Distributed Signal Processing for Binaural Hearing Aids
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Distributed Signal Processing for Binaural Hearing Aids THÈSE NO 4220 (2008) PRÉSENTÉE LE 31 octobre 2008 À LA FACULTE INFORMATIQUE ET COMMUNICATIONS LABORATOIRE DE COMMUNICATIONS AUDIOVISUELLES 1 PROGRAMME DOCTORAL EN INFORMATIQUE, COMMUNICATIONS ET INFORMATION ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE POUR L'OBTENTION DU GRADE DE DOCTEUR ÈS SCIENCES PAR Olivier ROY ingénieur en systèmes de communication diplômé EPF de nationalité suisse et originaire de Epauvillers (JU) acceptée sur proposition du jury: Prof. M. Hasler, président du jury Prof. M. Vetterli, directeur de thèse Prof. D. Jones, rapporteur Prof. M. Moonen, rapporteur Prof. B. Rimoldi, rapporteur Suisse 2008 Contents Abstract v Résumé vii Acknowledgments ix Glossary xi 1 Introduction 1 1.1 A Brief History of Hearing Aids ................... 1 1.2 Challenges .............................. 4 1.3 Motivations ............................. 5 1.4 Thesis Outline and Contributions .................. 6 2 BinauralNoiseReductionasaSourceCodingProblem 11 2.1 Introduction ............................. 11 2.2 Information Sources ......................... 11 2.3 Centralized Source Coding ..................... 13 2.3.1 Lossless Case ........................ 13 2.3.2 Lossy Case .......................... 14 2.4 Distributed Source Coding ..................... 19 2.4.1 Lossless Case ........................ 19 2.4.2 Lossy Case .......................... 22 2.5 Binaural Hearing Aids ........................ 26 2.5.1 Problem Statement ..................... 26 2.5.2 Validity of the Assumptions ................. 29 2.6 Summary ............................... 31 3 Distributed Estimation under Communication Constraints 33 3.1 Introduction ............................. 33 3.2 Distributed Estimation ....................... 34 3.2.1 Linear Approximation .................... 34 3.2.2 Compression ......................... 35 3.3 Local Optimality for Memoryless Vector Sources .......... 36 3.3.1 Linear Approximation .................... 36 3.3.2 Compression ......................... 38 3.4 Local Optimality for Discrete-Time Sources with Memory ..... 41 3.4.1 Linear Approximation .................... 41 3.4.2 Compression ......................... 45 i ii Contents 3.5 Case Study: First-order Autoregressive Process .......... 46 3.5.1 Centralized Scenario ..................... 47 3.5.2 Perfect Side Information Scenario ............. 49 3.5.3 Partial Observation Scenario ................ 50 3.5.4 General Scenario ....................... 52 3.6 Summary ............................... 55 3.A Proofs ................................ 57 4 Gain-rate Optimality 71 4.1 Introduction ............................. 71 4.2 Coding Strategies .......................... 71 4.2.1 Side Information Aware Coding ............... 72 4.2.2 Side Information Unaware Coding ............. 73 4.3 Monaural Gain-rate Trade-offs ................... 74 4.4 Binaural Gain-rate Trade-offs .................... 78 4.5 Simulation Results .......................... 83 4.5.1 Setup ............................ 83 4.5.2 Coding Strategies ...................... 84 4.5.3 Spatial Extent ........................ 86 4.5.4 Rate Allocation ....................... 86 4.6 Summary ............................... 87 4.A Proofs ................................ 89 5 Multichannel Filtering in the Weighted Overlap-Add Domain 91 5.1 Introduction ............................. 91 5.2 Monaural Filtering .......................... 91 5.2.1 Processing Architecture ................... 92 5.2.2 Frame-Based Optimality Criterion ............. 97 5.2.3 Suboptimal Strategies .................... 100 5.2.4 Recursive Algorithms .................... 103 5.2.5 Practical Considerations ................... 105 5.3 Binaural Filtering .......................... 108 5.3.1 Processing Architecture ................... 108 5.3.2 Binaural Optimality ..................... 110 5.3.3 Practical Considerations ................... 111 5.4 Simulation Results .......................... 112 5.4.1 Annihilating Power ..................... 113 5.4.2 Signal-to-Noise Ratio Improvement and Speech Distortion 114 5.5 Summary ............................... 114 6 DistributedSourceCodingofBinauralInnovation 119 6.1 Introduction ............................. 119 6.2 Model Based on Auditory Cues ................... 119 6.2.1 Model Description ...................... 119 6.2.2 Distributed Source Coding of Binaural Cues ........ 121 6.3 Model Based on Sparsity Principles ................. 124 6.3.1 Model Description ...................... 124 6.3.2 Distributed Source Coding of the Binaural Filter ...... 124 6.3.3 Robustness to Model Mismatch ............... 126 6.4 Application: Distributed Spatial Audio Coding ........... 