Deep Neural Network-based source separation methods usually train independent models to optimize for the separation of individual sources. Although this can lead to good performance for well-defined targets, it can also be computationally expensive. The multitask alternative of a single network jointly optimizing for all targets simultaneously usually requires the availability of all target sources for each input. This requirement hampers the ability to create large training databases. In this paper, we present a model that decomposes the learnable parameters into a shared parametric model (encoder) and independent components (decoders) specific to each source. We propose an interleaved training procedure that optimizes the sub-task decoders independently and thus does not require each sample to possess a ground truth for all of its composing sources. Experimental results on MUSDB18 with the proposed method show comparable performance to independently trained models, with less trainable parameters, more efficient inference, and an encoder transferable to future target objectives. The results also show that using the proposed interleaved training procedure leads to better Source-to-Interference energy ratios when compared to the simultaneous optimization of all training objectives, even when all composing sources are available.
Considering a mixed signal composed of various audio sources and recorded with a single microphone, we consider on this paper the blind audio source separation problem which consists in isolating and extracting each of the sources. To perform this task, nonnegative matrix factorization (NMF) based on the Kullback-Leibler and Itakura-Saito $\beta$-divergences is a standard and state-of-the-art technique that uses the time-frequency representation of the signal. We present a new NMF model better suited for this task. It is based on the minimization of $\beta$-divergences along with a penalty term that promotes the columns of the dictionary matrix to have a small volume. Under some mild assumptions and in noiseless conditions, we prove that this model is provably able to identify the sources. In order to solve this problem, we propose multiplicative updates whose derivations are based on the standard majorization-minimization framework. We show on several numerical experiments that our new model is able to obtain more interpretable results than standard NMF models. Moreover, we show that it is able to recover the sources even when the number of sources present into the mixed signal is overestimated. In fact, our model automatically sets sources to zero in this situation, hence performs model order selection automatically.
Data-driven models for audio source separation such as U-Net or Wave-U-Net are usually models dedicated to and specifically trained for a single task, e.g. a particular instrument isolation. Training them for various tasks at once commonly results in worse performances than training them for a single specialized task. In this work, we introduce the Conditioned-U-Net (C-U-Net) which adds a control mechanism to the standard U-Net. The control mechanism allows us to train a unique and generic U-Net to perform the separation of various instruments. The C-U-Net decides the instrument to isolate according to a one-hot-encoding input vector. The input vector is embedded to obtain the parameters that control Feature-wise Linear Modulation (FiLM) layers. FiLM layers modify the U-Net feature maps in order to separate the desired instrument via affine transformations. The C-U-Net performs different instrument separations, all with a single model achieving the same performances as the dedicated ones at a lower cost.
In this paper, we propose a provably correct algorithm for convolutive nonnegative matrix factorization (CNMF) under separability assumptions. CNMF is a convolutive variant of nonnegative matrix factorization (NMF), which functions as an NMF with additional sequential structure. This model is useful in a number of applications, such as audio source separation and neural sequence identification. While a number of heuristic algorithms have been proposed to solve CNMF, to the best of our knowledge no provably correct algorithms have been developed. We present an algorithm that takes advantage of the NMF model underlying CNMF and exploits existing algorithms for separable NMF to provably find a solution under certain conditions. Our approach guarantees the solution in low noise settings, and runs in polynomial time. We illustrate its effectiveness on synthetic datasets, and on a singing bird audio sequence.
Generative adversarial networks (GANs) have shown great success in applications such as image generation and inpainting. However, they typically require large datasets, which are often not available, especially in the context of prediction tasks such as image segmentation that require labels. Therefore, methods such as the CycleGAN use more easily available unlabelled data, but do not offer a way to leverage additional labelled data for improved performance. To address this shortcoming, we show how to factorise the joint data distribution into a set of lower-dimensional distributions along with their dependencies. This allows splitting the discriminator in a GAN into multiple "sub-discriminators" that can be independently trained from incomplete observations. Their outputs can be combined to estimate the density ratio between the joint real and the generator distribution, which enables training generators as in the original GAN framework. We apply our method to image generation, image segmentation and audio source separation, and obtain improved performance over a standard GAN when additional incomplete training examples are available. For the Cityscapes segmentation task in particular, our method also improves accuracy by an absolute 14.9% over CycleGAN while using only 25 additional paired examples.
