A general algebraic algorithm for blind extraction of one source in a MIMO convolutive mixture

International audienceThe paper deals with the problem of blind source extraction from a MIMO convolutive mixture. We define a new criterion for source extraction which uses higher-order contrast functions based on so called reference signals. It generalizes existing reference-based contrasts. In order to optimize the new criterion, we propose a general algebraic algorithm based on best rank-1 tensor approximation. Computer simulations illustrate the good behavior and the interest of our algorithm in comparison with other approaches

Generalized identifiability conditions for blind convolutive MIMO separation

International audienceThis paper deals with the problem of source separation in the case where the output of a multivariate convolutive mixture is observed: we propose novel and generalized conditions for the blind identifiability of a separating system. The results are based on higher-order statistics and are valid in the case of stationary but not necessarily i.i.d. signals. In particular, we extend recent results based on second-order statistics only. The approach relies on the use of so called reference signals. Our new results also show that only weak conditions are required on the reference signals: this is illustrated by simulations and opens up the possibility of developing new methods

Blind Source Separation for the Processing of Contact-Less Biosignals

(Spatio-temporale) Blind Source Separation (BSS) eignet sich für die Verarbeitung von Multikanal-Messungen im Bereich der kontaktlosen Biosignalerfassung. Ziel der BSS ist dabei die Trennung von (z.B. kardialen) Nutzsignalen und Störsignalen typisch für die kontaktlosen Messtechniken. Das Potential der BSS kann praktisch nur ausgeschöpft werden, wenn (1) ein geeignetes BSS-Modell verwendet wird, welches der Komplexität der Multikanal-Messung gerecht wird und (2) die unbestimmte Permutation unter den BSS-Ausgangssignalen gelöst wird, d.h. das Nutzsignal praktisch automatisiert identifiziert werden kann. Die vorliegende Arbeit entwirft ein Framework, mit dessen Hilfe die Effizienz von BSS-Algorithmen im Kontext des kamera-basierten Photoplethysmogramms bewertet werden kann. Empfehlungen zur Auswahl bestimmter Algorithmen im Zusammenhang mit spezifischen Signal-Charakteristiken werden abgeleitet. Außerdem werden im Rahmen der Arbeit Konzepte für die automatisierte Kanalauswahl nach BSS im Bereich der kontaktlosen Messung des Elektrokardiogramms entwickelt und bewertet. Neuartige Algorithmen basierend auf Sparse Coding erwiesen sich dabei als besonders effizient im Vergleich zu Standard-Methoden.(Spatio-temporal) Blind Source Separation (BSS) provides a large potential to process distorted multichannel biosignal measurements in the context of novel contact-less recording techniques for separating distortions from the cardiac signal of interest. This potential can only be practically utilized (1) if a BSS model is applied that matches the complexity of the measurement, i.e. the signal mixture and (2) if permutation indeterminacy is solved among the BSS output components, i.e the component of interest can be practically selected. The present work, first, designs a framework to assess the efficacy of BSS algorithms in the context of the camera-based photoplethysmogram (cbPPG) and characterizes multiple BSS algorithms, accordingly. Algorithm selection recommendations for certain mixture characteristics are derived. Second, the present work develops and evaluates concepts to solve permutation indeterminacy for BSS outputs of contact-less electrocardiogram (ECG) recordings. The novel approach based on sparse coding is shown to outperform the existing concepts of higher order moments and frequency-domain features

Improving independent vector analysis in speech and noise separation tasks

Independent vector analysis (IVA) is an efficient multichannel blind source separation method. However, source models conventionally assumed in IVA present some limitations in case of speech and noise separation tasks. Consequently, it is expected that using better source models that overcome these limitations will improve the source separation performance of IVA. In this work, an extension of IVA is proposed, with a new source model more suitable for speech and noise separation tasks. The proposed extended IVA was evaluated in a speech and noise separation task, where it was proven to improve separation performance over baseline IVA. Furthermore, extended IVA was evaluated with several post-filters, aiming to realize an analogous setup to a multichannel Wiener filter (MWF) system. This kind of setup proved to further increase the separation performance of IVA

Blind, MIMO system estimation based on PARAFAC decomposition of higher order output tensors

IEEE Transactions on Signal Processing, 54(11): pp. 4156-4168.We present a novel framework for the identification of a multiple-input multiple-output (MIMO) system driven by white, mutually independent unobservable inputs. Samples of the system frequency response are obtained based on parallel factorization (PARAFAC) of three- or four-way tensors constructed based on, respectively, third- or fourth-order cross spectra of the system outputs. The main difficulties in frequency-domain methods are frequency- dependent permutation and filtering ambiguities.We show that the information available in the higher order spectra allows for the ambiguities to be resolved up to a constant scaling and permutation ambiguities and a linear phase ambiguity. Important features of the proposed approach are that it does not require channel length information, needs no phase unwrapping, and unlike the majority of existing methods, needs no prewhitening of the system outputs

