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14
Performance analysis of l0 norm constraint least mean square algorithm
 IEEE Transactions on Signal Processing
, 2012
"... As one of the recently proposed algorithms for sparse system identification, l0 norm constraint Least Mean Square (l0LMS) algorithm modifies the cost function of the traditional method with a penalty of tapweight sparsity. The performance of l0LMS is quite attractive compared with its various pre ..."
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As one of the recently proposed algorithms for sparse system identification, l0 norm constraint Least Mean Square (l0LMS) algorithm modifies the cost function of the traditional method with a penalty of tapweight sparsity. The performance of l0LMS is quite attractive compared with its various precursors. However, there has been no detailed study of its performance. This paper presents comprehensive theoretical performance analysis of l0LMS for white Gaussian input data based on some assumptions which are reasonable in a large range of parameter setting. Expressions for steadystate mean square deviation (MSD) are derived and discussed with respect to algorithm parameters and system sparsity. The parameter selection rule is established for achieving the best performance. Approximated with Taylor series, the instantaneous behavior is also derived. In addition, the relationship between l0LMS and some previous arts and the sufficient conditions for l0LMS to accelerate convergence are set up. Finally, all of the theoretical results are compared with simulations and are shown to agree well in a wide range of parameters.
The lms, pnlms, and exponentiated gradient algorithms
 in Proc. European Signal Processing Conf
, 2004
"... Sparse impulse responses are encountered in many applications (network and acoustic echo cancellation, feedback cancellation in hearing aids, etc). Recently, a class of exponentiated gradient (EG) algorithms has been proposed. One of the algorithms belonging to this class, the socalled EG ± alg ..."
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Sparse impulse responses are encountered in many applications (network and acoustic echo cancellation, feedback cancellation in hearing aids, etc). Recently, a class of exponentiated gradient (EG) algorithms has been proposed. One of the algorithms belonging to this class, the socalled EG ± algorithm, converges and tracks much better than the classical stochastic gradient, or LMS, algorithm for sparse impulse responses. In this paper, we show how to derive the different algorithms. We analyze the EG ± algorithm and explain when to expect it to behave like the LMS algorithm. It is also shown that the proportionate normalized LMS (PNLMS) algorithm proposed by Duttweiler in the context of network echo cancellation is an approximation of the EG±. 1.
1 A PrimalDual Proximal Algorithm for Sparse TemplateBased Adaptive Filtering: Application to Seismic Multiple Removal
"... Abstract—Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured “noises”. As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. W ..."
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Abstract—Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured “noises”. As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wavefield bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for timevarying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimonypromoting wavelet frames. The designed primaldual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signaltonoise ratio conditions, both for simulated and real field seismic data. Index Terms—Convex optimization, Parallel algorithms, Wavelet transforms, Adaptive filters, Geophysical signal processing, Signal restoration, Sparsity, Signal separation.
Signal modality characterisation using collaborative adaptive filters
 in 1st IAPR Workshop on Cognitive Information Process
, 2008
"... A method for extracting information (or knowledge) about the nature of a signal is presented, this is achieved by tracking the dynamics of the mixing parameter within a hybrid filter rather than the actual filter performance. Implementations of the hybrid filter for tracking the nonlinearity and the ..."
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A method for extracting information (or knowledge) about the nature of a signal is presented, this is achieved by tracking the dynamics of the mixing parameter within a hybrid filter rather than the actual filter performance. Implementations of the hybrid filter for tracking the nonlinearity and the sparsity of a signal are illustrated and simulations on benchmark synthetic data in a prediction configuration support the analysis. It is then shown that by combining the information obtained from both hybrid filters it is possible to use this method to gain a more complete understanding of the nature of signals and changes in signal modality. Index Terms — adaptive filters, collaborative signal processing, distributed signal processing, signal modality characterisation 1.
LEARNING SPARSE SYSTEMS AT SUBNYQUIST RATES: A FREQUENCYDOMAIN APPROACH
"... We propose a novel algorithm for sparse system identification in the frequency domain. Key to our result is the observation that the Fourier transform of the sparse impulse response is a simple sum of complex exponentials, whose parameters can be efficiently determined from only a narrow frequency b ..."
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We propose a novel algorithm for sparse system identification in the frequency domain. Key to our result is the observation that the Fourier transform of the sparse impulse response is a simple sum of complex exponentials, whose parameters can be efficiently determined from only a narrow frequency band. From this perspective, we present a subNyquist sampling scheme, and show that the original continuoustime system can be learned by considering an equivalent lowrate discrete system. The impulse response of that discrete system can then be adaptively obtained by a novel frequencydomain LMS filter, which exploits the parametric structure of the model. Numerical experiments confirm the effectiveness of the proposed scheme for sparse system identification tasks. Index Terms — Sparse system identification, LMS, finite rate of innovation, subNyquist sampling. 1.
