Herbert Buchner

Bio: Herbert Buchner is an academic researcher from University of Cambridge. The author has contributed to research in topics: Blind signal separation & Adaptive filter. The author has an hindex of 27, co-authored 116 publications receiving 2602 citations. Previous affiliations of Herbert Buchner include University of Erlangen-Nuremberg & Huawei.

A generalization of blind source separation algorithms for convolutive mixtures based on second-order statistics

Abstract: We present a general broadband approach to blind source separation (BSS) for convolutive mixtures based on second-order statistics. This avoids several known limitations of the conventional narrowband approximation, such as the internal permutation problem. In contrast to traditional narrowband approaches, the new framework simultaneously exploits the nonwhiteness property and nonstationarity property of the source signals. Using a novel matrix formulation, we rigorously derive the corresponding time-domain and frequency-domain broadband algorithms by generalizing a known cost-function which inherently allows joint optimization for several time-lags of the correlations. Based on the broadband approach time-domain, constraints are obtained which provide a deeper understanding of the internal permutation problem in traditional narrowband frequency-domain BSS. For both the time-domain and the frequency-domain versions, we discuss links to well-known, and also, to novel algorithms that constitute special cases. Moreover, using the so-called generalized coherence, links between the time-domain and the frequency-domain algorithms can be established, showing that our cost function leads to an update equation with an inherent normalization ensuring a robust adaptation behavior. The concept is applicable to offline, online, and block-online algorithms by introducing a general weighting function allowing for tracking of time-varying real acoustic environments.

Audio signal decorrelator, multi channel audio signal processor, audio signal processor, method for deriving an output audio signal from an input audio signal and computer program

Abstract: An audio signal decorrelator for deriving an output audio signal from an input audio signal has a frequency analyzer for extracting from the input audio signal a first partial signal descriptive of an audio content in a first audio frequency range and a second partial signal descriptive of an audio content in a second audio frequency range having higher frequencies compared to the second audio frequency range. A partial signal modifier modifies the first and second partial signals, to obtain first and second processed partial signals, so that a modulation amplitude of a time variant phase shift or time variant delay applied to the first partial signal is higher than that applied to the second partial signal, or for modifying only the first partial signal. A signal combiner combines the first and second processed partial signals, or combines the first processed partial signal and the second partial signal, to obtain an output audio signal.

TRINICON: a versatile framework for multichannel blind signal processing

Abstract: In this paper we present a framework for multichannel blind signal processing for convolutive mixtures, such as blind source separation (BSS) and multichannel blind deconvolution (MCBD). It is based on the use of multivariate pdf and a compact matrix notation which considerably simplifies the representation and handling of the algorithms. By introducing these techniques into an information theoretic cost function, we can exploit the three fundamental signal properties nonwhiteness, nongaussianity, and nonstationarity. This results in a versatile tool that we call TRINICON (Triple-N ICA for convolutive mixtures). Both, links to popular algorithms and several novel algorithms follow from the general approach. In particular, we introduce a new concept of multichannel blind partial deconvolution (MCBPD) for speech which prevents a complete whitening of the output signals, i.e., the vocal tract is excluded from the equalization. This is especially interesting for automatic speech recognition applications. Moreover, we show results for BSS using multivariate spherically invariant random processes (SIRP) to efficiently model speech, and show how the approach carries over to MCBPD. These concepts are also suitable for an efficient implementation in the frequency domain by using a rigorous broadband derivation avoiding the internal permutation problem and circularity effects.

Blind Source Separation for Convolutive Mixtures: A Unified Treatment

Abstract: Blind source separation (BSS) algorithms for time series can exploit three properties of the source signals: nonwhiteness, nonstationarity, and nongaussianity While methods utilizing the first two properties are usually based on second-order statistics (SOS), higher-order statistics (HOS) must be considered to exploit nongaussianity In this chapter, we consider all three properties simultaneously to design BSS algorithms for convolutive mixtures within a new generic framework This concept derives its generality from an appropriate matrix notation combined with the use of multivariate probability densities for considering the time-dependencies of the source signals Based on a generalized cost function we rigorously derive the corresponding time-domain and frequency-domain broadband algorithms Due to the broadband approach, time-domain constraints are obtained which provide a more detailed understanding of the internal permutation problem in traditional narrowband frequency-domain BSS For both, the time-domain and the frequency-domain versions, we discuss links to well-known and also to novel algorithms that follow as special cases of the framework Moreover, we use models for correlated spherically invariant random processes (SIRPs) which are well suited for a variety of source signals including speech to obtain efficient solutions in the HOS case The concept provides a basis for off-line, online, and block-on-line algorithms by introducing a general weighting function, thereby allowing for tracking of time-varying real acoustic environments

TDOA Estimation for Multiple Sound Sources in Noisy and Reverberant Environments Using Broadband Independent Component Analysis

Abstract: In this paper, we show that minimization of the statistical dependence using broadband independent component analysis (ICA) can be successfully exploited for acoustic source localization. As the ICA signal model inherently accounts for the presence of several sources and multiple sound propagation paths, the ICA criterion offers a theoretically more rigorous framework than conventional techniques based on an idealized single-path and single-source signal model. This leads to algorithms which outperform other localization methods, especially in the presence of multiple simultaneously active sound sources and under adverse conditions, notably in reverberant environments. Three methods are investigated to extract the time difference of arrival (TDOA) information contained in the filters of a two-channel broadband ICA scheme. While for the first, the blind system identification (BSI) approach, the number of sources should be restricted to the number of sensors, the other methods, the averaged directivity pattern (ADP) and composite mapped filter (CMF) approaches can be used even when the number of sources exceeds the number of sensors. To allow fast tracking of moving sources, the ICA algorithm operates in block-wise batch mode, with a proportionate weighting of the natural gradient to speed up the convergence of the algorithm. The TDOA estimation accuracy of the proposed schemes is assessed in highly noisy and reverberant environments for two, three, and four stationary noise sources with speech-weighted spectral envelopes as well as for moving real speech sources.

