We propose a novel method for the blind separation of audio signals produced by musical instruments. While the approach of applying non-negative matrix factorization (NMF) has been studied in many papers, it does not make use of the pitch-invariance that the sounds of instruments exhibit. This limitation can be overcome by using tensor factorization, in which context the use of log-frequency spectrograms was initiated, but this still requires the specific tuning of the instruments to be hard-coded into the algorithm. We develop a time-frequency representation that is both shift-invariant and frequency-aligned, with a variant that can also be used for wideband signals. Our separation algorithm exploits this shift-invariance in order to find patterns of peaks related to specific instruments, while non-linear optimization enables it to represent arbitrary frequencies and incorporate inharmonicity, and the reasonability of the representation is ensured by a sparsity condition. The relative amplitudes of the harmonics are saved in a dictionary, which is trained via a modified version of ADAM. For a realistic monaural piece with acoustic recorder and violin, we achieve qualitatively good separation with a signal-to-distortion ratio (SDR) of 12.5 dB, a signal-to-interference ratio (SIR) of 25.7 dB, and a signal-to-artifacts ratio (SAR) of 12.7 dB, averaged.
In order to apply dictionary learning on audio data, it is helpful to regard a time-frequency representation which subdivides the problem into smaller time frames and highlights the frequency characteristics of the signal. Classically, such a representation is computed via application of the short-time Fourier transform (STFT) (cf. @cite_8 ) on the audio signal, and the resulting spectrogram (i.e., the magnitude of the STFT) is then decomposed via non-negative matrix factorization (NMF) @cite_22 in order to obtain a dictionary. This approach was initially studied by Smaragdis and Brown @cite_19 for the purpose of polyphonic music transcription and then applied to audio source separation by Wang and Plumbley @cite_27 .
@cite_19 @cite_27 @cite_22 @cite_8
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We consider inference in a general data-driven object-based model of multichannel audio data, assumed generated as a possibly underdetermined convolutive mixture of source signals. We work in the short-time Fourier transform (STFT) domain, where convolution is routinely approximated as linear instantaneous mixing in each frequency band. Each source STFT is given a model inspired from nonnegative matrix factorization (NMF) with the Itakura-Saito divergence, which underlies a statistical model of superimposed Gaussian components. We address estimation of the mixing and source parameters using two methods. The first one consists of maximizing the exact joint likelihood of the multichannel data using an expectation-maximization (EM) algorithm. The second method consists of maximizing the sum of individual likelihoods of all channels using a multiplicative update algorithm inspired from NMF methodology. Our decomposition algorithms are applied to stereo audio source separation in various settings, covering blind and supervised separation, music and speech sources, synthetic instantaneous and convolutive mixtures, as well as professionally produced music recordings. Our EM method produces competitive results with respect to state-of-the-art as illustrated on two tasks from the international Signal Separation Evaluation Campaign (SiSEC 2008). Non-negative Matrix Factorisation (NMF) based algorithms have found application in monaural audio source separation due to their ability to factorize audio spectrogram into additive part-based basis functions, which typically corresponds to individual notes or chords in music. These separated basis functions are usually greater in number than the active sources, hence clustering is needed for individual source signal synthesis. Although, many attempts have been made to improve the clustering of the basis functions to sources, much research is still required in this area. Recently, Shifted NMF based methods have been proposed as a means to avoid clustering these pitched basis functions to sources. However, the Shifted NMF algorithm uses a log-frequency spectrogram with a xed number of frequency bins per octave which compromises the quality of separated sources.We show that by replacing the method used to calculate the log-frequency spectrogram with a recently proposed invertible Constant Q Transform (CQT), we can considerably improve the separation quality of the individual sound signals. In this paper, a signal is shown to be uniquely represented by the magnitude of its short-time Fourier transform (STFT) under mild restrictions on the signal and the analysis window of the STFT. Furthermore, various algorithms are developed which reconstruct signal from appropriate samples of the STFT magnitude. Several of the algorithms can also be used to obtain signal estimates from the processed STFT magnitude, which generally does not have a valid short-time structure. These algorithms are successfully applied to the time-scale modification and noise reduction problems