고유 특성을 활용한 음악에서의 보컬 분리

학위논문 (박사)-- 서울대학교 대학원 : 융합과학기술대학원 융합과학부, 2018. 2. 이교구.보컬 분리란 음악 신호를 보컬 성분과 반주 성분으로 분리하는 일 또는 그 방법을 의미한다. 이러한 기술은 음악의 특정한 성분에 담겨 있는 정보를 추출하기 위한 전처리 과정에서부터, 보컬 연습과 같이 분리 음원 자체를 활용하는 등의 다양한 목적으로 사용될 수 있다. 본 논문의 목적은 보컬과 반주가 가지고 있는 고유한 특성에 대해 논의하고 그것을 활용하여 보컬 분리 알고리즘들을 개발하는 것이며, 특히 `특징 기반' 이라고 불리는 다음과 같은 상황에 대해 중점적으로 논의한다. 우선 분리 대상이 되는 음악 신호는 단채널로 제공된다고 가정하며, 이 경우 신호의 공간적 정보를 활용할 수 있는 다채널 환경에 비해 더욱 어려운 환경이라고 볼 수 있다. 또한 기계 학습 방법으로 데이터로부터 각 음원의 모델을 추정하는 방법을 배제하며, 대신 저차원의 특성들로부터 모델을 유도하여 이를 목표 함수에 반영하는 방법을 시도한다. 마지막으로, 가사, 악보, 사용자의 안내 등과 같은 외부의 정보 역시 제공되지 않는다고 가정한다. 그러나 보컬 분리의 경우 암묵 음원 분리 문제와는 달리 분리하고자 하는 음원이 각각 보컬과 반주에 해당한다는 최소한의 정보는 제공되므로 각각의 성질들에 대한 분석은 가능하다. 크게 세 종류의 특성이 본 논문에서 중점적으로 논의된다. 우선 연속성의 경우 주파수 또는 시간 측면으로 각각 논의될 수 있는데, 주파수축 연속성의 경우 소리의 음색적 특성을, 시간축 연속성은 소리가 안정적으로 지속되는 정도를 각각 나타낸다고 볼 수 있다. 또한, 저행렬계수 특성은 신호의 구조적 성질을 반영하며 해당 신호가 낮은 행렬계수를 가지는 형태로 표현될 수 있는지를 나타내며, 성김 특성은 신호의 분포 형태가 얼마나 성기거나 조밀한지를 나타낸다. 본 논문에서는 크게 두 가지의 보컬 분리 방법에 대해 논의한다. 첫 번째 방법은 연속성과 성김 특성에 기반을 두고 화성 악기-타악기 분리 방법 (harmonic-percussive sound separation, HPSS) 을 확장하는 방법이다. 기존의 방법이 두 번의 HPSS 과정을 통해 보컬을 분리하는 것에 비해 제안하는 방법은 성긴 잔여 성분을 추가해 한 번의 보컬 분리 과정만을 사용한다. 논의되는 다른 방법은 저행렬계수 특성과 성김 특성을 활용하는 것으로, 반주가 저행렬계수 모델로 표현될 수 있는 반면 보컬은 성긴 분포를 가진다는 가정에 기반을 둔다. 이러한 성분들을 분리하기 위해 강인한 주성분 분석 (robust principal component analysis, RPCA) 을 이용하는 방법이 대표적이다. 본 논문에서는 보컬 분리 성능에 초점을 두고 RPCA 알고리즘을 일반화하거나 확장하는 방식에 대해 논의하며, 트레이스 노름과 l1 노름을 각각 샤텐 p 노름과 lp 노름으로 대체하는 방법, 스케일 압축 방법, 주파수 분포 특성을 반영하는 방법 등을 포함한다. 제안하는 알고리즘들은 다양한 데이터셋과 대회에서 평가되었으며 최신의 보컬 분리 알고리즘들보다 더 우수하거나 비슷한 결과를 보였다.Singing voice separation (SVS) refers to the task or the method of decomposing music signal into singing voice and its accompanying instruments. It has various uses, from the preprocessing step, to extract the musical features implied in the target source, to applications for itself such as vocal training. This thesis aims to discover the common properties of singing voice and accompaniment, and apply it to advance the state-of-the-art SVS algorithms. In particular, the separation approach as follows, which is named `characteristics-based,' is concentrated in this thesis. First, the music signal is assumed to be provided in monaural, or as a single-channel recording. It is more difficult condition compared to multiple-channel recording since spatial information cannot be applied in the separation procedure. This thesis also focuses on unsupervised approach, that does not use machine learning technique to estimate the source model from the training data. The models are instead derived based on the low-level characteristics and applied to the objective function. Finally, no external information such as lyrics, score, or user guide is provided. Unlike blind source separation problems, however, the classes of the target sources, singing voice and accompaniment, are known in SVS problem, and it allows to estimate those respective properties. Three different characteristics are primarily discussed in this thesis. Continuity, in the spectral or temporal dimension, refers the smoothness of the source in the particular aspect. The spectral continuity is related with the timbre, while the temporal continuity represents the stability of sounds. On the other hand, the low-rankness refers how the signal is well-structured and can be represented as a low-rank data, and the sparsity represents how rarely the sounds in signals occur in time and