the encoding vector is modeled as a multivariate exponential PDF (MVE) with a single scaling factor for each source. In Section 8, several sparse penalty terms for NMF are analyzed and compared in terms of signal to distortion ratio, sparseness of encoding vectors, reconstruction error, and entropy of basis vectors. The new objective function which applied sparse representation and discriminative NMF (DNMF) is also proposed.1 Introduction 1 1.1 Audio source separation 1 1.2 Speech enhancement 3 1.3 Measurements 4 1.4 Outline of the dissertation 6 2 Compositional model and NMF 9 2.1 Compositional model 9 2.2 NMF 14 2.2.1 Update rules: MuR, PGD 16 2.2.2 Modied NMF 20 3 NMF-based audio source separation and issues 23 3.1 NMF-based audio source separation 23 3.2 Problems of NMF in audio source separation 26 3.2.1 A high dependency to the prior knowledge 26 3.2.2 A overlapped subspace between the target and interfering basis matrices 28 3.2.3 A non-uniqueness of the bases 29 3.2.4 A prior knowledge of the encoding vectors 30 3.2.5 Sparse NMF for the source separation 32 4 Online bases update 33 4.1 Introduction 33 4.2 NMF-based speech enhancement using spectral gain function 36 4.3 Speech enhancement combining statistical model-based and NMFbased methods with the on-line bases update 38 4.3.1 On-line update of speech and noise bases 40 4.3.2 Determining maximum update rates 42 4.4 Experiment result 43 5 Discriminative NMF 47 5.1 Introduction 47 5.2 Discriminative NMF utilizing cross reconstruction error 48 5.2.1 DNMF using the reconstruction error of the other source 49 5.2.2 DNMF using the interference factors 50 5.3 Experiment result 52 6 Incremental approach for bases estimate 57 6.1 Introduction 57 6.2 Incremental approach based on modied k-means clustering and Linde-Buzo-Gray algorithm 59 6.2.1 Based on modied k-means clustering 59 6.2.2 LBG based incremental approach 62 6.3 Experiment result 63 6.3.1 Modied k-means clustering based approach 63 6.3.2 LBG based approach 66 7 Prior model of encoding vectors 77 7.1 Introduction 77 7.2 Prior model of encoding vectors based on multivariate exponential distribution 78 7.3 Experiment result 82 8 Conclusions 87 Bibliography 91 국문초록 105Docto

Audio source separation for music in low-latency and high-latency scenarios

Aquesta tesi proposa mètodes per tractar les limitacions de les tècniques existents de separació de fonts musicals en condicions de baixa i alta latència. En primer lloc, ens centrem en els mètodes amb un baix cost computacional i baixa latència. Proposem l'ús de la regularització de Tikhonov com a mètode de descomposició de l'espectre en el context de baixa latència. El comparem amb les tècniques existents en tasques d'estimació i seguiment dels tons, que són passos crucials en molts mètodes de separació. A continuació utilitzem i avaluem el mètode de descomposició de l'espectre en tasques de separació de veu cantada, baix i percussió. En segon lloc, proposem diversos mètodes d'alta latència que milloren la separació de la veu cantada, gràcies al modelatge de components específics, com la respiració i les consonants. Finalment, explorem l'ús de correlacions temporals i anotacions manuals per millorar la separació dels instruments de percussió i dels senyals musicals polifònics complexes.Esta tesis propone métodos para tratar las limitaciones de las técnicas existentes de separación de fuentes musicales en condiciones de baja y alta latencia. En primer lugar, nos centramos en los métodos con un bajo coste computacional y baja latencia. Proponemos el uso de la regularización de Tikhonov como método de descomposición del espectro en el contexto de baja latencia. Lo comparamos con las técnicas existentes en tareas de estimación y seguimiento de los tonos, que son pasos cruciales en muchos métodos de separación. A continuación utilizamos y evaluamos el método de descomposición del espectro en tareas de separación de voz cantada, bajo y percusión. En segundo lugar, proponemos varios métodos de alta latencia que mejoran la separación de la voz cantada, gracias al modelado de componentes que a menudo no se toman en cuenta, como la respiración y las consonantes. Finalmente, exploramos el uso de correlaciones temporales y anotaciones manuales para mejorar la separación de los instrumentos de percusión y señales musicales polifónicas complejas.This thesis proposes specific methods to address the limitations of current music source separation methods in low-latency and high-latency scenarios. First, we focus on methods with low computational cost and low latency. We propose the use of Tikhonov regularization as a method for spectrum decomposition in the low-latency context. We compare it to existing techniques in pitch estimation and tracking tasks, crucial steps in many separation methods. We then use the proposed spectrum decomposition method in low-latency separation tasks targeting singing voice, bass and drums. Second, we propose several high-latency methods that improve the separation of singing voice by modeling components that are often not accounted for, such as breathiness and consonants. Finally, we explore using temporal correlations and human annotations to enhance the separation of drums and complex polyphonic music signals