in speech processing. Finally, the results presented here have similar potential for other application areas, including those with multidimensional signals. Non-negative Matrix Factorization (NMF) has found use in single channel separation of audio signals, as it gives a parts-based decomposition of audio spectrograms where the parts typically correspond to individual notes or chords. However, a notable shortcoming of NMF is the need to cluster the basis functions to their sources after decomposition. Despite recent improvements in algorithms for clustering the basis functions to sources, much work still remains to further improve these algorithms. To this end we present a novel clustering algorithm which overcomes some of the limitations of previous clustering methods. This involves the use of Shifted Nonnegative Matrix Factorization (SNMF) as a means of clustering the frequency basis functions obtained from NMF. Results show that this gives improved clustering of pitched basis functions over previous methods. Recent research in machine learning has focused on breaking audio spectrograms into separate sources of sound using latent variable decompositions. These methods require that the number of sources be specified in advance, which is not always possible. To address this problem, we develop Gamma Process Nonnegative Matrix Factorization (GaP-NMF), a Bayesian nonparametric approach to decomposing spectrograms. The assumptions behind GaP-NMF are based on research in signal processing regarding the expected distributions of spectrogram data, and GaP-NMF automatically discovers the number of latent sources. We derive a mean-field variational inference algorithm and evaluate GaP-NMF on both synthetic data and recorded music. Many if not most audio features used in MIR research are inspired by work done in speech recognition and are variations on the spectrogram. Recently, much attention has been given to new representations of audio that are sparse and time-relative. These representations are efficient and able to avoid the time-frequency trade-off of a spectrogram. Yet little work with music streams has been conducted and these features remain mostly unused in the MIR community. In this paper we further explore the use of these features for musical signals. In particular, we investigate their use on realistic music examples (i.e. released commercial music) and their use as input features for supervised learning. Furthermore, we identify three specific issues related to these features which will need to be further addressed in order to obtain the full benefit for MIR applications. The major time and frequency analysis methods that have been applied to music processing are traced and application areas described. Techniques are examined in the context of Cohen's class, facilitating comparison and the design of new approaches. A trumpet example illustrates most techniques. The impact of different analysis methods on pitch and timbre examination is shown. Analyses spanning Fourier series and transform, pitch synchronous analysis, heterodyne filter, short-time Fourier transform (STFT), phase vocoder, constant-Q and wavelet transforms, the Wigner (1932) distribution, and the modal distribution are all covered. The limitations of windowing methods and their reliance on steady-state assumptions and infinite duration sinusoids to define frequency and amplitude are detailed. The Wigner distribution, in contrast, uses the analytic signal to define instantaneous frequency and power parameters. The modal distribution is shown to be a linear transformation of the Wigner distribution optimized for estimating those parameters for a musical signal model. Application areas consider analysis, resynthesis, transcription, and visualization. The more stringent requirements for time-frequency (TF) distributions in these applications are compared with the weaker requirements found in speech analysis and highlight the need for further theoretical research. Deep neural network (DNN) have become a popular means of separating a target source from a mixed signal. Most of DNN-based methods modify only the magnitude spectrum of the mixture. The phase spectrum is left unchanged, which is inherent in the short-time Fourier transform (STFT) coefficients of the input signal. However, recent studies have revealed that incorporating phase information can improve the quality of separated sources. To estimate simultaneously the magnitude and the phase of STFT coefficients, this work paper developed a fully complex-valued deep neural network (FCDNN) that learns the nonlinear mapping from complex-valued STFT coefficients of a mixture to sources. In addition, to reinforce the sparsity of the estimated spectra, a sparse penalty term is incorporated into the objective function of the FCDNN. Finally, the proposed method is applied to singing source separation. Experimental results indicate that the proposed method outperforms the state-of-the-art DNN-based methods. In this paper, we propose an efficient sinusoidal model of polyphonic audio signals especially good for the application of timescale modification. One of the critical problem of sinusoidal modeling is that the signal is