A Family of Robust Algorithms Exploiting Sparsity in Adaptive Filters
"... Abstract—We introduce a new family of algorithms to exploit sparsity in adaptive filters. It is based on a recently introduced new framework for designing robust adaptive filters. It results from minimizing a certain cost function subject to a timedependent constraint on the norm of the filter upd ..."
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Abstract—We introduce a new family of algorithms to exploit sparsity in adaptive filters. It is based on a recently introduced new framework for designing robust adaptive filters. It results from minimizing a certain cost function subject to a timedependent constraint on the norm of the filter update. Although in general this problem does not have a closedform solution, we propose an approximate one which is very close to the optimal solution. We take a particular algorithm from this family and provide some theoretical results regarding the asymptotic behavior of the algorithm. Finally, we test it in different environments for system identification and acoustic echo cancellation applications. Index Terms—Acoustic echo cancellation, adaptive filtering, impulsive noise, robust filtering, sparse systems. I.
A MODELBASED APPROACH FOR THE DEVELOPMENT OF LMS ALGORITHMS
"... The LMS algorithm is one of the most popular adaptive filter algorithms. Many variants of the algorithm have been developed for different applications. In this paper, we propose a unified modelbased approach for developing LMS algorithms. We use a number of probability density functions to model the ..."
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The LMS algorithm is one of the most popular adaptive filter algorithms. Many variants of the algorithm have been developed for different applications. In this paper, we propose a unified modelbased approach for developing LMS algorithms. We use a number of probability density functions to model the filtering error and the filter coefficients. The filter coefficients are determined by maximizing the posterior distribution function. We demonstrate that using this approach, we can not only develop existing LMS algorithms with further insights, we can also explore a number of new algorithms with certain desired properties such as robustness and sparseness. 1.
RESEARCH Design and complexity an
"... an s b re c ve ze S+ po it achieves optimal proportionate step size, it converges This paper is organized as follows. In Section 2, the Sun et al. EURASIP Journal on Wireless Communications and Networking 2014, 2014:14 ..."
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an s b re c ve ze S+ po it achieves optimal proportionate step size, it converges This paper is organized as follows. In Section 2, the Sun et al. EURASIP Journal on Wireless Communications and Networking 2014, 2014:14
C2 Justification of Budget
"... project. We expect the RA to be involved in both aspects of the project (theoretical and algorithmic), depending to an extent on the background of the person we manage to recruit. We have asked for level A step 6 which is the lowest level of appointment the ANU makes for someone with a PhD. The sala ..."
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project. We expect the RA to be involved in both aspects of the project (theoretical and algorithmic), depending to an extent on the background of the person we manage to recruit. We have asked for level A step 6 which is the lowest level of appointment the ANU makes for someone with a PhD. The salary for that position would be topped up with a market loading by RSISE because of the huge starting salaries offered in the machine learning field ($100,000US/yr for PhD graduates is not uncommon). We have built in standard annual increments. Programmer (ANU06) Although the majority of the work in this project will be theoretical the eventual goals are practical ones — the development of improved learning algorithms. In order to make honest assessments of the algorithms, and more significantly to attempt their deployment on a range of practical problems, we will need the use of a parttime programmer. We are asking for a programmer for 5 days a month at ANU06 level. This is at a salary that is typically commanded by a good programmer of the sort we seek (we are looking to final year computer science students who would be interested in this sort of parttime work). PhD Scholarships Machine learning is an attractive area for PhD students and we expect to be able to make considerable use of at least two students on this project. Their presence is necessary in order
Signal Processing for Sparse Discrete Time Systems
, 2013
"... In recent years compressive sampling (CS) has appeared in the signal processing literature as a legitimate contender for processing of sparse signals. Natural signals such as speech, image and video are compressible. In most signal processing systems dealing with these signals the signal is first sa ..."
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In recent years compressive sampling (CS) has appeared in the signal processing literature as a legitimate contender for processing of sparse signals. Natural signals such as speech, image and video are compressible. In most signal processing systems dealing with these signals the signal is first sampled and later on compressed. The philosophy of CS however is to sample and compress the signal at the same time. CS is finding applications in a wide variety of areas including medical imaging, seismology, cognitive radio, and channel estimation among others. Although CS has been given a great deal of attention in the past few years the theory is still naive and its fullest potential is still to be proven. The research in CS covers a wide span from theory of sampling and recovery algorithms to sampling device design to sparse CSbased signal processing applications. The contributions of this thesis are as follows; (i) The analogtoinformation converter (AIC) is the device that is designed to collect compressed samples. It is a replacement for the analogtodigital converter in a traditional signal processing system. We propose a modified structure for the AIC which leads to reducing the complexity of the current