frequency. This thesis discusses two SVS approaches using above characteristics. First one is based on the continuity and sparsity, which extends the harmonic-percussive sound separation (HPSS). While the conventional algorithm separates singing voice by using a two-stage HPSS, the proposed one has a single stage procedure but with an additional sparse residual term in the objective function. Another SVS approach is based on the low-rankness and sparsity. Assuming that accompaniment can be represented as a low-rank model, whereas singing voice has a sparse distribution, conventional algorithm decomposes the sources by using robust principal component analysis (RPCA). In this thesis, generalization or extension of RPCA especially for SVS is discussed, including the use of Schatten p-/lp-norm, scale compression, and spectral distribution. The presented algorithms are evaluated using various datasets and challenges and achieved the better comparable results compared to the state-of-the-art algorithms.Chapter 1 Introduction 1 1.1 Motivation 4 1.2 Applications 5 1.3 Definitions and keywords 6 1.4 Evaluation criteria 7 1.5 Topics of interest 11 1.6 Outline of the thesis 13 Chapter 2 Background 15 2.1 Spectrogram-domain separation framework 15 2.2 Approaches for singing voice separation 19 2.2.1 Characteristics-based approach 20 2.2.2 Spatial approach 21 2.2.3 Machine learning-based approach 22 2.2.4 informed approach 23 2.3 Datasets and challenges 25 2.3.1 Datasets 25 2.3.2 Challenges 26 Chapter 3 Characteristics of music sources 28 3.1 Introduction 28 3.2 Spectral/temporal continuity 29 3.2.1 Continuity of a spectrogram 29 3.2.2 Continuity of musical sources 30 3.3 Low-rankness 31 3.3.1 Low-rankness of a spectrogram 31 3.3.2 Low-rankness of musical sources 33 3.4 Sparsity 34 3.4.1 Sparsity of a spectrogram 34 3.4.2 Sparsity of musical sources 36 3.5 Experiments 38 3.6 Summary 39 Chapter 4 Singing voice separation using continuity and sparsity 43 4.1 Introduction 43 4.2 SVS using two-stage HPSS 45 4.2.1 Harmonic-percussive sound separation 45 4.2.2 SVS using two-stage HPSS 46 4.3 Proposed algorithm 48 4.4 Experimental evaluation 52 4.4.1 MIR-1k Dataset 52 4.4.2 Beach boys Dataset 55 4.4.3 iKala dataset in MIREX 2014 56 4.5 Conclusion 58 Chapter 5 Singing voice separation using low-rankness and sparsity 61 5.1 Introduction 61 5.2 SVS using robust principal component analysis 63 5.2.1 Robust principal component analysis 63 5.2.2 Optimization for RPCA using augmented Lagrangian multiplier method 63 5.2.3 SVS using RPCA 65 5.3 SVS using generalized RPCA 67 5.3.1 Generalized RPCA using Schatten p- and lp-norm 67 5.3.2 Comparison of pRPCA with robust matrix completion 68 5.3.3 Optimization method of pRPCA 69 5.3.4 Discussion of the normalization factor for λ 69 5.3.5 Generalized RPCA using scale compression 71 5.3.6 Experimental results 72 5.4 SVS using RPCA and spectral distribution 73 5.4.1 RPCA with weighted l1-norm 73 5.4.2 Proposed method: SVS using wRPCA 74 5.4.3 Experimental results using DSD100 dataset 78 5.4.4 Comparison with state-of-the-arts in SiSEC 2016 79 5.4.5 Discussion 85 5.5 Summary 86 Chapter 6 Conclusion and Future Work 88 6.1 Conclusion 88 6.2 Contributions 89 6.3 Future work 91 6.3.1 Discovering various characteristics for SVS 91 6.3.2 Expanding to other SVS approaches 92 6.3.3 Applying the characteristics for deep learning models 92 Bibliography 94 초 록 110Docto