Nonnegative matrix factorization (NMF) is a linear dimensionality technique for nonnegative data with applications such as image analysis, text mining, audio source separation and hyperspectral unmixing. Given a data matrix $M$ and a factorization rank $r$, NMF looks for a nonnegative matrix $W$ with $r$ columns and a nonnegative matrix $H$ with $r$ rows such that $M \approx WH$. NMF is NP-hard to solve in general. However, it can be computed efficiently under the separability assumption which requires that the basis vectors appear as data points, that is, that there exists an index set $\mathcal{K}$ such that $W = M(:,\mathcal{K})$. In this paper, we generalize the separability assumption: We only require that for each rank-one factor $W(:,k)H(k,:)$ for $k=1,2,\dots,r$, either $W(:,k) = M(:,j)$ for some $j$ or $H(k,:) = M(i,:)$ for some $i$. We refer to the corresponding problem as generalized separable NMF (GS-NMF). We discuss some properties of GS-NMF and propose a convex optimization model which we solve using a fast gradient method. We also propose a heuristic algorithm inspired by the successive projection algorithm. To verify the effectiveness of our methods, we compare them with several state-of-the-art separable NMF algorithms on synthetic, document and image data sets.
Learning how objects sound from video is challenging, since they often heavily overlap in a single audio channel. Current methods for visually-guided audio source separation sidestep the issue by training with artificially mixed video clips, but this puts unwieldy restrictions on training data collection and may even prevent learning the properties of "true" mixed sounds. We introduce a co-separation training paradigm that permits learning object-level sounds from unlabeled multi-source videos. Our novel training objective requires that the deep neural network's separated audio for similar-looking objects be consistently identifiable, while simultaneously reproducing accurate video-level audio tracks for each source training pair. Our approach disentangles sounds in realistic test videos, even in cases where an object was not observed individually during training. We obtain state-of-the-art results on visually-guided audio source separation and audio denoising for the MUSIC, AudioSet, and AV-Bench datasets.
Modern audio source separation techniques rely on optimizing sequence model architectures such as, 1D-CNNs, on mixture recordings to generalize well to unseen mixtures. Specifically, recent focus is on time-domain based architectures such as Wave-U-Net which exploit temporal context by extracting multi-scale features. However, the optimality of the feature extraction process in these architectures has not been well investigated. In this paper, we examine and recommend critical architectural changes that forge an optimal multi-scale feature extraction process. To this end, we replace regular $1-$D convolutions with adaptive dilated convolutions that have innate capability of capturing increased context by using large temporal receptive fields. We also investigate the impact of dense connections on the extraction process that encourage feature reuse and better gradient flow. The dense connections between the downsampling and upsampling paths of a U-Net architecture capture multi-resolution information leading to improved temporal modelling. We evaluate the proposed approaches on the MUSDB test dataset. In addition to providing an improved performance over the state-of-the-art, we also provide insights on the impact of different architectural choices on complex data-driven solutions for source separation.
We study the use of the Wave-U-Net architecture for speech enhancement, a model introduced by Stoller et al for the separation of music vocals and accompaniment. This end-to-end learning method for audio source separation operates directly in the time domain, permitting the integrated modelling of phase information and being able to take large temporal contexts into account. Our experiments show that the proposed method improves several metrics, namely PESQ, CSIG, CBAK, COVL and SSNR, over the state-of-the-art with respect to the speech enhancement task on the Voice Bank corpus (VCTK) dataset. We find that a reduced number of hidden layers is sufficient for speech enhancement in comparison to the original system designed for singing voice separation in music. We see this initial result as an encouraging signal to further explore speech enhancement in the time-domain, both as an end in itself and as a pre-processing step to speech recognition systems.