Time-Frequency Analysis as Probabilistic Inference

This is the final published version. It was originally published by IEEE at http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6918491.This paper proposes a new view of time-frequency analysis framed in terms of probabilistic inference. Natural signals are assumed to be formed by the superposition of distinct time-frequency components, with the analytic goal being to infer these components by application of Bayes' rule. The framework serves to unify various existing models for natural time-series; it relates to both the Wiener and Kalman filters, and with suitable assumptions yields inferential interpretations of the short-time Fourier transform, spectrogram, filter bank, and wavelet representations. Value is gained by placing time-frequency analysis on the same probabilistic basis as is often employed in applications such as denoising, source separation, or recognition. Uncertainty in the time-frequency representation can be propagated correctly to application-specific stages, improving the handing of noise and missing data. Probabilistic learning allows modules to be co-adapted; thus, the time-frequency representation can be adapted to both the demands of the application and the time-varying statistics of the signal at hand. Similarly, the application module can be adapted to fine properties of the signal propagated by the initial time-frequency processing. We demonstrate these benefits by combining probabilistic time-frequency representations with non-negative matrix factorization, finding benefits in audio denoising and inpainting tasks, albeit with higher computational cost than incurred by the standard approach.Funding was provided by EPSRC (grant numbers EP/G050821/1 and EP/L000776/1) and Google (R.E.T.) and by the Gatsby Charitable Foundation (M.S.)

Single channel audio separation using deep neural networks and matrix factorizations

PhD ThesisSource Separation has become a significant research topic in the signal processing community and the machine learning area. Due to numerous applications, such as automatic speech recognition and speech communication, separation of target speech from the mixed signal is of great importance. In many practical applications, speech separation from a single recorder is most desirable from an application standpoint. In this thesis, two novel approaches have been proposed to address this single channel audio separation problem. This thesis first reviews traditional approaches for single channel source separation, and later elicits a generic approach, which is more capable of feature learning, i.e. deep graphical models. In the first part of this thesis, a novel approach based on matrix factorization and hierarchical model has been proposed. In this work, an artificial stereo mixture is formulated to provide extra information. In addition, a hybrid framework that combines the generalized Expectation-Maximization algorithm with a multiplicative update rule is proposed to optimize the parameters of a matrix factorization based approach to approximatively separate the mixture. Furthermore, a hierarchical model based on an extreme learning machine is developed to check the validity of the approximately separated sources followed by an energy minimization method to further improve the quality of the separated sources by generating a time-frequency mask. Various experiments have been conducted and the obtained results have shown that the proposed approach outperforms conventional approaches not only in reduction of computational complexity, but also the separation performance. In the second part, a deep neural network based ensemble system is proposed. In this work, the complementary property of different features are fully explored by ‘wide’ and ‘forward’ ensemble system. In addition, instead of using the features learned from the output layer, the features learned from the penultimate layer are investigated. The final embedded features are classified with an extreme learning machine to generate a binary mask to separate a mixed signal. The experiment focuses on speech in the presence of music and the obtained results demonstrated that the proposed ensemble system has the ability to explore the complementary property of various features thoroughly under various conditions with promising separation performance

