Results 1  10
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16
Penalty functionbased joint diagonalization approach for convolutive blind separation of nonstationary sources
 IEEE Transactions on Signal Processing
, 2005
"... Abstract—A new approach for convolutive blind source separation (BSS) by explicitly exploiting the secondorder nonstationarity of signals and operating in the frequency domain is proposed. The algorithm accommodates a penalty function within the crosspower spectrumbased cost function and thereby ..."
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Cited by 13 (1 self)
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Abstract—A new approach for convolutive blind source separation (BSS) by explicitly exploiting the secondorder nonstationarity of signals and operating in the frequency domain is proposed. The algorithm accommodates a penalty function within the crosspower spectrumbased cost function and thereby converts the separation problem into a joint diagonalization problem with unconstrained optimization. This leads to a new member of the family of joint diagonalization criteria and a modification of the search direction of the gradientbased descent algorithm. Using this approach, not only can the degenerate solution induced by a null unmixing matrix and the effect of large errors within the elements of covariance matrices at lowfrequency bins be automatically removed, but in addition, a unifying view to joint diagonalization with unitary or nonunitary constraint is provided. Numerical experiments are presented to verify the performance of the new method, which show that a suitable penalty function may lead the algorithm to a faster convergence and a better performance for the separation of convolved speech signals, in particular, in terms of shape preservation and amplitude ambiguity reduction, as compared with the conventional secondorder based algorithms for convolutive mixtures that exploit signal nonstationarity. Index Terms—Blind source separation, convolutive mixtures, frequency domain, orthogonal/nonorthogonal constraints, penalty function, speech signals. I.
A joint diagonalization method for convolutive blind separation of nonstationary sources
 in the frequency domain,” Proc
"... A joint diagonalization algorithm for convolutive blind source separation by explicitly exploiting the nonstationarity and second order statistics of signals is proposed. The algorithm incorporates a nonunitary penalty term within the crosspower spectrum based cost function in the frequency domain ..."
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Cited by 10 (6 self)
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A joint diagonalization algorithm for convolutive blind source separation by explicitly exploiting the nonstationarity and second order statistics of signals is proposed. The algorithm incorporates a nonunitary penalty term within the crosspower spectrum based cost function in the frequency domain. This leads to a modification of the search direction of the gradientbased descent algorithm and thereby yields more robust convergence performance. Simulation results show that the algorithm leads to faster speed of convergence, together with a better performance for the separation of the convolved speech signals, in particular in terms of shape preservation and amplitude ambiguity reduction, as compared to Parra’s nonstationary algorithm for convolutive mixtures. 1.
Penalty function based joint diagonalization approach for convolutive blind separation of nonstationary sources
 IEEE Trans. Sig. Proc
, 2004
"... In this paper, we address convolutive blind source separation (BSS) of speech signals in the frequency domain and explicitly exploit the second order statistics (SOS) of nonstationary signals. Based on certain constraints on the BSS solution, we propose to reformulate the problem as an unconstrain ..."
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Cited by 8 (6 self)
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In this paper, we address convolutive blind source separation (BSS) of speech signals in the frequency domain and explicitly exploit the second order statistics (SOS) of nonstationary signals. Based on certain constraints on the BSS solution, we propose to reformulate the problem as an unconstrained optimization problem by using nonlinear programming techniques. The proposed algorithm therefore utilizes penalty functions with the crosspower spectrum based criterion and thereby converts the task into a joint diagonalization problem with unconstrained optimization. Using this approach, not only can the degenerate solution induced by a null unmixing matrix and the overlearning effect existing at low frequency bins be automatically removed, but a unifying view to joint diagonalization with unitary or nonunitary constraint is provided. Numerical experiments verify the validity of the proposed approach. 1.
Y.H.: A framework of constraint preserving update schemes for optimization on Stiefel manifold
 Institue of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Sciences, Chinese Academy of Sicences (2012
"... ar ..."
On Using Exact Joint Diagonalization for Noniterative Approximate Joint Diagonalization
"... Abstract—We propose a novel, noniterative approach for the problem of nonunitary, leastsquares (LS) approximate joint diagonalization (AJD) of several Hermitian target matrices. Dwelling on the fact that exact joint diagonalization (EJD) of two Hermitian matrices can almost always be easily obtaine ..."
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Cited by 3 (1 self)
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Abstract—We propose a novel, noniterative approach for the problem of nonunitary, leastsquares (LS) approximate joint diagonalization (AJD) of several Hermitian target matrices. Dwelling on the fact that exact joint diagonalization (EJD) of two Hermitian matrices can almost always be easily obtained in closed form, we show how two “representative matrices ” can be constructed out of the original set of all target matrices, such that their EJD would be useful in the AJD of the original set. Indeed, for the twobytwo case, we show that the EJD of the representative matrices yields the optimal AJD solution. For largerscale cases, the EJD can provide a suboptimal AJD solution, possibly serving as a good initial guess for a subsequent iterative algorithm. Additionally, we provide an informative lower bound on the attainable LS fit, which is useful in gauging the distance of prospective solutions from optimality. Index Terms—Blind source separation, independent components analysis, nonunitary approximate joint diagonalization. I.