128 Contents iii 6.4.1 Model Based on Auditory Cues ............... 129 6.4.2 Model Based on Sparsity Principles ............. 131 6.5 Summary ............................... 131 7 Conclusions 135 7.1 Thesis Summary ........................... 135 7.2 Future Research ........................... 136 A Weighted Mean Squared Linear Estimation 139 A.1 General Transform Matrix ...................... 139 A.2 Diagonal Transform Matrix ..................... 142 Bibliography 143 Curriculum Vitae 155 iv Contents Abstract Over the last centuries, hearing aids have evolved from crude and bulky horn- shaped instruments to lightweight and almost invisible digital signal processing devices. While most of the research has focused on the design of monaural ap- paratus, the use of a wireless link has been recently advocated to enable data transfer between hearing aids such as to obtain a binaural system. The avail- ability of a wireless link offers brand new perspectives but also poses great tech- nical challenges. It requires the design of novel signal processing schemes that address the restricted communication bitrates, processing delays and power consumption limitations imposed by wireless hearing aids. The goal of this dissertation is to address these issues at both a theoretical and a practical level. We start by taking a distributed source coding view on the problem of binaural noise reduction. The proposed analysis allows deriv- ing mean square optimal coding strategies, and to quantify the noise reduction enabled by a wireless link as a function of the communication bitrate. The problem of rate allocation between the hearing aids is also studied. In a more general setting, these findings are used to design algorithms for distributed estimation in sensor networks, under both a linear approximation and a com- pression constraint. The potential of our approach in this context is illustrated by means of a simple case study based on a first-order autoregressive model. Two important practical aspects of binaural noise reduction are then inves- tigated. The first issue pertains to multichannel filtering in the transformed domain using a weighted overlap-add filter bank. We propose three subband filtering strategies together with recursive algorithms for the computation of the filter coefficients. Some numerical methods to reduce their computational complexity are also discussed. The second problem concerns the estimation of binaural characteristics using the wireless link. These characteristics are mod- eled in two different ways. The first approach is based on binaural cues. A source coding method to estimate these cues in a distributed fashion is pro- posed. It takes advantage of the particularities of the recording setup to reduce the transmission bitrate. The second approach involves a filter that is sparse in the time domain. This sparsity allows for the design of a novel distributed scheme based on annihilating filters. Finally, application of these methods to the distributed coding of spatial audio is presented. Keywords: binaural hearing aids, distributed source coding, wireless com- munication link. v vi Abstract Résumé Durant les dernières décennies, les aides auditives ont évolué de manière sig- nificative, passant d’instruments en forme de cor, à la fois rudimentaires et volumineux, à des appareils de traitement numérique du signal légers et quasi invisibles. Alors que la majeure partie de la recherche s’est focalisée sur la conception de dispositifs monauraux, l’utilisation d’un lien de communication sans fil a récemment été préconisée afin de permettre la transmission de données entre aides auditives et ainsi d’obtenir un système binaural. L’accès à la tech- nologie sans fil offre de nouvelles perspectives mais pose également d’énormes défis techniques. Elle nécessite le développement de nouvelles méthodes de traitement du signal qui prennent en compte les limites imposées par les aides auditives sans fil en termes de débits de communication, de délais de traitement et de consommation énergétique. L’objectif de cette thèse est d’aborder ces problèmes sous un angle théorique et pratique. Nous considérons, en premier lieu, le problème de la réduction de bruit binaurale en adoptant un point de vue de codage source distribué. Notre analyse permet d’obtenir des stratégies de codage optimales au sens des moin- dres carrés, et de quantifier la réduction de bruit obtenue grâce à un lien sans fil en fonction du débit de communication. Le problème de l’allocation du débit entre les deux aides auditives est également étudié. Plus généralement, ces résultats nous permettent de concevoir des algorithmes d’estimation distribués pour des réseaux de capteurs, en considérant une contrainte de communica- tion basée soit sur l’approximation linéaire, soit sur la compression. Dans ce contexte, le potentiel de notre approche