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Conference paperLawson M, Brookes M, Dragotti PL, 2017,
IDENTIFYING A MULTIPLE PLANE PLENOPTIC FUNCTION FROM A SWIPED IMAGE
, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Publisher: IEEE, Pages: 1423-1427, ISSN: 1520-6149 -
BookJarrett DP, Habets EAP, Naylor PA, 2017,
Theory and Applications of Spherical Microphone Array Processing Introduction
, Publisher: SPRINGER-VERLAG BERLIN, ISBN: 978-3-319-42209-1 -
Conference paperAlqurashi Y, Moss J, Nakamura T, et al., 2017,
The Efficacy Of In-Ear Electroencephalography (eeg) To Monitor Sleep Latency And The Impact Of Sleep Deprivation
, International Conference of the American-Thoracic-Society (ATS), Publisher: AMER THORACIC SOC, ISSN: 1073-449X -
Journal articleClerckx B,
MISO Networks with Imperfect CSIT: A Topological Rate-Splitting Approach
, IEEE Transactions on Communications, ISSN: 1558-0857 -
Conference paperLeung KK, Nazemi S, Swami A, 2016,
QoI-aware Tradeoff Between Communication and Computation in Wireless Ad-hoc Networks
, 27th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, Publisher: IEEE, ISSN: 2166-9589Data aggregation techniques exploit spatial and temporalcorrelations among data and aggregate data into a smallervolume as a means to optimize usage of limited network resourcesincluding energy. There is a trade-off among the Quality ofInformation (QoI) requirement and energy consumption for computationand communication. We formulate the energy-efficientdata aggregation problem as a non-linear optimization problemto optimize the trade-off and control the degree of informationreduction at each node subject to given QoI requirement. Usingthe theory of duality optimization, we prove that under a set ofreasonable cost assumptions, the optimal solution can be obtaineddespite non-convexity of the problem. Moreover, we propose adistributed, iterative algorithm that will converge to the optimalsolution. Extensive numerical results are presented to confirmthe validity of the proposed solution approach.
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Journal articleAhmed MU, Chanwimalueang T, Thayyil S, et al., 2016,
A multivariate multiscale fuzzy entropy algorithm with application to uterine EMG complexity analysis
, Entropy, Vol: 19, ISSN: 1099-4300The recently introduced multivariate multiscale entropy (MMSE) has been successfully used to quantify structural complexity in terms of nonlinear within- and cross-channel correlations as well as to reveal complex dynamical couplings and various degrees of synchronization over multiple scales in real-world multichannel data. However, the applicability of MMSE is limited by the coarse-graining process which defines scales, as it successively reduces the data length for each scale and thus yields inaccurate and undefined entropy estimates at higher scales and for short length data. To that cause, we propose the multivariate multiscale fuzzy entropy (MMFE) algorithm and demonstrate its superiority over the MMSE on both synthetic as well as real-world uterine electromyography (EMG) short duration signals. Based on MMFE features, an improvement in the classification accuracy of term-preterm deliveries was achieved, with a maximum area under the curve (AUC) value of 0.99.
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Journal articleCichocki A, Lee N, Oseledets I, et al., 2016,
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions
, Foundations and Trends in Machine Learning, Vol: 9, Pages: 249-429, ISSN: 1935-8237Modern applications in engineering and data science are increasingly based on multidimensional data of exceedingly high volume, variety, and structural richness. However, standard machine learning algorithms typically scale exponentially with data volume and complexity of cross-modal couplings - the so called curse of dimensionality - which is prohibitive to the analysis of large-scale, multi-modal and multi-relational datasets. Given that such data are often efficiently represented as multiway arrays or tensors, it is therefore timely and valuable for the multidisciplinary machine learning and data analytic communities to review low-rank tensor decompositions and tensor networks as emerging tools for dimensionality reduction and large scale optimization problems. Our particular emphasis is on elucidating that, by virtue of the underlying low-rank approximations, tensor networks have the ability to alleviate the curse of dimensionality in a number of applied areas. In Part 1 of this monograph we provide innovative solutions to low-rank tensor network decompositions and easy to interpret graphical representations of the mathematical operations on tensor networks. Such a conceptual insight allows for seamless migration of ideas from the flat-view matrices to tensor network operations and vice versa, and provides a platform for further developments, practical applications, and non-Euclidean extensions. It also permits the introduction of various tensor network operations without an explicit notion of mathematical expressions, which may be beneficial for many research communities that do not directly rely on multilinear algebra. Our focus is on the Tucker and tensor train (TT) decompositions and their extensions, and on demonstrating the ability of tensor networks to provide linearly or even super-linearly (e.g., logarithmically) scalable solutions, as illustrated in detail in Part 2 of this monograph.