Statistical Approaches for Signal Processing with Application to Automatic Singer Identification

In the music world, the oldest instrument is known as the singing voice that plays an important role in musical recordings. The singer\u27s identity serves as a primary aid for people to organize, browse, and retrieve music recordings. In this thesis, we focus on the problem of singer identification based on the acoustic features of singing voice. An automatic singer identification system is constructed and has achieved a very high identification accuracy. This system consists of three crucial parts: singing voice detection, background music removal and pattern recognition. These parts are introduced and explored in great details in this thesis. To be specific, in terms of the singing voice detection, we firstly study a traditional method, double GMM. Then an improved method, namely single GMM, is proposed. The experimental result shows that the detection accuracy of single GMM can be achieved as high as 96.42%. In terms of the background music removal, Non-negative Matrix Factorization (NMF) and Robust Principal Component Analysis (RPCA) are demonstrated. The evaluation result shows that RPCA outperforms NMF. In terms of pattern recognition, we explore the algorithms of Support Vector Machine (SVM) and Gaussian Mixture Model (GMM). Based on the experimental results, it turns out that the prediction accuracy of GMM classifier is about 16% higher than SVM

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

Principled methods for mixtures processing

This document is my thesis for getting the habilitation à diriger des recherches, which is the french diploma that is required to fully supervise Ph.D. students. It summarizes the research I did in the last 15 years and also provides the short­term research directions and applications I want to investigate. Regarding my past research, I first describe the work I did on probabilistic audio modeling, including the separation of Gaussian and α­stable stochastic processes. Then, I mention my work on deep learning applied to audio, which rapidly turned into a large effort for community service. Finally, I present my contributions in machine learning, with some works on hardware compressed sensing and probabilistic generative models.My research programme involves a theoretical part that revolves around probabilistic machine learning, and an applied part that concerns the processing of time series arising in both audio and life sciences