Blind identification of possibly under-determined convolutive MIMO systems

Blind identi¯cation of a Linear Time Invariant (LTI) Multiple-Input Multiple-Output (MIMO) system is of great importance in many applications, such as speech processing, multi-access communication, multi-sensor sonar/radar systems, and biomedical applications. The objective of blind identi¯cation for a MIMO system is to identify an unknown system, driven by Ni unobservable inputs, based on the No system outputs. We ¯rst present a novel blind approach for the identi¯cation of a over-determined (No ¸ Ni) MIMO system driven by white, mutually independent unobservable inputs. Samples of the system frequency response are obtained based on Parallel Factorization (PARAFAC) of three- or four-way tensors constructed respectively based on third- or fourth-order cross-spectra of the system outputs. We show that the information available in the higher-order spectra allows for the system response to be identi¯ed up to a constant scaling and permutation ambiguities and a linear phase ambiguity. Important features of the proposed approaches are that they do not require channel length information, need no phase unwrapping, and unlike the majority of existing methods, need no pre-whitening of the system outputs.While several methods have been proposed to blindly identify over-determined convolutive MIMO systems, very scarce results exist for under-determined (No < Ni) case, all of which refer to systems that either have some special structure, or special No, Ni values. We propose a novel approach for blind identi¯cation of under-determined convolutive MIMO systems of general dimensions. As long as min(No;Ni) ¸ 2, we can always ¯nd the appropriate order of statistics that guarantees identi¯ability of the system response within trivial ambiguities. We provide the description of the class of identi¯able MIMO systems for a certain order of statistics K, and an algorithm to reach the solution.Finally we propose a novel approach for blind identi¯cation and symbol recovery of a distributed antenna system with multiple carrier-frequency o®sets (CFO), arising due to mismatch between the oscillators of transmitters and receivers. The received base-band signal is over-sampled, and its polyphase components are used to formulate a virtual MIMO problem. By applying blind MIMO system estimation techniques, the system response is estimated and used to subsequently decouple the users and transform the multiple CFOs estimation problem into a set of independent single CFO estimation problems.Ph.D., Electrical Engineering -- Drexel University, 200

Independent EEG Sources Are Dipolar

Independent component analysis (ICA) and blind source separation (BSS) methods are increasingly used to separate individual brain and non-brain source signals mixed by volume conduction in electroencephalographic (EEG) and other electrophysiological recordings. We compared results of decomposing thirteen 71-channel human scalp EEG datasets by 22 ICA and BSS algorithms, assessing the pairwise mutual information (PMI) in scalp channel pairs, the remaining PMI in component pairs, the overall mutual information reduction (MIR) effected by each decomposition, and decomposition ‘dipolarity’ defined as the number of component scalp maps matching the projection of a single equivalent dipole with less than a given residual variance. The least well-performing algorithm was principal component analysis (PCA); best performing were AMICA and other likelihood/mutual information based ICA methods. Though these and other commonly-used decomposition methods returned many similar components, across 18 ICA/BSS algorithms mean dipolarity varied linearly with both MIR and with PMI remaining between the resulting component time courses, a result compatible with an interpretation of many maximally independent EEG components as being volume-conducted projections of partially-synchronous local cortical field activity within single compact cortical domains. To encourage further method comparisons, the data and software used to prepare the results have been made available (http://sccn.ucsd.edu/wiki/BSSComparison)

New kurtosis optimization schemes for MISO equalization

International audienceThis paper deals with efficient optimization of cumulant based contrast functions. Such a problem occurs in the blind source separation framework, where contrast functions are criteria to be maximized in order to retrieve the sources. More precisely, we focus on the extraction of one source signal and our method applies in deflation approaches, where the sources are extracted one by one. We propose new methods to maximize the kurtosis contrast function. These methods are intermediate between a gradient and an iterative "fixed-point" optimization of so-called reference contrasts. They rely on iterative updates of the parameters which monotonically increase the contrast function value: we point out the strong similarity with the Expectation-Maximization (EM) method and with recent generalizations referred to as Minimization-Maximization (MM). We also prove the global convergence of the algorithm to a stationary point. Simulations confirm the convergence of our methods to a separating solution. They also show experimentally that our methods have a much lower computational cost than former classical optimization methods. Finally, simulations suggest that the methods remain valid under weaker conditions than those required for proving convergence

Trennung und Schätzung der Anzahl von Audiosignalquellen mit Zeit- und Frequenzüberlappung