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Journal articleMoore AH, Peso P, Naylor PA, 2016,
Speech enhancement for robust automatic speech recognition: Evaluation using a baseline system and instrumental measures
, Computer Speech and Language, Vol: 46, Pages: 574-584, ISSN: 1095-8363Automatic speech recognition in everyday environments must be robust to significant levels of reverberation andnoise. One strategy to achieve such robustness is multi-microphone speech enhancement. In this study, we presentresults of an evaluation of different speech enhancement pipelines using a state-of-the-artASRsystem for a widerange of reverberation and noise conditions. The evaluation exploits the recently released ACE Challenge databasewhich includes measured multichannel acoustic impulse responses from 7 different rooms with reverberation timesranging from 0.33 s to 1.34 s. The reverberant speech is mixed with ambient, fan and babble noise recordings madewith the same microphone setups in each of the rooms. In the first experiment performance of theASRwithoutspeech processing is evaluated. Results clearly indicate the deleterious effect of both noise and reverberation. In thesecond experiment, different speech enhancement pipelines are evaluated with relative word error rate reductions ofup to 82%. Finally, the ability of selected instrumental metrics to predictASRperformance improvement is assessed.The best performing metric, Short-Time Objective Intelligibility Measure, is shown to have a Pearson correlationcoefficient of 0.79, suggesting that it is a useful predictor of algorithm performance in these tests.
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Conference paperLiu Q, Manikas A, 2016,
Experimental Comparison of Localisation Techniques in the Presence of Array Uncertainties
, European Conference on Antennas and Propagation (EuCAP) -
Conference paperDionelis N, Brookes M, 2016,
Active speech level estimation in noisy signals with quadrature noise suppression
, European Signal Processing Conference ( EUSIPCO'16), Publisher: IEEE, ISSN: 2076-1465We present a noise-robust algorithm for estimating the active level ofspeech, which is the average speech power during intervals of speechactivity. The proposed algorithm uses the clean speech phase to removethe quadrature noise component from the short-time powerspectrum of the noisy speech, as well as SNR-dependent techniquesto improve the estimation. The pitch of voiced speech frames isdetermined using a noise-robust pitch tracker and the speech levelis estimated from the energy of the pitch harmonics using the harmonicsummation principle. At low noise levels, the resultant activespeech level estimate is combined with that from the standardizedITU-T P.56 algorithm to give a final composite estimate. The algorithmhas been evaluated using a range of noise signals and givesconsistently lower errors than previous methods and than the ITU-TP.56 algorithm, which is accurate for SNR levels of above 15 dB.
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Journal articleSridhar V, Gabillard T, Manikas A, 2016,
Spatiotemporal-MIMO channel estimator and beamformer for 5G
, IEEE Transactions on Wireless Communications, Vol: 15, Pages: 8025-8038, ISSN: 1536-1276With requirements of spiraling data rates and limited spectrum availability, there is an increased interest in mm-wave beamformer-based communications for 5G. For upcoming cellular networks, the critical point is to exploit the increased number of employable antennas at both Tx and Rx to: 1) combat increased path loss; 2) tackle higher interference due to higher user density; and 3) handle multipath effects in frequency selective channels. Toward this, a multi-beam spatiotemporal superresolution beamforming framework is proposed in this paper as a promising candidate to design beampatterns that mitigate/suppress co-channel interference and deliver massive gain in the desired directions. Initially, channel and signal models suitable for the mm-wave MIMO system are presented using the manifold vectors of both Tx and Rx antenna arrays. Based on these models, a novel subspace-based channel estimator is employed, which estimates delays, directions, velocities, and fading coefficients of the desired signal paths. This information is then exploited by the proposed spatiotemporal beamformer to provide a massive array gain that combats path loss without increasing the number of antenna array elements and to be tolerant to the near-far problem in a high interference environment. The performance of the proposed channel estimator and beamformer is examined using computer simulation studies.