Blind MIMO Identification Using the Second Characteristic Function
"... Abstract—We propose a new approach for the blind identification of a multiinputmultioutput (MIMO) system. As a substitute to using “classical ” highorder statistics (HOS) in the form of timelagged joint cumulants, or polyspectra, we use the estimated Hessian matrices of the second joint general ..."
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Cited by 2 (0 self)
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Abstract—We propose a new approach for the blind identification of a multiinputmultioutput (MIMO) system. As a substitute to using “classical ” highorder statistics (HOS) in the form of timelagged joint cumulants, or polyspectra, we use the estimated Hessian matrices of the second joint generalized characteristic function of timelagged observations, evaluated at several preselected “processingpoints. ” These matrices admit straightforward consistent estimates, whose statistical stability can be finely tuned (by proper selection of the processingpoints)—in contrast to classical HOS. Transforming the obtained matrix sequence into the frequencydomain, we obtain (and solve) a sequence of frequencydependent joint diagonalization problems. This yields a set of estimated frequency response matrices, which are transformed back into the time domain after resolving frequencydependent phase and permutation ambiguities. The performance of the proposed algorithm depends on the choice of processingpoints, yet compares favorably with other algorithms, especially at moderate signaltonoise ratio conditions, as we demonstrate in simulation results. Index Terms—Blind MIMO Deconvolution, blind MIMO identification, characteristic function, convolutive blind source separation, joint diagonalization, permutation ambiguity, phase ambiguity. I.
Blind identification using secondorder statistics: a nonstationarity and nonwhiteness approach
 in Proc. IEEE ICASSP’05
"... We consider an approach to the blind identification problem of instantaneous mixtures using secondorder statistics through the nonstationarity and nonwhiteness properties of signals. We propose the use of natural gradient learning to form offline/block processing (BP) and online processing (OP) a ..."
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Cited by 2 (2 self)
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We consider an approach to the blind identification problem of instantaneous mixtures using secondorder statistics through the nonstationarity and nonwhiteness properties of signals. We propose the use of natural gradient learning to form offline/block processing (BP) and online processing (OP) algorithms suitable respectively for blind identification with batch data and online data and show that the proposed algorithms can be considered as a class of algorithms offering quasiuniform performance. The identifiability conditions are presented which provide a key insight into these algorithms. The paper shows simulation results and concludes with some connections of the proposed algorithms to other existing algorithms. 1.
Mimo instantaneous blind identification based on secondorder temporal structure,” Signal Processing
 IEEE Transactions on
, 2008
"... Abstract—Blind identification is a crucial subtask in signal processing problems such as blind signal separation (BSS) and directionofarrival (DOA) estimation. This paper presents a procedure for multipleinput multipleoutput instantaneous blind identification based on secondorder temporal prope ..."
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Cited by 2 (2 self)
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Abstract—Blind identification is a crucial subtask in signal processing problems such as blind signal separation (BSS) and directionofarrival (DOA) estimation. This paper presents a procedure for multipleinput multipleoutput instantaneous blind identification based on secondorder temporal properties of the signals, such as coloredness and nonstationarity. The procedure consists of two stages. First, based on assumptions on the secondorder temporal structure (SOTS) of the source and noise signals, and using subspace techniques, the problem is reformulated in a particular way such that each column of the unknown mixing matrix satisfies a system of multivariate homogeneous polynomial equations. Then, this nonlinear system of equations is solved by means of a socalled homotopy method, which provides a general tool for solving (possibly nonexact) systems of nonlinear equations by smoothly deforming the known solutions of a simple start system into the desired solutions of the target system. Our blind identification procedure allows to estimate the mixing matrix for scenarios with more sources than sensors without resorting to sparsity assumptions, something that is often believed to be impossible when using only secondorder statistics. In addition, since our algorithm does not require any assumption on the mixing matrix, also mixing matrices that are rankdeficient or even have identical columns can be identified. Finally, we give examples and performance results for speech source signals. Index Terms—Blind identification/separation, homogeneous system, homotopy, secondorder statistics, temporal structure.
Penalty Function Approach for Constrained Convolutive Blind Source Separation
"... Abstract. A new approach for convolutive blind source separation (BSS) using penalty functions is proposed in this paper. Motivated by nonlinear programming techniques for the constrained optimization problem, it converts the convolutive BSS into a joint diagonalization problem with unconstrained op ..."
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Cited by 1 (1 self)
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Abstract. A new approach for convolutive blind source separation (BSS) using penalty functions is proposed in this paper. Motivated by nonlinear programming techniques for the constrained optimization problem, it converts the convolutive BSS into a joint diagonalization problem with unconstrained optimization. Theoretical analyses together with numerical evaluations reveal that the proposed method not only improves the separation performance by significantly reducing the effect of large errors within the elements of covariance matrices at low frequency bins and removes the degenerate solution induced by a null unmixing matrix, but also provides an unified framework to constrained BSS. 1