smeared during the synthesis frame, which is a very undesirable effect for transient parts. We solve this problem by introducing multiresolution analysis-synthesis and dynamic segmentation methods. A signal is modeled with a sinusoidal component and a noise component. A multiresolution filter bank is applied to an input signal which splits it into octave-spaced subbands without causing aliasing and then sinusoidal analysis is applied to each subband signal. To alleviate smearing of transients during synthesis, a dynamic segmentation method is applied to the subband signals that determines the optimal analysis-synthesis frame size adaptively to fit its time-frequency characteristics. To extract sinusoidal components and calculate respective parameters, a matching pursuit algorithm is applied to each analysis frame of the subband signal. A psychoacoustic model implementing frequency masking is incorporated with matching pursuit to provide a reasonable stop condition of iteration and reduce the number of sinusoids. The noise component obtained by subtracting the synthesized signal with sinusoidal components from the original signal is modeled by a line-segment model of short time spectrum envelope. For various polyphonic audio signals, the results of simulation shows the proposed sinusoidal modeling can synthesize original signals without loss of perceptual quality and do more robust and high-quality timescale modification for large scale factors. Content-based music information retrieval tasks have traditionally been solved using engineered features and shallow processing architectures. In recent years, there has been increasing interest in using feature learning and deep architectures instead, thus reducing the required engineering effort and the need for prior knowledge. However, this new approach typically still relies on mid-level representations of music audio, e.g. spectrograms, instead of raw audio signals. In this paper, we investigate whether it is possible to apply feature learning directly to raw audio signals. We train convolutional neural networks using both approaches and compare their performance on an automatic tagging task. Although they do not outperform a spectrogram-based approach, the networks are able to autonomously discover frequency decompositions from raw audio, as well as phase-and translation-invariant feature representations. Up to now, there has only been little work on using features from temporal approximations of signals for audio recognition. Time-frequency tradeoffs are an important issue in signal processing; sparse representations using overcomplete dictionaries may (or may not, depending on the dictionary) have more time-frequency flexibility than standard short-time Fourier transform. Also, the precise temporal structure of signals cannot be captured by spectral-based feature methods. Here, we present a biologically inspired three-step process for audio classification: 1) Efficient atomic functions are learned in an unsupervised manner on mixtures of percussion sounds (drum phrases), optimizing the length as well as the shape of the atoms. 2) An analog spike model is used to sparsely approximate percussion sound signals (bass drum, snare drum, hi-hat). The spike model consists of temporally shifted versions of the learned atomic functions, each having a precise temporal position and amplitude. To obtain the decomposition given a set of atomic functions, matching pursuit is used. 3) Features are extracted from the resulting spike representation of the signal. The classification accuracy of our method using a support vector machine (SVM) in a 3-class database transfer task is 87.8 . Using gammatone functions instead of the learned sparse functions yields an even better classification rate of 97.6 . Testing the features on sounds containing additive white Gaussian noise reveals that sparse approximation features are far more robust to such distortions than our benchmark feature set of timbre descriptor (TD) features. This paper proposes an end-to-end approach for single-channel speaker-independent multi-speaker speech separation, where time-frequency (T-F) masking, the short-time Fourier transform (STFT), and its inverse are represented as layers within a deep network. Previous approaches, rather than computing a loss on the reconstructed signal, used a surrogate loss based on the target STFT magnitudes. This ignores reconstruction error introduced by phase inconsistency. In our approach, the loss function is directly defined on the reconstructed signals, which are optimized for best separation. In addition, we train through unfolded iterations of a phase reconstruction algorithm, represented as a series of STFT and inverse STFT layers. While mask values are typically limited to lie between zero and one for approaches using the mixture phase for reconstruction, this limitation is less relevant if the estimated magnitudes are to be used together with phase reconstruction. We thus propose several novel activation functions for the output layer of the T-F masking, to allow mask values beyond one. On the publicly-available wsj0-2mix dataset, our approach achieves state-of-the-art 12.6 dB scale-invariant