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Conference paperDorfan Y, Evers C, Gannot S, et al., 2016,
Speaker Localization with Moving Microphone Arrays
, European Signal Processing Conference (EUSIPCO), Publisher: IEEE, ISSN: 2076-1465Speaker localization algorithms often assume staticlocation for all sensors. This assumption simplifies the modelsused, since all acoustic transfer functions are linear time invariant.In many applications this assumption is not valid. Inthis paper we address the localization challenge with movingmicrophone arrays. We propose two algorithms to find thespeaker position. The first approach is a batch algorithm basedon the maximum likelihood criterion, optimized via expectationmaximizationiterations. The second approach is a particle filterfor sequential Bayesian estimation. The performance of bothapproaches is evaluated and compared for simulated reverberantaudio data from a microphone array with two sensors.
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Journal articleRassouli B, Clerckx B, 2016,
On the capacity of vector Gaussian channels with bounded inputs
, IEEE Transactions on Information Theory, Vol: 62, Pages: 6884-6903, ISSN: 0018-9448The capacity of a deterministic multiple-input multiple-output channel under the peak and average power constraints is investigated. For the identity channel matrix, the approach of Shamai et al. is generalized to the higher dimension settings to derive the necessary and sufficient conditions for the optimal input probability density function. This approach prevents the usage of the identity theorem of the holomorphic functions of several complex variables which seems to fail in the multi-dimensional scenarios. It is proved that the support of the capacity-achieving distribution is a finite set of hyper-spheres with mutual independent phases and amplitude in the spherical domain. Subsequently, it is shown that when the average power constraint is relaxed, if the number of antennas is large enough, the capacity has a closed-form solution and constant amplitude signaling at the peak power achieves it. Moreover, it will be observed that in a discrete-time memoryless Gaussian channel, the average power constrained capacity, which results from a Gaussian input distribution, can be closely obtained by an input where the support of its magnitude is a discrete finite set. Finally, we investigate some upper and lower bounds for the capacity of the non-identity channel matrix and evaluate their performance as a function of the condition number of the channel.
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Conference paperMoore AH, Evers C, Naylor PA, 2016,
2D direction of arrival estimation of multiple moving sources using a spherical microphone array
, European Signal Processing Conference, Publisher: IEEE, ISSN: 2219-5491Direction of arrival estimation using a spherical microphonearray is an important and growing research area. One promisingalgorithm is the recently proposed Subspace PseudoIntensityVector method. In this contribution the SubspacePseudo-Intensity Vector method is combined with a state-ofthe-artmethod for robustly estimating the centres of mass in a2D histogram based on matching pursuits. The performanceof the improved Subspace Pseudo-Intensity Vector method isevaluated in the context of localising multiple moving sourceswhere it is shown to outperform competing methods in termsof clutter rate and the number of missed detections whilstremaining comparable in terms of localisation accuracy.
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Conference paperHafezi S, Moore AH, Naylor PA, 2016,
Multiple source localization in the spherical harmonic domain using augmented intensity vectors based on grid search
, European Signal Processing Conference, Publisher: IEEE, ISSN: 2219-5491Multiple source localization is an important task in acousticsignal processing with applications including dereverberation,source separation, source tracking and environmentmapping. When using spherical microphone arrays, it hasbeen previously shown that Pseudo-intensity Vectors (PIV),and Augmented Intensity Vectors (AIV), are an effective approachfor direction of arrival estimation of a sound source.In this paper, we evaluate AIV-based localization in acousticscenarios involving multiple sound sources. Simulations areconducted where the number of sources, their angular separationand the reverberation time of the room are varied. Theresults indicate that AIV outperforms PIV and Steered ResponsePower (SRP) with an average accuracy between 5 and10 degrees for sources with angular separation of 30 degreesor more. AIV also shows better robustness to reverberationtime than PIV and SRP.