Pattern Recognition and Machine Learning

Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Intelligent Automated Assistant

Abstract: An intelligent automated assistant system engages with the user in an integrated, conversational manner using natural language dialog, and invokes external services when appropriate to obtain information or perform various actions. The system can be implemented using any of a number of different platforms, such as the web, email, smartphone, and the like, or any combination thereof. In one embodiment, the system is based on sets of interrelated domains and tasks, and employs additional functionally powered by external services with which the system can interact.

A robust and precise method for solving the permutation problem of frequency-domain blind source separation

Abstract: Blind source separation (BSS) for convolutive mixtures can be solved efficiently in the frequency domain, where independent component analysis (ICA) is performed separately in each frequency bin. However, frequency-domain BSS involves a permutation problem: the permutation ambiguity of ICA in each frequency bin should be aligned so that a separated signal in the time-domain contains frequency components of the same source signal. This paper presents a robust and precise method for solving the permutation problem. It is based on two approaches: direction of arrival (DOA) estimation for sources and the interfrequency correlation of signal envelopes. We discuss the advantages and disadvantages of the two approaches, and integrate them to exploit their respective advantages. Furthermore, by utilizing the harmonics of signals, we make the new method robust even for low frequencies where DOA estimation is inaccurate. We also present a new closed-form formula for estimating DOAs from a separation matrix obtained by ICA. Experimental results show that our method provided an almost perfect solution to the permutation problem for a case where two sources were mixed in a room whose reverberation time was 300 ms.

Using context information to facilitate processing of commands in a virtual assistant

Abstract: A virtual assistant uses context information to supplement natural language or gestural input from a user. Context helps to clarify the user's intent and to reduce the number of candidate interpretations of the user's input, and reduces the need for the user to provide excessive clarification input. Context can include any available information that is usable by the assistant to supplement explicit user input to constrain an information-processing problem and/or to personalize results. Context can be used to constrain solutions during various phases of processing, including, for example, speech recognition, natural language processing, task flow processing, and dialog generation.

Linear Differential Operators. By C. Lanczos. Pp. 580. 80s. 1961. (Van Nostrand, London)

Abstract: Preface Bibliography 1. Interpolation. Introduction The Taylor expansion The finite Taylor series with the remainder term Interpolation by polynomials The remainder of Lagrangian interpolation formula Equidistant interpolation Local and global interpolation Interpolation by central differences Interpolation around the midpoint of the range The Laguerre polynomials Binomial expansions The decisive integral transform Binomial expansions of the hypergeometric type Recurrence relations The Laplace transform The Stirling expansion Operations with the Stirling functions An integral transform of the Fourier type Recurrence relations associated with the Stirling series Interpolation of the Fourier transform The general integral transform associated with the Stirling series Interpolation of the Bessel functions 2. Harmonic Analysis. Introduction The Fourier series for differentiable functions The remainder of the finite Fourier expansion Functions of higher differentiability An alternative method of estimation The Gibbs oscillations of the finite Fourier series The method of the Green's function Non-differentiable functions Dirac's delta function Smoothing of the Gibbs oscillations by Fejer's method The remainder of the arithmetic mean method Differentiation of the Fourier series The method of the sigma factors Local smoothing by integration Smoothing of the Gibbs oscillations by the sigma method Expansion of the delta function The triangular pulse Extension of the class of expandable functions Asymptotic relations for the sigma factors The method of trigonometric interpolation Error bounds for the trigonometric interpolation method Relation between equidistant trigonometric and polynomial interpolations The Fourier series in the curve fitting 3. Matrix Calculus. Introduction Rectangular matrices The basic rules of matrix calculus Principal axis transformation of a symmetric matrix Decomposition of a symmetric matrix Self-adjoint systems Arbitrary n x m systems Solvability of the general n x m system The fundamental decomposition theorem The natural inverse of a matrix General analysis of linear systems Error analysis of linear systems Classification of linear systems Solution of incomplete systems Over-determined systems The method of orthogonalisation The use of over-determined systems The method of successive orthogonalisation The bilinear identity Minimum property of the smallest eigenvalue 4. The Function Space. Introduction The viewpoint of pure and applied mathematics The language of geometry Metrical spaces of infinitely many dimensions The function as a vector The differential operator as a matrix The length of a vector The scalar product of two vectors The closeness of the algebraic approximation The adjoint operator The bilinear identity The extended Green's identity The adjoint boundary conditions Incomplete systems Over-determined systems Compatibility under inhomogeneous boundary conditions Green's identity in the realm of partial differential operators The fundamental field operations of vector analysis Solution of incomplete systems 5. The Green's Function. Introduction The role of the adjoint equation The role of Green's identity The delta function -- The existence of the Green's function Inhomogeneous boundary conditions The Green's vector Self-adjoint systems The calculus of variations The canonical equations of Hamilton The Hamiltonisation of partial operators The reciprocity theorem Self-adjoint problems Symmetry of the Green's function Reciprocity of the Green's vector The superposition principle of linear operators The Green's function in the realm of ordinary differential operators The change of boundary conditions The remainder of the Taylor series The remainder of the Lagrangian interpolation formula