Musical source separation with deep learning and large-scale datasets

Throughout this thesis we will explore automatic music source separation by utilizing modern (at the time of writing) techniques and tools from machine learning and big data processing. The bulk of this work was carried out between 2016 and 2019. In Chapter 2 we conduct a review of source separation literature. We start by outlining a subset of applications of source separation in some depth. We describe some of the early, pioneering work in automatic source separation: Auditory Scene Analysis, and its digital counterpart, Computational Auditory Scene Analysis. We then introduce matrix decomposition-based methods such as Independent Component Analysis and Non-Negative Matrix factorization, and pitch informed methods where the separation algorithm is guided by pitch information that is known a priori. We brie y discuss user-guided methods, before conducting a thorough review of Deep Learning based source separation, including recurrent, convolutional, deep clustering-based, and Generative Adversarial Networks. We then proceed to describe common evaluation metrics and training datasets. Finally, we list a number of current challenges and drawbacks of current systems. Chapter 3 focuses on datasets for musical source separation. First we show the growth of dataset sizes for both machine learning in general and music information retrieval specifically. We give several examples of the complexities and idiosyncrasies that are intrinsic to music datasets. We then proceed to present a method for extracting ground truth data for source separation from large unstructured musical catalogs. In Chapter 4 we design a novel deep learning-based source separation algorithm. Motivation is provided by means of a musicological study1 that showed the high importance of vocals relative to other musical factors, in the minds of listeners. At the core of the vocal separation algorithm is the U-Net, a deep learning architecture that uses skip connections to preserve fine-grained detail. It was originally developed in the biomedical imaging domain, and later adapted to image-to-image translation. We adapt it to the source separation domain by treating spectrograms as images, and we use the dataset mining methods from Chapter 3 to generate sufficiently large training data. We evaluate our model objectively using standard evaluation metrics, subjectively using \crowdsourced" human subjects. To the best of our knowledge, this is the first use of U-Nets for source separation. In the introduction above we proposed joint learning to optimize source separation and other objectives. In Chapter 5 we investigate one such instance: multi-task learning of vocal removal and vocal pitch tracking. We combine the vocal separation model from Chapter 4 with a state of the art pitch salience estimation model2, exploring several ways of combining the two models. We find that vocal pitch estimation benefits from joint learning when the two tasks are trained in sequence, with the source separation model preceding the pitch estimation model. We also report benefits from fine-tuning by iteratively applying the model. Chapter 6 extends the U-Net model to multiple instruments. In order to minimize the phase artifacts that were a common issue in Chapter 4, we modify the model to operate in the complex domain. We run experiments with several loss functions: Time-domain loss, magnitude-only frequency domain loss, and joint time and frequency-domain loss. Our experiments are evaluated both objectively and subjectively, and we carry out extensive qualitative analysis to investigate the effects of complex masking. Finally, we conclude the thesis in Chapter 7 by summarizing this work and highlighting several future directions of research

Semi-Supervised Suppression of Background Music in Monaural Speech Recordings

Projecte final de carrera fet en col.laboració amb TU München. Fakultät für Elektrotechnik und Informationstechnik.English: After a presentation of Non-Negative Matrix Factorization (NMF) and its applications in audio processing, we introduce a semi-supervised algorithm NMF based to improve separation of speech from background music in monaural signals. In this approach, fixed speech basis vectors are obtained from training data whereas music bases are estimated iteratively to cope with spectral variability. A small number of NMF components is used for decreased computation effort and most important NMF parameters are optimized, as the DFT window size used for transformation to the frequency domain. Extensive experimental validation with 168 speakers from the TIMIT database test set and four different music genres mixed at various speech-to-music ratios reveals that the semi-supervised method outperforms conventional supervised NMF for low speech-to-music ratios and low music bases, and that sparsity constraints on the music bases to enforce harmonicity can further improve separation performance depending on the music style.Castellano: Después de presentar la factorización de matrices no negativas (NMF) y sus aplicaciones en procesamiento de audio, introducimos un algoritmo semi-supervisado basado en NMF para mejorar la separación de la voz de la música de fondo en señales monoaurales. Con este método, los vectores base de la voz no cambian y se obtienen de datos de entrenamiento mientras que las bases de la música son estimadas iterativamente para aproximar su variabilidad espectral. Se usa un nombre pequeño de componentes de NMF para disminuir el coste computacional y los parámetros más importantes de NMF son optimizados, así como el tamaño de la ventana de la DFT usada para la transformación al dominio frecuencial. Una validación experimental extensiva con 168 hablantes de la base de datos TIMIT test set y 4 diferentes estilos musicales mezclados con diferentes relaciones voz-música revelan que el método semi-supervisado mejora el método convencional supervisado para relaciones voz-música bajas y pocas bases musicales, y que las restricciones de escasez en las bases de la música para forzar harmonicidad pueden mejorar todavía más los resultados de la separación dependiendo del estilo musical.Català: Després de presentar la factorització de matrius no negatives (NMF) i les seves aplicacions en processament d'àudio, introduïm un algoritme semi-supervisat basat en NMF per a millorar la separació de la veu de la música de fons en senyals monoaurals. Amb aquest mètode, els vectors base de la veu no varien i s'obtenen de dades d'entrenament mentre que les bases de la música son estimades iterativament per copsar la seva variabilitat espectral. S'usa un nombre petit de components de NMF per dismunuïr el cost computacional i els paràmetres més importants de NMF són optimitzats, així com el tamany de finestra de la DFT usat per la transformació al domini frequencial. Una validació experimental extensiva amb 168 parlants de la base de dades TIMIT test set i 4 estils musicals diferents mesclats amb diferents relacions veu-música revelen que el mètode semi-supervisat millora el mètode convencional supervisat per a relacions veu-música baixes i poques bases musicals, i que les restriccions d'escassetat a les bases de la música per forçar harmonicitat poden millorar encara més els resultats de la separació depenent de l'estil musical

