Speech Enhancement in the Karhunen-Loeve Expansion Domain (Synthesis Lectures on Speech and Audio Processing S)

This book is devoted to the study of the problem of speech enhancement whose objective is the recovery of a signal of interest (i.e., speech) from noisy observations. Typically, the recovery process is accomplished by passing the noisy observations through a linear filter (or a linear transformation). Since both the desired speech and undesired noise are filtered at the same time, the most critical issue of speech enhancement resides in how to design a proper optimal filter that can fully take advantage of the difference between the speech and noise statistics to mitigate the noise effect as much as possible while maintaining the speech perception identical to its original form. The optimal filters can be designed either in the time domain or in a transform space. As the title indicates, this book will focus on developing and analyzing optimal filters in the Karhunen-Lo?ve expansion (KLE) domain. We begin by describing the basic problem of speech enhancement and the fundamental principles to solve it in the time domain. We then explain how the problem can be equivalently formulated in the KLE domain. Next, we divide the general problem in the KLE domain into four groups, depending on whether interframe and interband information is accounted for, leading to four linear models for speech enhancement in the KLE domain. For each model, we introduce signal processing measures to quantify the performance of speech enhancement, discuss the formation of different cost functions, and address the optimization of these cost functions for the derivation of different optimal filters. Both theoretical analysis and experiments will be provided to study the performance of these filters and the links between the KLE-domain and time-domain optimal filters will be examined. Table of Contents: Introduction / Problem Formulation / Optimal Filters in the Time Domain / Linear Models for Signal Enhancement in the KLE Domain / Optimal Filters in the KLE Domain with Model 1 / Optimal Filters in the KLE Domain with Model 2 / Optimal Filters in the KLE Domain with Model 3 / Optimal Filters in the KLE Domain with Model 4 / Experimental Study This book is devoted to the study of the problem of speech enhancement whose objective is the recovery of a signal of interest (i.e., speech) from noisy observations. Typically, the recovery process is accomplished by passing the noisy observations through a linear filter (or a linear transformation). Since both the desired speech and undesired noise are filtered at the same time, the most critical issue of speech enhancement resides in how to design a proper optimal filter that can fully take advantage of the difference between the speech and noise statistics to mitigate the noise effect as much as possible while maintaining the speech perception identical to its original form. The optimal filters can be designed either in the time domain or in a transform space. As the title indicates, this book will focus on developing and analyzing optimal filters in the Karhunen-Loève expansion (KLE) domain. We begin by describing the basic problem of speech enhancement and the fundamental principles to solve it in the time domain. We then explain how the problem can be equivalently formulated in the KLE domain. Next, we divide the general problem in the KLE domain into four groups, depending on whether interframe and interband information is accounted for, leading to four linear models for speech enhancement in the KLE domain. For each model, we introduce signal processing measures to quantify the performance of speech enhancement, discuss the formation of different cost functions, and address the optimization of these cost functions for the derivation of different optimal filters. Both theoretical analysis and experiments will be provided to study the performance of these filters and the links between the KLE-domain and time-domain optimal filters will be examined. Table of Contents: Introduction / Problem Formulation / Optimal Filters in the Time Domain / Linear Models for Signal Enhancement in the KLE Domain / Optimal Filters in the KLE Domain with Model 1 / Optimal Filtersin the KLE Domain with Model 2 / Optimal Filters in the KLE Domain with Model 3 / Optimal Filters in the KLE Domain with Model 4 / Experimental Study The Problem of Speech Enhancement......Page 11 Organization of the Book......Page 15 Signal Model......Page 17 Karhunen-Loève Expansion (KLE)......Page 18 Performance Measures......Page 21 Mean-Square Error (MSE) Criterion......Page 23 Wiener Filter......Page 25 Tradeoff Filters......Page 28 Subspace-Type Filter......Page 30 Maximum Signal-to-Noise Ratio (SNR) Filter......Page 31 Model 1......Page 35 Model 2......Page 36 Model 3......Page 39 Model 4......Page 40 Performance Measures......Page 43 MSE Criterion......Page 45 Wiener Filter......Page 48 Tradeoff Filter......Page 50 Maximum SNR Filter......Page 51 Performance Measures......Page 53 MSE Criterion......Page 56 Wiener Filter......Page 58 Minimum Variance Distortionless Response (MVDR) Filter......Page 60 Tradeoff Filter......Page 62 Performance Measures......Page 67 MSE Criterion......Page 70 Wiener Filter......Page 72 Tradeoff Filter......Page 73 Maximum SNR Filter......Page 74 Performance Measures......Page 77 MSE Criterion......Page 80 Wiener Filter......Page 82 MVDR Filter......Page 83 Maximum SNR Filter......Page 84 Experimental Conditions......Page 85 Estimation of the Correlation Matrices and Vectors......Page 86 Performance Measures......Page 87 Performance of the Time-Domain Filters......Page 88 Wiener Filter......Page 89 Performance of the KLE-Domain Filters with Model 1......Page 91 KLE-Domain Wiener Filter......Page 92 KLE-Domain Tradeoff Filter......Page 93 Performance of the KLE-Domain Filters with Model 3......Page 95 Performance of the KLE-Domain Filters with Model 2......Page 97 KLE-Domain Filters with Model 4......Page 99 Bibliography......Page 101 Authors' Biographies......Page 107 Index......Page 109 1. Introduction The problem of speech enhancement Organization of the book 2. Problem formulation Signal model Karhunen-Loève expansion (KLE) 3. Optimal filters in the time domain Performance measures Mean-square error (MSE) criterion Wiener filter Tradeoff filters Subspace-type filter Maximum signal-to-noise ratio (SNR) filter 4. Linear models for signal enhancement in the KLE domain Model 1 Model 2 Model 3 Model 4 5. Optimal filters in the KLE domain with model 1 Performance measures MSE criterion Wiener filter Tradeoff filter Maximum SNR filter 6. Optimal filters in the KLE domain with model 2 Performance measures Maximum SNR filter MSE criterion Wiener filter Minimum variance distortionless response (MVDR) filter Tradeoff filter 7. Optimal filters in the KLE domain with model 3 Performance measures MSE criterion Wiener filter Tradeoff filter Maximum SNR filter 8. Optimal filters in the KLE domain with model 4 Performance measures MSE criterion Wiener filter Tradeoff filter MVDR filter Maximum SNR filter 9. Experimental study Experimental conditions Estimation of the correlation matrices and vectors Performance measures Performance of the time-domain filters Wiener filter Tradeoff filter Performance of the KLE-domain filters with model 1 KLE-domain wiener filter KLE-domain tradeoff filter Performance of the KLE-domain filters with model 3 Performance of the KLE-domain filters with model 2 KLE-domain filters with model 4 Bibliography Authors' biographies Index. Examines the problem of speech enhancement where the objective is the recovery of a signal of interest (i.e., speech) from noisy observations. The book focuses on developing and analysing optimal filters in the Karhunen-Loève expansion (KLE) domain. Both theoretical analysis and experiments are provided to study the performance of these filters. Examines the problem of speech enhancement where the objective is the recovery of a signal of interest (i.e., speech) from noisy observations. The book focuses on developing and analysing optimal filters in the Karhunen-Loeve expansion (KLE) domain. Both theoretical analysis and experiments are provided to study the performance of these filters.