PEVD-based speech enhancement in reverberant environments

The enhancement of noisy speech is important for applications involving human-to-human interactions, such as telecommunications and hearing aids, as well as human-to-machine interactions, such as voice-controlled systems and robot audition. In this work, we focus on reverberant environments. It is shown that, by exploiting the lack of correlation between speech and the late reflections, further noise reduction can be achieved. This is verified using simulations involving actual acoustic impulse responses and noise from the ACE corpus. The simulations show that even without using a noise estimator, our proposed method simultaneously achieves noise reduction, and enhancement of speech quality and intelligibility, in reverberant environments over a wide range of SNRs. Furthermore, informal listening examples highlight that our approach does not introduce any significant processing artefacts such as musical noise

Using reconfigurable computing technology to accelerate matrix decomposition and applications

Matrix decomposition plays an increasingly significant role in many scientific and engineering applications. Among numerous techniques, Singular Value Decomposition (SVD) and Eigenvalue Decomposition (EVD) are widely used as factorization tools to perform Principal Component Analysis for dimensionality reduction and pattern recognition in image processing, text mining and wireless communications, while QR Decomposition (QRD) and sparse LU Decomposition (LUD) are employed to solve the dense or sparse linear system of equations in bioinformatics, power system and computer vision. Matrix decompositions are computationally expensive and their sequential implementations often fail to meet the requirements of many time-sensitive applications. The emergence of reconfigurable computing has provided a flexible and low-cost opportunity to pursue high-performance parallel designs, and the use of FPGAs has shown promise in accelerating this class of computation. In this research, we have proposed and implemented several highly parallel FPGA-based architectures to accelerate matrix decompositions and their applications in data mining and signal processing. Specifically, in this dissertation we describe the following contributions: • We propose an efficient FPGA-based double-precision floating-point architecture for EVD, which can efficiently analyze large-scale matrices. • We implement a floating-point Hestenes-Jacobi architecture for SVD, which is capable of analyzing arbitrary sized matrices. • We introduce a novel deeply pipelined reconfigurable architecture for QRD, which can be dynamically configured to perform either Householder transformation or Givens rotation in a manner that takes advantage of the strengths of each. • We design a configurable architecture for sparse LUD that supports both symmetric and asymmetric sparse matrices with arbitrary sparsity patterns. • By further extending the proposed hardware solution for SVD, we parallelize a popular text mining tool-Latent Semantic Indexing with an FPGA-based architecture. • We present a configurable architecture to accelerate Homotopy l1-minimization, in which the modification of the proposed FPGA architecture for sparse LUD is used at its core to parallelize both Cholesky decomposition and rank-1 update. Our experimental results using an FPGA-based acceleration system indicate the efficiency of our proposed novel architectures, with application and dimension-dependent speedups over an optimized software implementation that range from 1.5ÃÂ to 43.6ÃÂ in terms of computation time

Formulating and solving broadband multichannel problems using matrices of functions

The analysis and design of broadband multichannel systems typically involves convolutive mixing, characterised by matrices of transfer functions. Further, many broadband multichannel problems can be formulated using space-time covariance matrices that include an explicit lag variable and thus cross-correlation sequences as entries. This is in contrast to narrowband challenges, where the problem formulation relies on standard (i.e. constant) matrices; a rich set of solutions that are optimal in various senses can be reached from these formulations by matrix factorisations such as the eigenvalue or singular value decompositions. In order to extend the utility of such linear algebraic techniques to the broadband case, the diagonalisation or factorisation of matrices of functions is key. In this webinar, I will show that such matrices are quite ubiquitous in multichannel signal processing, review some of the theory for their factorisations, and show how with such broadband formulations and solutions directly generalise from their narrowband counterparts. I will sketch out a number of algorithms and illustrate their use in a few example applications such as beamforming, angle or arrival estimation, and signal compaction

Mathematical tools for processing broadband multi-sensor signals

Spatial information in broadband array signals is embedded in the relative delay with which sources illuminate different sensors. Therefore, second order statistics, on which cost functions such as the mean square rest, must include such delays. Typically, a space-time covariance matrix therefore arises, which can be represented as a Laurent polynomial matrix. The optimisation of a cost function then requires extending the utility of the eigenvalue decomposition from narrowband covariance matrices to the broadband case of operating in a space-time covariance matrix. This overview paper summarises efforts in performing such factorisations, and demonstrated via the exemplar application of a broadband beamformer how thus well-known narrowband solutions can be extended to the broadband case using polynomial matrices and their factorisations