An investigation of the utility of monaural sound source separation via nonnegative matrix factorization applied to acoustic echo and reverberation mitigation for hands-free telephony

In this thesis we investigate the applicability and utility of Monaural Sound Source Separation (MSSS) via Nonnegative Matrix Factorization (NMF) for various problems related to audio for hands-free telephony. We first investigate MSSS via NMF as an alternative acoustic echo reduction approach to existing approaches such as Acoustic Echo Cancellation (AEC). To this end, we present the single-channel acoustic echo problem as an MSSS problem, in which the objective is to extract the users signal from a mixture also containing acoustic echo and noise. To perform separation, NMF is used to decompose the near-end microphone signal onto the union of two nonnegative bases in the magnitude Short Time Fourier Transform domain. One of these bases is for the spectral energy of the acoustic echo signal, and is formed from the in- coming far-end user’s speech, while the other basis is for the spectral energy of the near-end speaker, and is trained with speech data a priori. In comparison to AEC, the speaker extraction approach obviates Double-Talk Detection (DTD), and is demonstrated to attain its maximal echo mitigation performance immediately upon initiation and to maintain that performance during and after room changes for similar computational requirements. Speaker extraction is also shown to introduce distortion of the near-end speech signal during double-talk, which is quantified by means of a speech distortion measure and compared to that of AEC. Subsequently, we address Double-Talk Detection (DTD) for block-based AEC algorithms. We propose a novel block-based DTD algorithm that uses the available signals and the estimate of the echo signal that is produced by NMF-based speaker extraction to compute a suitably normalized correlation-based decision variable, which is compared to a fixed threshold to decide on doubletalk. Using a standard evaluation technique, the proposed algorithm is shown to have comparable detection performance to an existing conventional block-based DTD algorithm. It is also demonstrated to inherit the room change insensitivity of speaker extraction, with the proposed DTD algorithm generating minimal false doubletalk indications upon initiation and in response to room changes in comparison to the existing conventional DTD. We also show that this property allows its paired AEC to converge at a rate close to the optimum. Another focus of this thesis is the problem of inverting a single measurement of a non- minimum phase Room Impulse Response (RIR). We describe the process by which percep- tually detrimental all-pass phase distortion arises in reverberant speech filtered by the inverse of the minimum phase component of the RIR; in short, such distortion arises from inverting the magnitude response of the high-Q maximum phase zeros of the RIR. We then propose two novel partial inversion schemes that precisely mitigate this distortion. One of these schemes employs NMF-based MSSS to separate the all-pass phase distortion from the target speech in the magnitude STFT domain, while the other approach modifies the inverse minimum phase filter such that the magnitude response of the maximum phase zeros of the RIR is not fully compensated. Subjective listening tests reveal that the proposed schemes generally produce better quality output speech than a comparable inversion technique