signal-to-distortion ratio (SI-SDR) and 13.1 dB SDR, revealing new possibilities for deep learning based phase reconstruction and representing a fundamental progress towards solving the notoriously-hard cocktail party problem. This paper addresses the problem of sound source separation from a multichannel microphone array capture via estimation of source spatial covariance matrix (SCM) of a short-time Fourier transformed mixture signal. In many conventional audio separation algorithms the source mixing parameter estimation is done separately for each frequency thus making them prone to errors and leading to suboptimal source estimates. In this paper we propose a SCM model which consists of a weighted sum of direction of arrival (DoA) kernels and estimate only the weights dependent on the source directions. In the proposed algorithm, the spatial properties of the sources become jointly optimized over all frequencies, leading to more coherent source estimates and mitigating the effect of spatial aliasing at high frequencies. The proposed SCM model is combined with a linear model for magnitudes and the parameter estimation is formulated in a complex-valued non-negative matrix factorization (CNMF) framework. Simulations consist of recordings done with a hand-held device sized array having multiple microphones embedded inside the device casing. Separation quality of the proposed algorithm is shown to exceed the performance of existing state of the art separation methods with two sources when evaluated by objective separation quality metrics. In this work, we introduce a new discriminative training method for nonnegative dictionary learning. The new method can be used in single channel source separation (SCSS) applications. In SCSS, nonnegative matrix factorization (NMF) is used to learn a dictionary (a set of basis vectors) for each source in the magnitude spectrum domain. The trained dictionaries are then used in decomposing the mixed signal to find the estimate for each source. Learning discriminative dictionaries for the source signals can improve the separation performance. To achieve discriminative dictionaries, we try to avoid the bases set of one source dictionary from representing the other source signals. We propose to minimize cross-coherence between the dictionaries of all sources in the mixed signal. We incorporate a simplified cross-coherence penalty using a regularized NMF cost function to simultaneously learn discriminative and reconstructive dictionaries. The new regularized NMF update rules that are used to discriminatively train the dictionaries are introduced in this work. Experimental results show that using discriminative training gives better separation results than using conventional NMF. Copyright © 2013 ISCA. Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ... We apply machine learning techniques to the problem of separating multiple speech sources from a single microphone recording. The method of choice is a sparse non-negative matrix factorization algorithm, which in an unsupervised manner can learn sparse representations of the data. This is applied to the learning of personalized dictionaries from a speech corpus, which in turn are used to separate the audio stream into its components. We show that computational savings can be achieved by segmenting the training data on a phoneme level. To split the data, a conventional speech recognizer is used. The performance of the unsupervised and supervised adaptation schemes result in significant improvements in terms of the target-to-masker ratio. Mallat's book is the undisputed reference in this field - it is the only one that covers the essential material in such breadth and depth. - Laurent Demanet, Stanford UniversityThe new edition of this classic book gives all the major concepts, techniques and applications of sparse representation, reflecting the key role the subject plays in today's signal processing. The book clearly presents the standard representations with Fourier, wavelet and time-frequency transforms, and the construction of orthogonal bases with fast algorithms. The central concept of sparsity is explained and applied to signal compression, noise reduction, and inverse problems, while coverage is given to sparse representations in redundant dictionaries, super-resolution and compressive sensing applications.Features:* Balances presentation of the mathematics with applications to signal processing* Algorithms and numerical examples are implemented in WaveLab, a MATLAB toolbox* Companion website for instructors and selected solutions and code available for studentsNew in this edition* Sparse signal representations in dictionaries* Compressive sensing, super-resolution and source separation* Geometric image processing with curvelets and bandlets* Wavelets for computer graphics with lifting on surfaces* Time-frequency audio processing and denoising* Image compression with JPEG-2000* New and updated exercisesA Wavelet Tour of Signal Processing: The Sparse Way, third edition, is an invaluable resource for researchers and R&D engineers wishing to apply the theory in fields such as image processing, video processing and compression, bio-sensing, medical