Using parallel computation to apply the singular value decomposition (SVD) in solving for large Earth gravity fields based on satellite data

textUsing satellite data only to estimate for an Earth gravity field introduces the problem of an ill-conditioned system of equations. This mathematical difficulty amplifies as the number of unknown gravity field parameters increases, requiring a stabilization of the inversion for solution. But the number of parameters to be estimated can also be too large to allow inversion using a sequential algorithm (one computer processor). Therefore the challenge is two-fold. A stabilized inversion must be performed with a parallel (multi-processor) algorithm. Thus, new code was developed in the parallel computing infrastructure of Parallel Linear Algebra Package (PLAPACK) to achieve the task of applying the Singular Value Decomposition (SVD) to invert for (and stabilize) very large gravity fields of well over 25,000 unknown parameters. This new code is given the name (Parallel LArge Svd Solver) PLASS. The choice of the SVD was made because it offers multiple opportunities of stabilization techniques. Poorly observed parameter corrections are removed from the culpable eigenspace of the normal matrix of CHAMP or the singular vector space of the upper R triangular matrix of GRACE. Solutions were stabilized based on the removal of either eigenvalues or singular values using four different standard optimization criteria: Inspection, Relative Error, Norm Norm minimization, trace of the Mean Square Error (MSE) matrix, and with a fifth method, independently introduced for this investigation, that optimizes removal of eigenvalues or singular values based on Kaula’s power rule of thumb. This method is given the name “Kaula Eigenvalue (KEV) or Kaula Singular Value (KSV) relation”. For the gravity fields of this investigation, orbital fits, geodetic evaluations and error propagations of the best of the resulting SVD gravity fields were performed, and shown to be comparable to the CHAMP solution obtained by the GeoForschungsZentrum (GFZ) and to the full rank GRACE solution obtained by the Center for Space Research (CSR).Aerospace Engineering and Engineering Mechanic

Applications of polynomial eigenvalue decomposition to multichannel broadband signal processing : part 2: eigenvalue decomposition

Multichannel broadband signals arise at the core of many essential military technologies such as radar, sonar and communications, and commercial applications like telecommunications, speech processing, healthcare monitoring and seismic surveillance. The success of these applications often depends on the performance of signal processing tasks such as source localization, channel coding, signal enhancement, and source separation. U n multichannel broadband arrays or convolutively mixed signals, the array signals are generally correlated in time across different sensors. Therefore, the time delays for broadband signals cannot be represented by phase shift alone but need to be explicitly modelled. The relative time shifts are captured using the polynomial space-time covariance matrix, where decorrelation over a range of time shifts can be achieved using a polynomial EVD (PEVD). This tutorial is dedicated to recent developments in PEVD for multichannel broadband signal processing applications. We believe this tutorial and resources, such as code and demo webpages, will motivate and inspire many colleagues and aspiring PhD students working on broadband multichannel signal processing to try PEVD. The applications and demonstrations covered in this proposed tutorial include direction of arrival estimation, beamforming, source identification, weak transient detection, voice activity detection, speech enhancement, source separation and subband coding

Algorithms and techniques for polynomial matrix decompositions

The concept of polynomial matrices is introduced and the potential application of polynomial matrix decompositions is discussed within the general context of multi-channel digital signal processing. A recently developed technique, known as the second order sequential rotation algorithm (SBR2), for performing the eigenvalue decomposition of a para-Hermitian polynomial matrix (PEVD) is presented. The potential benefit of using the SBR2 algorithm to impose strong decorrelation on the signals received by a broadband sensor array is demonstrated by means of a suitable numerical simulation. This demonstrates how the polynomial matrices produced as a result of the PEVD can be of unnecessarily high order. This is undesirable for many practical applications and slows down the iterative computational procedure. An effective truncation technique for controlling the growth in order of these polynomial matrices is proposed. Depending on the choice of truncation parameters, it provides an excellent compromise between reduced order polynomial matrix factors and accuracy of the resulting decomposition. This is demonstrated by means of a set of numerical simulations performed by applying the modified SBR2 algorithm with a variety of truncation parameters to a representative set of test matrices. Three new polynomial matrix decompositions are then introduced - one for implementing a polynomial matrix QR decomposition (PQRD) and two for implementing a polynomial matrix singular value decomposition (PSVD). Several variants of the PQRD algorithm (including polynomial order reduction) are proposed and compared by numerical simulation using an appropriate set of test matrices. The most effective variant w.r.t. computational speed, order of the polynomial matrix factors and accuracy of the resulting decomposition is identified. The PSVD can be computed using either the PEVD technique, based on the SBR2 algorithm, or the new algorithm proposed for implementing the PQRD. These two approaches are also compared by means of computer simulations which demonstrate that the method based on the PQRD is numerically superior. The potential application of the preferred PQRD and PSVD algorithms to multiple input multiple output (MIMO) communications for the purpose of counteracting both co-channel interference and inter-symbol interference (multi-channel equalisation) is demonstrated in terms of reduced bit error rate by means of representative computer simulations

Numerical Linear Algebra applications in Archaeology: the seriation and the photometric stereo problems

The aim of this thesis is to explore the application of Numerical Linear Algebra to Archaeology. An ordering problem called the seriation problem, used for dating findings and/or artifacts deposits, is analysed in terms of graph theory. In particular, a Matlab implementation of an algorithm for spectral seriation, based on the use of the Fiedler vector of the Laplacian matrix associated with the problem, is presented. We consider bipartite graphs for describing the seriation problem, since the interrelationship between the units (i.e. archaeological sites) to be reordered, can be described in terms of these graphs. In our archaeological metaphor of seriation, the two disjoint nodes sets into which the vertices of a bipartite graph can be divided, represent the excavation sites and the artifacts found inside them. Since it is a difficult task to determine the closest bipartite network to a given one, we describe how a starting network can be approximated by a bipartite one by solving a sequence of fairly simple optimization problems. Another numerical problem related to Archaeology is the 3D reconstruction of the shape of an object from a set of digital pictures. In particular, the Photometric Stereo (PS) photographic technique is considered