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Journal articleClerckx B, Bayguzina E, 2016,
Waveform design for Wireless Power Transfer
, IEEE Transactions on Signal Processing, Vol: 64, Pages: 6313-6328, ISSN: 1053-587XFar-field Wireless Power Transfer (WPT) has attracted significant attention in recent years. Despite the rapid progress, the emphasis of the research community in the last decade has remained largely concentrated on improving the design of energy harvester (so-called rectenna) and has left aside the effect of transmitter design. In this paper, we study the design of transmit waveform so as to enhance the dc power at the output of the rectenna. We derive a tractable model of the nonlinearity of the rectenna and compare with a linear model conventionally used in the literature. We then use those models to design novel multisine waveforms that are adaptive to the channel state information (CSI). Interestingly, while the linear model favours narrowband transmission with all the power allocated to a single frequency, the nonlinear model favours a power allocation over multiple frequencies. Through realistic simulations, waveforms designed based on the nonlinear model are shown to provide significant gains (in terms of harvested dc power) over those designed based on the linear model and over nonadaptive waveforms. We also compute analytically the theoretical scaling laws of the harvested energy for various waveforms as a function of the number of sinewaves and transmit antennas. Those scaling laws highlight the benefits of CSI knowledge at the transmitter in WPT and of a WPT design based on a nonlinear rectenna model over a linear model. Results also motivate the study of a promising architecture relying on large-scale multisine multiantenna waveforms for WPT. As a final note, results stress the importance of modeling and accounting for the nonlinearity of the rectenna in any system design involving wireless power.
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Conference paperDragotti P, Murray-Bruce M, 2016,
Solving physics-driven inverse problems via structured least squares
, EUSIPCO 2016, Publisher: IEEE, Pages: 331-335, ISSN: 2076-1465Numerous physical phenomena are well modeled by partialdifferential equations (PDEs); they describe a wide range ofphenomena across many application domains, from model-ing EEG signals in electroencephalography to, modeling therelease and propagation of toxic substances in environmentalmonitoring. In these applications it is often of interest to findthe sources of the resulting phenomena, given some sparsesensor measurements of it. This will be the main task of thiswork. Specifically, we will show that finding the sources ofsuch PDE-driven fields can be turned into solving a class ofwell-known multi-dimensional structured least squares prob-lems. This link is achieved by leveraging from recent resultsin modern sampling theory – in particular, the approximateStrang-Fix theory. Subsequently, numerical simulation re-sults are provided in order to demonstrate the validity androbustness of the proposed framework.
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Conference paperEvers C, Moore A, Naylor P, 2016,
Localization of Moving Microphone Arrays from Moving Sound Sources for Robot Audition
, European Signal Processing Conference (EUSIPCO), Publisher: IEEE, ISSN: 2076-1465Acoustic Simultaneous Localization and Mapping(a-SLAM) jointly localizes the trajectory of a microphone arrayinstalled on a moving platform, whilst estimating the acousticmap of surrounding sound sources, such as human speakers.Whilst traditional approaches for SLAM in the vision and opticalresearch literature rely on the assumption that the surroundingmap features are static, in the acoustic case the positions oftalkers are usually time-varying due to head rotations and bodymovements. This paper demonstrates that tracking of movingsources can be incorporated in a-SLAM by modelling the acousticmap as a Random Finite Set (RFS) of multiple sources andexplicitly imposing models of the source dynamics. The proposedapproach is verified and its performance evaluated for realisticsimulated data.