imaging, machine vision and communications engineering.Stephane Mallat is Professor in Applied Mathematics at cole Polytechnique, Paris, France. From 1986 to 1996 he was a Professor at the Courant Institute of Mathematical Sciences at New York University, and between 2001 and 2007, he co-founded and became CEO of an image processing semiconductor company.Companion website: A Numerical Tour of Signal Processing Includes all the latest developments since the book was published in 1999, including itsapplication to JPEG 2000 and MPEG-4Algorithms and numerical examples are implemented in Wavelab, a MATLAB toolboxBalances presentation of the mathematics with applications to signal processing Mallat's book is the undisputed reference in this field - it is the only one that covers the essential material in such breadth and depth. - Laurent Demanet, Stanford University The new edition of this classic book gives all the major concepts, techniques and applications of sparse representation, reflecting the key role the subject plays in today's signal processing. The book clearly presents the standard representations with Fourier, wavelet and time-frequency transforms, and the construction of orthogonal bases with fast algorithms. The central concept of sparsity is explained and applied to signal compression, noise reduction, and inverse problems, while coverage is given to sparse representations in redundant dictionaries, super-resolution and compressive sensing applications. Features: * Balances presentation of the mathematics with applications to signal processing * Algorithms and numerical examples are implemented in WaveLab, a MATLAB toolbox * Companion website for instructors and selected solutions and code available for students New in this edition * Sparse signal representations in dictionaries * Compressive sensing, super-resolution and source separation * Geometric image processing with curvelets and bandlets * Wavelets for computer graphics with lifting on surfaces * Time-frequency audio processing and denoising * Image compression with JPEG-2000 * New and updated exercises A Wavelet Tour of Signal Processing: The Sparse Way, third edition, is an invaluable resource for researchers and R&D engineers wishing to apply the theory in fields such as image processing, video processing and compression, bio-sensing, medical imaging, machine vision and communications engineering. Stephane Mallat is Professor in Applied Mathematics at cole Polytechnique, Paris, France. From 1986 to 1996 he was a Professor at the Courant Institute of Mathematical Sciences at New York University, and between 2001 and 2007, he co-founded and became CEO of an image processing semiconductor company. Companion website: A Numerical Tour of Signal Processing * Includes all the latest developments since the book was published in 1999, including its application to JPEG 2000 and MPEG-4 * Algorithms and numerical examples are implemented in Wavelab, a MATLAB toolbox * Balances presentation of the mathematics with applications to signal processing Progress in solving the cocktail party problem, i.e., separating the speech from multiple overlapping speakers, has recently accelerated with the invention of techniques such as deep clustering and permutation free mask inference. These approaches typically focus on estimating target STFT magnitudes and ignore problems of phase inconsistency. In this paper, we explicitly integrate phase reconstruction into our separation algorithm using a loss function defined on time-domain signals. A deep neural network structure is defined by unfolding a phase reconstruction algorithm and treating each iteration as a layer in our network. Furthermore, instead of using fixed STFT iSTFT time-frequency representations, we allow our network to learn a modified version of these representations from data. We compare several variants of these unfolded phase reconstruction networks achieving state of the art results on the publicly available wsj0-2mix dataset, and show improved performance when the STFT iSTFT-like representations are allowed to adapt. Source separation techniques like independent component analysis and the more recent non-negative matrix factorization are gaining widespread use for the monaural separation of individual tracks present in a music sample. The underlying principle behind these approaches characterises only stationary signals and fails to separate nonstationary sources like speech or vocals. In this paper, we make an attempt to solve this problem and propose solutions to the extraction of vocal tracks from polyphonic audio recordings. We also present techniques to identify vocal sections in a music sample and design a classifier to perform a vocal–nonvocal segmentation task. Finally, we describe an application wherein we try to extract the melody from the separated vocal track using existing monophonic transcription techniques. The experimental work leads us to the conclusion that the quality of vocal source separation, albeit satisfactory, is not sufficient enough for further F0 analysis to extract the melody line from the vocal track. We identify areas that need further investigation to improve the quality of vocal source separation.