Approximate Message Passing for Underdetermined Audio Source Separation

Approximate message passing (AMP) algorithms have shown great promise in sparse signal reconstruction due to their low computational requirements and fast convergence to an exact solution. Moreover, they provide a probabilistic framework that is often more intuitive than alternatives such as convex optimisation. In this paper, AMP is used for audio source separation from underdetermined instantaneous mixtures. In the time-frequency domain, it is typical to assume a priori that the sources are sparse, so we solve the corresponding sparse linear inverse problem using AMP. We present a block-based approach that uses AMP to process multiple time-frequency points simultaneously. Two algorithms known as AMP and vector AMP (VAMP) are evaluated in particular. Results show that they are promising in terms of artefact suppression.Comment: Paper accepted for 3rd International Conference on Intelligent Signal Processing (ISP 2017

Sparse Estimation using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models

In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued models, this paper proposes a GSM model - the Bessel K model - that induces concave penalty functions for the estimation of complex sparse signals. The properties of the Bessel K model are analyzed when it is applied to Type I and Type II estimation. This analysis reveals that, by tuning the parameters of the mixing pdf different penalty functions are invoked depending on the estimation type used, the value of the noise variance, and whether real or complex signals are estimated. Using the Bessel K model, we derive a sparse estimator based on a modification of the expectation-maximization algorithm formulated for Type II estimation. The estimator includes as a special instance the algorithms proposed by Tipping and Faul [1] and by Babacan et al. [2]. Numerical results show the superiority of the proposed estimator over these state-of-the-art estimators in terms of convergence speed, sparseness, reconstruction error, and robustness in low and medium signal-to-noise ratio regimes.Comment: The paper provides a new comprehensive analysis of the theoretical foundations of the proposed estimators. Minor modification of the titl

A stochastic algorithm for probabilistic independent component analysis

The decomposition of a sample of images on a relevant subspace is a recurrent problem in many different fields from Computer Vision to medical image analysis. We propose in this paper a new learning principle and implementation of the generative decomposition model generally known as noisy ICA (for independent component analysis) based on the SAEM algorithm, which is a versatile stochastic approximation of the standard EM algorithm. We demonstrate the applicability of the method on a large range of decomposition models and illustrate the developments with experimental results on various data sets.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS499 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Random Finite Set Theory and Optimal Control of Large Collaborative Swarms

Controlling large swarms of robotic agents has many challenges including, but not limited to, computational complexity due to the number of agents, uncertainty in the functionality of each agent in the swarm, and uncertainty in the swarm's configuration. This work generalizes the swarm state using Random Finite Set (RFS) theory and solves the control problem using Model Predictive Control (MPC) to overcome the aforementioned challenges. Computationally efficient solutions are obtained via the Iterative Linear Quadratic Regulator (ILQR). Information divergence is used to define the distance between the swarm RFS and the desired swarm configuration. Then, a stochastic optimal control problem is formulated using a modified L2^2 distance. Simulation results using MPC and ILQR show that swarm intensities converge to a target destination, and the RFS control formulation can vary in the number of target destinations. ILQR also provides a more computationally efficient solution to the RFS swarm problem when compared to the MPC solution. Lastly, the RFS control solution is applied to a spacecraft relative motion problem showing the viability for this real-world scenario.Comment: arXiv admin note: text overlap with arXiv:1801.0731

High-Dimensional Regression with Gaussian Mixtures and Partially-Latent Response Variables

In this work we address the problem of approximating high-dimensional data with a low-dimensional representation. We make the following contributions. We propose an inverse regression method which exchanges the roles of input and response, such that the low-dimensional variable becomes the regressor, and which is tractable. We introduce a mixture of locally-linear probabilistic mapping model that starts with estimating the parameters of inverse regression, and follows with inferring closed-form solutions for the forward parameters of the high-dimensional regression problem of interest. Moreover, we introduce a partially-latent paradigm, such that the vector-valued response variable is composed of both observed and latent entries, thus being able to deal with data contaminated by experimental artifacts that cannot be explained with noise models. The proposed probabilistic formulation could be viewed as a latent-variable augmentation of regression. We devise expectation-maximization (EM) procedures based on a data augmentation strategy which facilitates the maximum-likelihood search over the model parameters. We propose two augmentation schemes and we describe in detail the associated EM inference procedures that may well be viewed as generalizations of a number of EM regression, dimension reduction, and factor analysis algorithms. The proposed framework is validated with both synthetic and real data. We provide experimental evidence that our method outperforms several existing regression techniques

Co-Localization of Audio Sources in Images Using Binaural Features and Locally-Linear Regression

This paper addresses the problem of localizing audio sources using binaural measurements. We propose a supervised formulation that simultaneously localizes multiple sources at different locations. The approach is intrinsically efficient because, contrary to prior work, it relies neither on source separation, nor on monaural segregation. The method starts with a training stage that establishes a locally-linear Gaussian regression model between the directional coordinates of all the sources and the auditory features extracted from binaural measurements. While fixed-length wide-spectrum sounds (white noise) are used for training to reliably estimate the model parameters, we show that the testing (localization) can be extended to variable-length sparse-spectrum sounds (such as speech), thus enabling a wide range of realistic applications. Indeed, we demonstrate that the method can be used for audio-visual fusion, namely to map speech signals onto images and hence to spatially align the audio and visual modalities, thus enabling to discriminate between speaking and non-speaking faces. We release a novel corpus of real-room recordings that allow quantitative evaluation of the co-localization method in the presence of one or two sound sources. Experiments demonstrate increased accuracy and speed relative to several state-of-the-art methods.Comment: 15 pages, 8 figure