Current performance evaluation for audio source separation depends on comparing the processed or separated signals with reference signals. Therefore, common performance evaluation toolkits are not applicable to real-world situations where the ground truth audio is unavailable. In this paper, we propose a performance evaluation technique that does not require reference signals in order to assess separation quality. The proposed technique uses a deep neural network (DNN) to map the processed audio into its quality score. Our experiment results show that the DNN is capable of predicting the sources-to-artifacts ratio from the blind source separation evaluation toolkit without the need for reference signals.
In this paper, we propose a source separation method that is trained by observing the mixtures and the class labels of the sources present in the mixture without any access to isolated sources. Since our method does not require source class labels for every time-frequency bin but only a single label for each source constituting the mixture signal, we call this scenario as weak class supervision. We associate a variational autoencoder (VAE) with each source class within a non-negative (compositional) model. Each VAE provides a prior model to identify the signal from its associated class in a sound mixture. After training the model on mixtures, we obtain a generative model for each source class and demonstrate our method on one-second mixtures of utterances of digits from 0 to 9. We show that the separation performance obtained by source class supervision is as good as the performance obtained by source signal supervision.
Gaussian process (GP) audio source separation is a time-domain approach that circumvents the inherent phase approximation issue of spectrogram based methods. Furthermore, through its kernel, GPs elegantly incorporate prior knowledge about the sources into the separation model. Despite these compelling advantages, the computational complexity of GP inference scales cubically with the number of audio samples. As a result, source separation GP models have been restricted to the analysis of short audio frames. We introduce an efficient application of GPs to time-domain audio source separation, without compromising performance. For this purpose, we used GP regression, together with spectral mixture kernels, and variational sparse GPs. We compared our method with LD-PSDTF (positive semi-definite tensor factorization), KL-NMF (Kullback-Leibler non-negative matrix factorization), and IS-NMF (Itakura-Saito NMF). Results show that the proposed method outperforms these techniques.
This paper deals with a multichannel audio source separation problem under underdetermined conditions. Multichannel Non-negative Matrix Factorization (MNMF) is one of powerful approaches, which adopts the NMF concept for source power spectrogram modeling. This concept is also employed in Independent Low-Rank Matrix Analysis (ILRMA), a special class of the MNMF framework formulated under determined conditions. While these methods work reasonably well for particular types of sound sources, one limitation is that they can fail to work for sources with spectrograms that do not comply with the NMF model. To address this limitation, an extension of ILRMA called the Multichannel Variational Autoencoder (MVAE) method was recently proposed, where a Conditional VAE (CVAE) is used instead of the NMF model for source power spectrogram modeling. This approach has shown to perform impressively in determined source separation tasks thanks to the representation power of DNNs. While the original MVAE method was formulated under determined mixing conditions, this paper generalizes it so that it can also deal with underdetermined cases. We call the proposed framework the Generalized MVAE (GMVAE). The proposed method was evaluated on a underdetermined source separation task of separating out three sources from two microphone inputs. Experimental results revealed that the GMVAE method achieved better performance than the MNMF method.
This paper proposes a novel framework for unsupervised audio source separation using a deep autoencoder. The characteristics of unknown source signals mixed in the mixed input is automatically by properly configured autoencoders implemented by a network with many layers, and separated by clustering the coefficient vectors in the code layer. By investigating the weight vectors to the final target, representation layer, the primitive components of the audio signals in the frequency domain are observed. By clustering the activation coefficients in the code layer, the previously unknown source signals are segregated. The original source sounds are then separated and reconstructed by using code vectors which belong to different clusters. The restored sounds are not perfect but yield promising results for the possibility in the success of many practical applications.