An investigation of the utility of monaural sound source separation via nonnegative matrix factorization applied to acoustic echo and reverberation mitigation for hands-free telephony

In this thesis we investigate the applicability and utility of Monaural Sound Source Separation (MSSS) via Nonnegative Matrix Factorization (NMF) for various problems related to audio for hands-free telephony. We first investigate MSSS via NMF as an alternative acoustic echo reduction approach to existing approaches such as Acoustic Echo Cancellation (AEC). To this end, we present the single-channel acoustic echo problem as an MSSS problem, in which the objective is to extract the users signal from a mixture also containing acoustic echo and noise. To perform separation, NMF is used to decompose the near-end microphone signal onto the union of two nonnegative bases in the magnitude Short Time Fourier Transform domain. One of these bases is for the spectral energy of the acoustic echo signal, and is formed from the in- coming far-end user’s speech, while the other basis is for the spectral energy of the near-end speaker, and is trained with speech data a priori. In comparison to AEC, the speaker extraction approach obviates Double-Talk Detection (DTD), and is demonstrated to attain its maximal echo mitigation performance immediately upon initiation and to maintain that performance during and after room changes for similar computational requirements. Speaker extraction is also shown to introduce distortion of the near-end speech signal during double-talk, which is quantified by means of a speech distortion measure and compared to that of AEC. Subsequently, we address Double-Talk Detection (DTD) for block-based AEC algorithms. We propose a novel block-based DTD algorithm that uses the available signals and the estimate of the echo signal that is produced by NMF-based speaker extraction to compute a suitably normalized correlation-based decision variable, which is compared to a fixed threshold to decide on doubletalk. Using a standard evaluation technique, the proposed algorithm is shown to have comparable detection performance to an existing conventional block-based DTD algorithm. It is also demonstrated to inherit the room change insensitivity of speaker extraction, with the proposed DTD algorithm generating minimal false doubletalk indications upon initiation and in response to room changes in comparison to the existing conventional DTD. We also show that this property allows its paired AEC to converge at a rate close to the optimum. Another focus of this thesis is the problem of inverting a single measurement of a non- minimum phase Room Impulse Response (RIR). We describe the process by which percep- tually detrimental all-pass phase distortion arises in reverberant speech filtered by the inverse of the minimum phase component of the RIR; in short, such distortion arises from inverting the magnitude response of the high-Q maximum phase zeros of the RIR. We then propose two novel partial inversion schemes that precisely mitigate this distortion. One of these schemes employs NMF-based MSSS to separate the all-pass phase distortion from the target speech in the magnitude STFT domain, while the other approach modifies the inverse minimum phase filter such that the magnitude response of the maximum phase zeros of the RIR is not fully compensated. Subjective listening tests reveal that the proposed schemes generally produce better quality output speech than a comparable inversion technique

