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. 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. 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. We address the problem of blind audio source separation in the under-determined and convolutive case. The contribution of each source to the mixture channels in the time-frequency domain is modeled by a zero-mean Gaussian random vector with a full rank covariance matrix composed of two terms: a variance which represents the spectral properties of the source and which is modeled by a nonnegative matrix factorization (NMF) model and another full rank covariance matrix which encodes the spatial properties of the source contribution in the mixture. We address the estimation of these parameters by maximizing the likelihood of the mixture using an expectation-maximization (EM) algorithm. Theoretical propositions are corroborated by experimental studies on stereo reverberant music mixtures. 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. 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. 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. An unsupervised learning algorithm for the separation of sound sources in one-channel music signals is presented. The algorithm is based on factorizing the magnitude spectrogram of an input signal into a sum of components, each of which has a fixed magnitude spectrum and a time-varying gain. Each sound source, in turn, is modeled as a sum of one or more components. The parameters of the components are estimated by minimizing the reconstruction error between the input spectrogram and the model, while restricting the component spectrograms to be nonnegative and favoring components whose gains are slowly varying and sparse. Temporal continuity is favored by using a cost term which is the sum of squared differences between the gains in adjacent frames, and sparseness is favored by penalizing nonzero gains. The proposed iterative estimation algorithm is initialized with random values, and the gains and the spectra are then alternatively updated using multiplicative update rules until the values converge. Simulation experiments were carried out using generated mixtures of pitched musical instrument samples and drum sounds. The performance of the proposed method was compared with independent subspace analysis and basic nonnegative matrix factorization, which are based on the same linear model. According to these simulations, the proposed method enables a better separation quality than the previous algorithms. Especially, the temporal continuity criterion improved the detection of pitched musical sounds. The sparseness criterion did not produce significant improvements 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. In this work we present a system to automatically learn features from audio in an unsupervised manner. Our method first learns an overcomplete dictionary which can be used to sparsely decompose log-scaled spectrograms. It then trains an efficient encoder which quickly maps new inputs to approximations of their sparse representations using the learned dictionary. This avoids expensive iterative procedures usually required to infer sparse codes. We then use these sparse codes as inputs for a linear Support Vector Machine (SVM). Our system achieves 83.4 accuracy in predicting genres on the GTZAN dataset, which is competitive with current state-of-the-art approaches. Furthermore, the use of a simple linear classifier combined with a fast feature extraction system allows our approach to scale well to large datasets. In this work we investigate the applicability of unsupervised feature learning methods to the task of automatic genre prediction of music pieces. More specifically we evaluate a framework that recently has been successfully used to recognize objects in images. We first extract local patches from the time-frequency transformed audio signal, which are then pre-processed and used for unsupervised learning of an overcomplete dictionary of local features. For learning we either use a bootstrapped k-means clustering approach or select features randomly. We further extract feature responses in a convolutional manner and train a linear SVM for classification. We extensively evaluate the approach on the GTZAN dataset, emphasizing the influence of important design choices such as dimensionality reduction, pooling and patch dimension on the classification accuracy. We show that convolutional extraction of local feature responses is crucial to reach high performance. Furthermore we find that using this approach, simple and fast learning techniques such as k-means or randomly selected features are competitive with previously published results which also learn features from audio signals. 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 paper, we propose a semi-supervised algorithm based on sparse non-negative matrix factorization (NMF) to improve separation of speech from background music in monaural signals. In our approach, fixed speech basis vectors are obtained from training data whereas music bases are estimated on-the-fly to cope with spectral variability while preserving small NMF dimensionality for decreased computation effort. In a large-scale experimental evaluation with 168 speakers from the TIMIT database, we compare the semi-supervised method to supervised NMF with an explicit background music model. Our results reveal that the semi-supervised method outperforms supervised NMF at low speech-to-music ratios, and that sparsity constraints on the music spectra to enforce harmonicity can improve separation performance. To create systems that understand the sounds that humans are exposed to in everyday life, we need to represent sounds with features that can discriminate among many different sound classes. Here, we use a sound-ranking framework to quantitatively evaluate such representations in a large-scale task. We have adapted a machine-vision method, the passive-aggressive model for image retrieval (PAMIR), which efficiently learns a linear mapping from a very large sparse feature space to a large query-term space. Using this approach, we compare different auditory front ends and different ways of extracting sparse features from high-dimensional auditory images. We tested auditory models that use an adaptive pole--zero filter cascade (PZFC) auditory filter bank and sparse-code feature extraction from stabilized auditory images with multiple vector quantizers. In addition to auditory image models, we compare a family of more conventional mel-frequency cepstral coefficient (MFCC) front ends. The