Everyday audio recordings involve mixture signals: music contains a mixture of instruments; in a meeting or conference, there is a mixture of human voices. For these mixtures, automatically separating or estimating the number of sources is a challenging task. A common assumption when processing mixtures in the time-frequency domain is that sources are not fully overlapped. However, in this work we consider some cases where the overlap is severe — for instance, when instruments play the same note (unison) or when many people speak concurrently ("cocktail party") — highlighting the need for new representations and more powerful models. To address the problems of source separation and count estimation, we use conventional signal processing techniques as well as deep neural networks (DNN). We first address the source separation problem for unison instrument mixtures, studying the distinct spectro-temporal modulations caused by vibrato. To exploit these modulations, we developed a method based on time warping, informed by an estimate of the fundamental frequency. For cases where such estimates are not available, we present an unsupervised model, inspired by the way humans group time-varying sources (common fate). This contribution comes with a novel representation that improves separation for overlapped and modulated sources on unison mixtures but also improves vocal and accompaniment separation when used as an input for a DNN model. Then, we focus on estimating the number of sources in a mixture, which is important for real-world scenarios. Our work on count estimation was motivated by a study on how humans can address this task, which lead us to conduct listening experiments, confirming that humans are only able to estimate the number of up to four sources correctly. To answer the question of whether machines can perform similarly, we present a DNN architecture, trained to estimate the number of concurrent speakers. Our results show improvements compared to other methods, and the model even outperformed humans on the same task. In both the source separation and source count estimation tasks, the key contribution of this thesis is the concept of “modulation”, which is important to computationally mimic human performance. Our proposed Common Fate Transform is an adequate representation to disentangle overlapping signals for separation, and an inspection of our DNN count estimation model revealed that it proceeds to find modulation-like intermediate features.Im Alltag sind wir von gemischten Signalen umgeben: Musik besteht aus einer Mischung von Instrumenten; in einem Meeting oder auf einer Konferenz sind wir einer Mischung menschlicher Stimmen ausgesetzt. Für diese Mischungen ist die automatische Quellentrennung oder die Bestimmung der Anzahl an Quellen eine anspruchsvolle Aufgabe. Eine häufige Annahme bei der Verarbeitung von gemischten Signalen im Zeit-Frequenzbereich ist, dass die Quellen sich nicht vollständig überlappen. In dieser Arbeit betrachten wir jedoch einige Fälle, in denen die Überlappung immens ist zum Beispiel, wenn Instrumente den gleichen Ton spielen (unisono) oder wenn viele Menschen gleichzeitig sprechen (Cocktailparty) —, so dass neue Signal-Repräsentationen und leistungsfähigere Modelle notwendig sind. Um die zwei genannten Probleme zu bewältigen, verwenden wir sowohl konventionelle Signalverbeitungsmethoden als auch tiefgehende neuronale Netze (DNN). Wir gehen zunächst auf das Problem der Quellentrennung für Unisono-Instrumentenmischungen ein und untersuchen die speziellen, durch Vibrato ausgelösten, zeitlich-spektralen Modulationen. Um diese Modulationen auszunutzen entwickelten wir eine Methode, die auf Zeitverzerrung basiert und eine Schätzung der Grundfrequenz als zusätzliche Information nutzt. Für Fälle, in denen diese Schätzungen nicht verfügbar sind, stellen wir ein unüberwachtes Modell vor, das inspiriert ist von der Art und Weise, wie Menschen zeitveränderliche Quellen gruppieren (Common Fate). Dieser Beitrag enthält eine neuartige Repräsentation, die die Separierbarkeit für überlappte und modulierte Quellen in Unisono-Mischungen erhöht, aber auch die Trennung in Gesang und Begleitung verbessert, wenn sie in einem DNN-Modell verwendet wird. Im Weiteren beschäftigen wir uns mit der Schätzung der Anzahl von Quellen in einer Mischung, was für reale Szenarien wichtig ist. Unsere Arbeit an der Schätzung der Anzahl war motiviert durch eine Studie, die zeigt, wie wir Menschen diese Aufgabe angehen. Dies hat uns dazu veranlasst, eigene Hörexperimente durchzuführen, die bestätigten, dass Menschen nur in der Lage sind, die Anzahl von bis zu vier Quellen korrekt abzuschätzen. Um nun die Frage zu beantworten, ob Maschinen dies ähnlich gut können, stellen wir eine DNN-Architektur vor, die erlernt hat, die Anzahl der gleichzeitig sprechenden Sprecher zu ermitteln. Die Ergebnisse zeigen Verbesserungen im Vergleich zu anderen Methoden, aber vor allem auch im Vergleich zu menschlichen Hörern. Sowohl bei der Quellentrennung als auch bei der Schätzung der Anzahl an Quellen ist ein Kernbeitrag dieser Arbeit das Konzept der “Modulation”, welches wichtig ist, um die Strategien von Menschen mittels Computern nachzuahmen. Unsere vorgeschlagene Common Fate Transformation ist eine adäquate Darstellung, um die Überlappung von Signalen für die Trennung zugänglich zu machen und eine Inspektion unseres DNN-Zählmodells ergab schließlich, dass sich auch hier modulationsähnliche Merkmale finden lassen