Deep learning-based music source separation

Diese Dissertation befasst sich mit dem Problem der Trennung von Musikquellen durch den Einsatz von deep learning Methoden. Die auf deep learning basierende Trennung von Musikquellen wird unter drei Gesichtspunkten untersucht. Diese Perspektiven sind: die Signalverarbeitung, die neuronale Architektur und die Signaldarstellung. Aus der ersten Perspektive, soll verstanden werden, welche deep learning Modelle, die auf DNNs basieren, für die Aufgabe der Musikquellentrennung lernen, und ob es einen analogen Signalverarbeitungsoperator gibt, der die Funktionalität dieser Modelle charakterisiert. Zu diesem Zweck wird ein neuartiger Algorithmus vorgestellt. Der Algorithmus wird als NCA bezeichnet und destilliert ein optimiertes Trennungsmodell, das aus nicht-linearen Operatoren besteht, in einen einzigen linearen Operator, der leicht zu interpretieren ist. Aus der zweiten Perspektive, soll eine neuronale Netzarchitektur vorgeschlagen werden, die das zuvor erwähnte Konzept der Filterberechnung und -optimierung beinhaltet. Zu diesem Zweck wird die als Masker and Denoiser (MaD) bezeichnete neuronale Netzarchitektur vorgestellt. Die vorgeschlagene Architektur realisiert die Filteroperation unter Verwendung skip-filtering connections Verbindungen. Zusätzlich werden einige Inferenzstrategien und Optimierungsziele vorgeschlagen und diskutiert. Die Leistungsfähigkeit von MaD bei der Musikquellentrennung wird durch eine Reihe von Experimenten bewertet, die sowohl objektive als auch subjektive Bewertungsverfahren umfassen. Abschließend, der Schwerpunkt der dritten Perspektive liegt auf dem Einsatz von DNNs zum Erlernen von solchen Signaldarstellungen, für die Trennung von Musikquellen hilfreich sind. Zu diesem Zweck wird eine neue Methode vorgeschlagen. Die vorgeschlagene Methode verwendet ein neuartiges Umparametrisierungsschema und eine Kombination von Optimierungszielen. Die Umparametrisierung basiert sich auf sinusförmigen Funktionen, die interpretierbare DNN-Darstellungen fördern. Der durchgeführten Experimente deuten an, dass die vorgeschlagene Methode beim Erlernen interpretierbarer Darstellungen effizient eingesetzt werden kann, wobei der Filterprozess noch auf separate Musikquellen angewendet werden kann. Die Ergebnisse der durchgeführten Experimente deuten an, dass die vorgeschlagene Methode beim Erlernen interpretierbarer Darstellungen effizient eingesetzt werden kann, wobei der Filterprozess noch auf separate Musikquellen angewendet werden kann. Darüber hinaus der Einsatz von optimal transport (OT) Entfernungen als Optimierungsziele sind für die Berechnung additiver und klar strukturierter Signaldarstellungen.This thesis addresses the problem of music source separation using deep learning methods. The deep learning-based separation of music sources is examined from three angles. These angles are: the signal processing, the neural architecture, and the signal representation. From the first angle, it is aimed to understand what deep learning models, using deep neural networks (DNNs), learn for the task of music source separation, and if there is an analogous signal processing operator that characterizes the functionality of these models. To do so, a novel algorithm is presented. The algorithm, referred to as the neural couplings algorithm (NCA), distills an optimized separation model consisting of non-linear operators into a single linear operator that is easy to interpret. Using the NCA, it is shown that DNNs learn data-driven filters for singing voice separation, that can be assessed using signal processing. Moreover, by enabling DNNs to learn how to predict filters for source separation, DNNs capture the structure of the target source and learn robust filters. From the second angle, it is aimed to propose a neural network architecture that incorporates the aforementioned concept of filter prediction and optimization. For this purpose, the neural network architecture referred to as the Masker-and-Denoiser (MaD) is presented. The proposed architecture realizes the filtering operation using skip-filtering connections. Additionally, a few inference strategies and optimization objectives are proposed and discussed. The performance of MaD in music source separation is assessed by conducting a series of experiments that include both objective and subjective evaluation processes. Experimental results suggest that the MaD architecture, with some of the studied strategies, is applicable to realistic music recordings, and the MaD architecture has been considered one of the state-of-the-art approaches in the Signal Separation and Evaluation Campaign (SiSEC) 2018. Finally, the focus of the third angle is to employ DNNs for learning signal representations that are helpful for separating music sources. To that end, a new method is proposed using a novel re-parameterization scheme and a combination of optimization objectives. The re-parameterization is based on sinusoidal functions that promote interpretable DNN representations. Results from the conducted experimental procedure suggest that the proposed method can be efficiently employed in learning interpretable representations, where the filtering process can still be applied to separate music sources. Furthermore, the usage of optimal transport (OT) distances as optimization objectives is useful for computing additive and distinctly structured signal representations for various types of music sources