experimental results show a significant advantage for the auditory models over vector-quantized MFCCs. When thousands of sound files with a query vocabulary of thousands of words were ranked, the best precision at top-1 was 73 and the average precision was 35 , reflecting a 18 improvement over the best competing MFCC front end. Suppose a discrete-time signal S(t), 0 spl les t<N, is a superposition of atoms taken from a combined time-frequency dictionary made of spike sequences 1 sub t= spl tau and sinusoids exp 2 spl pi iwt N spl radic N. Can one recover, from knowledge of S alone, the precise collection of atoms going to make up S? Because every discrete-time signal can be represented as a superposition of spikes alone, or as a superposition of sinusoids alone, there is no unique way of writing S as a sum of spikes and sinusoids in general. We prove that if S is representable as a highly sparse superposition of atoms from this time-frequency dictionary, then there is only one such highly sparse representation of S, and it can be obtained by solving the convex optimization problem of minimizing the l sup 1 norm of the coefficients among all decompositions. Here "highly sparse" means that N sub t +N sub w < spl radic N 2 where N sub t is the number of time atoms, N sub w is the number of frequency atoms, and N is the length of the discrete-time signal. Underlying this result is a general l sup 1 uncertainty principle which says that if two bases are mutually incoherent, no nonzero signal can have a sparse representation in both bases simultaneously. For the above setting, the bases are sinusoids and spikes, and mutual incoherence is measured in terms of the largest inner product between different basis elements. The uncertainty principle holds for a variety of interesting basis pairs, not just sinusoids and spikes. The results have idealized applications to band-limited approximation with gross errors, to error-correcting encryption, and to separation of uncoordinated sources. Related phenomena hold for functions of a real variable, with basis pairs such as sinusoids and wavelets, and for functions of two variables, with basis pairs such as wavelets and ridgelets. In these settings, if a function f is representable by a sufficiently sparse superposition of terms taken from both bases, then there is only one such sparse representation; it may be obtained by minimum l sup 1 norm atomic decomposition. The condition "sufficiently sparse" becomes a multiscale condition; for example, that the number of wavelets at level j plus the number of sinusoids in the jth dyadic frequency band are together less than a constant times 2 sup j 2 . We systematically determined which spectrotemporal modulations in speech are necessary for comprehension by human listeners. Speech comprehension has been shown to be robust to spectral and temporal degradations, but the specific relevance of particular degradations is arguable due to the complexity of the joint spectral and temporal information in the speech signal. We applied a novel modulation filtering technique to recorded sentences to restrict acoustic information quantitatively and to obtain a joint spectrotemporal modulation transfer function for speech comprehension, the speech MTF. For American English, the speech MTF showed the criticality of low modulation frequencies in both time and frequency. Comprehension was significantly impaired when temporal modulations <12 Hz or spectral modulations <4 cycles kHz were removed. More specifically, the MTF was bandpass in temporal modulations and low-pass in spectral modulations: temporal modulations from 1 to 7 Hz and spectral modulations <1 cycles kHz were the most important. We evaluated the importance of spectrotemporal modulations for vocal gender identification and found a different region of interest: removing spectral modulations between 3 and 7 cycles kHz significantly increases gender misidentifications of female speakers. The determination of the speech MTF furnishes an additional method for producing speech signals with reduced bandwidth but high intelligibility. Such compression could be used for audio applications such as file compression or noise removal and for clinical applications such as signal processing for cochlear implants. Models for audio source separation usually operate on the magnitude spectrum, which ignores phase information and makes separation performance dependant on hyper-parameters for the spectral front-end. Therefore, we investigate end-to-end source separation in the time-domain, which allows modelling phase information and avoids fixed spectral transformations. Due to high sampling rates for audio, employing a long temporal input context on the sample level is difficult, but required for high quality separation results because of long-range temporal correlations. In this context, we propose the Wave-U-Net, an adaptation of the U-Net to the one-dimensional time domain, which repeatedly resamples feature maps to compute and combine features at different time scales. We introduce further architectural improvements, including an output layer that enforces source additivity, an upsampling technique and a context-aware prediction framework to reduce output artifacts. Experiments for singing voice separation indicate that our architecture yields a performance comparable to a state-of-the-art spectrogram-based U-Net architecture, given the same data. Finally, we reveal a problem with outliers in the currently used SDR evaluation metrics and suggest reporting rank-based statistics to alleviate this problem. 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. The objective of deep learning methods based on encoder-decoder architectures for music source separation is to approximate either ideal time-frequency masks or spectral representations of the target music source(s). The spectral representations are then used to derive time-frequency masks. In this work we introduce a method to directly learn time-frequency masks from an observed mixture magnitude spectrum. We employ recurrent neural networks and train them using prior knowledge only for the magnitude spectrum of the target source. To assess the performance of the proposed method, we focus on the task of singing voice separation. The results from an objective evaluation show that our proposed method provides comparable results to deep learning based methods which operate over complicated signal representations. Compared to previous methods that approximate time-frequency masks, our method has increased performance of signal to distortion ratio by an average of 3.8 dB.