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Journal articleArtuso M, Boviz D, Checko A, et al., 2016,
Enhancing LTE with Cloud-RAN and Load- Controlled Parasitic Antenna Arrays
, IEEE COMMUNICATIONS MAGAZINE, Vol: 54, Pages: 183-191, ISSN: 0163-6804 -
Journal articleTalebi SP, Kanna S, Mandic DP, 2016,
A Distributed Quaternion Kalman Filter With Applications to Smart Grid and Target Tracking
, IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS, Vol: 2, Pages: 477-488, ISSN: 2373-776X -
Journal articleEnshaeifar S, Took CC, Park C, et al., 2016,
Quaternion Common Spatial Patterns
, IEEE TRANSACTIONS ON NEURAL SYSTEMS AND REHABILITATION ENGINEERING, Vol: 25, Pages: 1278-1286, ISSN: 1534-4320A novel quaternion-valued common spatial patterns (QCSP) algorithm is introduced to model co-channel coupling of multi-dimensional processes. To cater for the generality of quaternion-valued non-circular data, we propose a generalized QCSP (G-QCSP) which incorporates the information on power difference between the real and imaginary parts of data channels. As an application, we demonstrate how G-QCSP can be used to provide high classification rates, even at a signal-to-noise ratio (SNR) as low as -10 dB. To illustrate the usefulness of our method in EEG analysis, we employ G-QCSP to extract features for discriminating between imagery left and right hand movements. The classification accuracy using these features is 70%. Furthermore, the proposed method is used to distinguish between Parkinson's disease (PD) patients and healthy control subjects, providing an accuracy of 87%.
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Journal articlevon Rosenberg W, Chanwimalueang T, Goverdovsky V, et al., 2016,
Smart helmet: wearable multichannel ECG & EEG
, IEEE Journal of Translational Engineering in Health and Medicine, Vol: 4, ISSN: 2168-2372Modern wearable technologies have enabled continuous recording of vital signs, however, for activities such as cycling, motor-racing, or military engagement, a helmet with embedded sensors would provide maximum convenience and the opportunity to monitor simultaneously both the vital signs and the electroencephalogram (EEG). To this end, we investigate the feasibility of recording the electrocardiogram (ECG), respiration, and EEG from face-lead locations, by embedding multiple electrodes within a standard helmet. The electrode positions are at the lower jaw, mastoids, and forehead, while for validation purposes a respiration belt around the thorax and a reference ECG from the chest serve as ground truth to assess the performance. The within-helmet EEG is verified by exposing the subjects to periodic visual and auditory stimuli and screening the recordings for the steady-state evoked potentials in response to these stimuli. Cycling and walking are chosen as real-world activities to illustrate how to deal with the so-induced irregular motion artifacts, which contaminate the recordings. We also propose a multivariate R-peak detection algorithm suitable for such noisy environments. Recordings in real-world scenarios support a proof of concept of the feasibility of recording vital signs and EEG from the proposed smart helmet.
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Journal articleLiu A, Lau VKN, Dai W, 2016,
Exploiting burst-sparsity in massive MIMO with partial channel support information
, IEEE Transactions on Wireless Communications, Vol: 15, Pages: 7820-7830, ISSN: 1536-1276How to obtain accurate channel state information at the base station (CSIT) is a key implementation challenge behind frequency-division duplex massive MIMO systems. Recently, compressive sensing (CS) has been applied to reduce pilot and CSIT feedback overheads in massive MIMO systems by exploiting the underlying channel sparsity. However, brute-force applications of standard CS may not lead to good performance in massive MIMO systems, because standard sparse recovery algorithms have quite a stringent requirement on the sparsity level for robust recovery and this severely limits the operating regime of the solution. Moreover, since the channel support is usually correlated across time, it is possible to obtain partial channel support information (P-CSPI) from previously estimated channel support. Motivated by the above observations, we propose a P-CSPI aided burst Least Absolute Shrinkage and Selection Operator (LASSO) algorithm to exploit both the P-CSPI and additional structured properties of the sparsity, namely, the burst sparsity in massive MIMO channels. We also accurately characterize the asymptotic channel estimation error of the P-CSPI aided burst LASSO algorithm. Both the analysis and simulations show that the P-CSPI aided burst LASSO algorithm can alleviate the stringent requirement on the sparsity level for robust channel recovery and substantially enhance the channel estimation performance over existing solutions.