Algoritmos de procesado de señal basados en Non-negative Matrix Factorization aplicados a la separación, detección y clasificación de sibilancias en señales de audio respiratorias monocanal

La auscultación es el primer examen clínico que un médico lleva a cabo para evaluar el estado del sistema respiratorio, debido a que es un método no invasivo, de bajo coste, fácil de realizar y seguro para el paciente. Sin embargo, el diagnóstico que se deriva de la auscultación sigue siendo un diagnóstico subjetivo que se encuentra condicionado a la habilidad, experiencia y entrenamiento de cada médico en la escucha e interpretación de las señales de audio respiratorias. En consecuencia, se producen un alto porcentaje de diagnósticos erróneos que ponen en riesgo la salud de los pacientes e incrementan el coste asociado a los centros de salud. Esta Tesis propone nuevos métodos basados en Non-negative Matrix Factorization aplicados a la separación, detección y clasificación de sonidos sibilantes para proporcionar una vía de información complementaria al médico que ayude a mejorar la fiabilidad del diagnóstico emitido por el especialista. Auscultation is the first clinical examination that a physician performs to evaluate the condition of the respiratory system, because it is a non-invasive, low-cost, easy-to-perform and safe method for the patient. However, the diagnosis derived from auscultation remains a subjective diagnosis that is conditioned by the ability, experience and training of each physician in the listening and interpretation of respiratory audio signals. As a result, a high percentage of misdiagnoses are produced that endanger the health of patients and increase the cost associated with health centres. This Thesis proposes new methods based on Non-negative Matrix Factorization applied to separation, detection and classification of wheezing sounds in order to provide a complementary information pathway to the physician that helps to improve the reliability of the diagnosis made by the doctor.Tesis Univ. Jaén. Departamento INGENIERÍA DE TELECOMUNICACIÓ

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Efficient and Robust Methods for Audio and Video Signal Analysis

This thesis presents my research concerning audio and video signal processing and machine learning. Specifically, the topics of my research include computationally efficient classifier compounds, automatic speech recognition (ASR), music dereverberation, video cut point detection and video classification.Computational efficacy of information retrieval based on multiple measurement modalities has been considered in this thesis. Specifically, a cascade processing framework, including a training algorithm to set its parameters has been developed for combining multiple detectors or binary classifiers in computationally efficient way. The developed cascade processing framework has been applied on video information retrieval tasks of video cut point detection and video classification. The results in video classification, compared to others found in the literature, indicate that the developed framework is capable of both accurate and computationally efficient classification. The idea of cascade processing has been additionally adapted for the ASR task. A procedure for combining multiple speech state likelihood estimation methods within an ASR framework in cascaded manner has been developed. The results obtained clearly show that without impairing the transcription accuracy the computational load of ASR can be reduced using the cascaded speech state likelihood estimation process.Additionally, this thesis presents my work on noise robustness of ASR using a nonnegative matrix factorization (NMF) -based approach. Specifically, methods for transformation of sparse NMF-features into speech state likelihoods has been explored. The results reveal that learned transformations from NMF activations to speech state likelihoods provide better ASR transcription accuracy than dictionary label -based transformations. The results, compared to others in a noisy speech recognition -challenge show that NMF-based processing is an efficient strategy for noise robustness in ASR.The thesis also presents my work on audio signal enhancement, specifically, on removing the detrimental effect of reverberation from music audio. In the work, a linear prediction -based dereverberation algorithm, which has originally been developed for speech signal enhancement, was applied for music. The results obtained show that the algorithm performs well in conjunction with music signals and indicate that dynamic compression of music does not impair the dereverberation performance