This work examines a semi-blind single-channel source separation problem. Our specific aim is to separate one source whose local structure is approximately known, from another a priori unspecified background source, given only a single linear combination of the two sources. We propose a separation technique based on local sparse approximations along the lines of recent efforts in sparse representations and dictionary learning. A key feature of our procedure is the online learning of dictionaries (using only the data itself) to sparsely model the background source, which facilitates its separation from the partially-known source. Our approach is applicable to source separation problems in various application domains; here, we demonstrate the performance of our proposed approach via simulation on a stylized audio source separation task.
In this report we describe an ongoing line of research for solving single-channel source separation problems. Many monaural signal decomposition techniques proposed in the literature operate on a feature space consisting of a time-frequency representation of the input data. A challenge faced by these approaches is to effectively exploit the temporal dependencies of the signals at scales larger than the duration of a time-frame. In this work we propose to tackle this problem by modeling the signals using a time-frequency representation with multiple temporal resolutions. The proposed representation consists of a pyramid of wavelet scattering operators, which generalizes Constant Q Transforms (CQT) with extra layers of convolution and complex modulus. We first show that learning standard models with this multi-resolution setting improves source separation results over fixed-resolution methods. As study case, we use Non-Negative Matrix Factorizations (NMF) that has been widely considered in many audio application. Then, we investigate the inclusion of the proposed multi-resolution setting into a discriminative training regime. We discuss several alternatives using different deep neural network architectures.
We augment the nonnegative matrix factorization method for audio source separation with cues about directionality of sound propagation. This improves separation quality greatly and removes the need for training data, with only a twofold increase in run time. This is the first method which can exploit directional information from microphone arrays much smaller than the wavelength of sound, working both in simulation and in practice on millimeter-scale microphone arrays.
This paper deals with the problem of audio source separation. To handle the complex and ill-posed nature of the problems of audio source separation, the current state-of-the-art approaches employ deep neural networks to obtain instrumental spectra from a mixture. In this study, we propose a novel network architecture that extends the recently developed densely connected convolutional network (DenseNet), which has shown excellent results on image classification tasks. To deal with the specific problem of audio source separation, an up-sampling layer, block skip connection and band-dedicated dense blocks are incorporated on top of DenseNet. The proposed approach takes advantage of long contextual information and outperforms state-of-the-art results on SiSEC 2016 competition by a large margin in terms of signal-to-distortion ratio. Moreover, the proposed architecture requires significantly fewer parameters and considerably less training time compared with other methods.
Audio source separation is the task of isolating sound sources that are active simultaneously in a room captured by a set of microphones. Convolutive audio source separation of equal number of sources and microphones has a number of shortcomings including the complexity of frequency-domain ICA, the permutation ambiguity and the problem's scalabity with increasing number of sensors. In this paper, the authors propose a multiple-microphone audio source separation algorithm based on a previous work of Mitianoudis and Davies (2003). Complex FastICA is substituted by Robust ICA increasing robustness and performance. Permutation ambiguity is solved using two methodologies. The first is using the Likelihood Ration Jump solution, which is now modified to decrease computational complexity in the case of multiple microphones. The application of the MuSIC algorithm, as a preprocessing step to the previous solution, forms a second methodology with promising results.
Directional or Circular statistics are pertaining to the analysis and interpretation of directions or rotations. In this work, a novel probability distribution is proposed to model multidimensional sparse directional data. The Generalised Directional Laplacian Distribution (DLD) is a hybrid between the Laplacian distribution and the von Mises-Fisher distribution. The distribution's parameters are estimated using Maximum-Likelihood Estimation over a set of training data points. Mixtures of Directional Laplacian Distributions (MDLD) are also introduced in order to model multiple concentrations of sparse directional data. The author explores the application of the derived DLD mixture model to cluster sound sources that exist in an underdetermined instantaneous sound mixture. The proposed model can solve the general K x L (K<L) underdetermined instantaneous source separation problem, offering a fast and stable solution.