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Journal articleJoudeh H, Clerckx B, 2016,
Sum-rate maximization for linearly precoded downlink multiuser MISO systems with partial CSIT: a rate-splitting approach
, IEEE Transactions on Communications, Vol: 64, Pages: 4847-4861, ISSN: 0090-6778This paper considers the sum-rate (SR) maximization problem in downlink multi-user multiple input simgle output (MU-MISO) systems under imperfect channel state information at the transmitter (CSIT). Contrary to existing works, we consider a rather unorthodox transmission scheme. In particular, the message intended to one of the users is split into two parts: a common part which can be recovered by all users, and a private part recovered by the corresponding user. On the other hand, the rest of users receive their information through private messages. This rate-splitting (RS) approach was shown to boost the achievable degrees of freedom when CSIT errors decay with increased SNR. In this paper, the RS strategy is married with linear precoder design and optimization techniques to achieve a maximized ergodic SR (ESR) performance over the entire range of SNRs. Precoders are designed based on partial CSIT knowledge by solving a stochastic rate optimization problem using means of sample average approximation coupled with the weighted minimum mean square error approach. Numerical results show that in addition to the ESR gains, the benefits of RS also include relaxed CSIT quality requirements and enhanced achievable rate regions compared with conventional transmission with no rate-splitting.
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Conference paperWang Z, Ling C, 2016,
Symmetric mettropolis-within-Gibbs algorithm for lattice Gaussian sampling
, IEEE Information theory workshop, Publisher: IEEEAs a key sampling scheme in Markov chain MonteCarlo (MCMC) methods, Gibbs sampling is widely used invarious research fields due to its elegant univariate conditionalsampling, especially in tacking with multidimensional samplingsystems. In this paper, a Gibbs-based sampler named as symmet-ric Metropolis-within-Gibbs (SMWG) algorithm is proposed forlattice Gaussian sampling. By adopting a symmetric Metropolis-Hastings (MH) step into the Gibbs update, we show the Markovchain arising from it is geometrically ergodic, which convergesexponentially fast to the stationary distribution. Moreover, byoptimizing its symmetric proposal distribution, the convergenceefficiency can be further enhanced.
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Conference paperCampello A, Ling C, Belfiore J-C, 2016,
Algebraic lattices achieve the capacity of the ergodic fading channel
, IEEE Information Theory Workshop, Publisher: IEEEIn this work we show that algebraic lattices con-structed from error-correcting codes achieve the ergodic capacityof the fading channel. The main ingredients for our constructionare a generalized version of the Minkowski-Hlawka theorem andshaping techniques based on the lattice Gaussian distribution.The structure of the ring of integers in a number field playsan important role in the proposed construction. In the caseof independent and identically distributed fadings, the latticesconsidered exhibit full diversity and an exponential decay of theprobability of error with respect to the blocklength.
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Conference paperXue W, Brookes DM, Naylor PA, 2016,
Under-modelled blind system identification for time delay estimation in reverberant environments
, 15th International Workshop on Acoustic Signal Enhancement (IWAENC), Publisher: IEEEIn multichannel systems, acoustic time delay estimation (TDE) is a challenging problem in reverberant environments. Although blind system identification (BSI) based methods have been proposed which utilize a realistic signal model for the room impulse response (RIR), their TDE performance depends strongly on that of the BSI, which is often inaccurate in practice when the identified responses are under-modelled. In this paper, we propose a new under-modelled BSI based method for TDE in reverberant environments. An under-modelled BSI algorithm is derived, which is based on maximizing the cross-correlation of the cross-filtered signals rather than minimizing the cross-relation error, and also exploits the sparsity of the early part of the RIR. For TDE, this new criterion can be viewed as a generalization of conventional cross-correlation-based TDE methods by considering a more realistic model for the early RIR. Depending on the microphone spacing, only a short early part of each RIR is identified, and the time delays are estimated based on the peak locations in the identified early RIRs. Experiments in different reverberant environments with speech source signals demonstrate the effectiveness of the proposed method.
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Conference paperLing C, 2016,
Achieving capacity and security in wireless communications with lattice codes
, International Symposium on Turbo Codes & Iterative Information Processing, Publisher: IEEEBased on lattice Gaussian distributions and ideallattices, we present a unified framework of lattice coding toachieve the channel capacity and secrecy capacity of wirelesschannels in the presence of Gaussian noise. The standard additivewhite Gaussian-noise (AWGN) channel, block fading channel, andmulti-input multi-output (MIMO) fading channel are considered,which form a hierarchy of increasingly challenging problems incoding theory. To achieve channel capacity, we apply Gaussianshaping to a suitably defined good lattice for channel coding.To achieve secrecy capacity, we use a secrecy-good lattice nestedwith a coding lattice.
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Journal articleKoulouri A, Brookes DM, Rimpiläinen V, 2016,
Vector tomography for reconstructing electric elds with non-zero divergence in bounded domains
, Journal of Computational Physics, Vol: 329, Pages: 73-90, ISSN: 0021-9991In vector tomography (VT), the aim is to reconstruct an unknown multi-dimensional vector field using line integral data. In the case of a 2-dimensional VT, two types of line integral data are usually required. These data correspond to integration of the parallel and perpendicular projection of the vector field along the integration lines and are called the longitudinal and transverse measurements, respectively. In most cases, however, the transverse measurements cannot be physically acquired. Therefore, the VT methods are typically used to reconstruct divergence-free (or source-free) velocity and flow fields that can be reconstructed solely from the longitudinal measurements. In this paper, we show how vector fields with non-zero divergence in a bounded domain can also be reconstructed from the longitudinal measurements without the need of explicitly evaluating the transverse measurements. To the best of our knowledge, VT has not previously been used for this purpose. In particular, we study low-frequency, time-harmonic electric fields generated by dipole sources in convex bounded domains which arise, for example, in electroencephalography (EEG) source imaging. We explain in detail the theoretical background, the derivation of the electric field inverse problem and the numerical approximation of the line integrals. We show that fields with non-zero divergence can be reconstructed from the longitudinal measurements with the help of two sparsity constraints that are constructed from the transverse measurements and the vector Laplace operator. As a comparison to EEG source imaging, we note that VT does not require mathematical modeling of the sources. By numerical simulations, we show that the pattern of the electric field can be correctly estimated using VT and the location of the source activity can be determined accurately from the reconstructed magnitudes of the field.
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Journal articleXiang M, Took CC, Mandic DP, 2016,
Cost-effective quaternion minimum mean square error estimation: From widely linear to four-channel processing
, Signal Processing, Vol: 136, Pages: 81-91, ISSN: 0165-1684Widely linear estimation plays an important role in quaternion signal processing, as it caters for both proper and improper quaternion signals. However, widely linear algorithms are computationally expensive owing to the use of augmented variables and statistics. To reduce the computation cost while maintaining the performance level, we propose a four-channel estimation framework as an efficient alternative to quaternion widely linear estimation. This is achieved by using four linear models to estimate the four components of quaternion signals. We also show that any of the four channels is able to replace a strictly linear quaternion estimator when estimating strictly linear systems. The proposed method is shown to reduce computational complexity and provide more flexible algorithms, while preserving the physical meaning inherent in the quaternion domain. The proposed framework is next applied to quaternion minimum mean square error estimation to yield the reduced-complexity versions of the quaternion least mean square (QLMS), quaternion recursive least squares (QRLS), and quaternion nonlinear gradient decent (QNGD) algorithms. For the proposed QLMS algorithm, an adaptive step-size strategy is also explored. The effectiveness of the so introduced estimation techniques is validated by simulations on synthetic and real-world signals.
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