D.-T. Pham. Blind separation of instantaneous mixture of sources based on order statistics. IEEE Transactions on Signal Processing, 48(2):363--375, 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Minimizing (12) is equivalent to maximizing the likelihood of the observations in a Gaussian stationary model where the DFT coe#cients are approximated as being normally and independently distributed. This is known as the Whittle approximation and and has been used for noise free ICA by Pham [5]. In the noise free case, the objective (12) boils down to a joint diagonalization criterion which can be optimized very e#ciently. Algorithms for the noisy case are briefly discussed next. Algorithmics We only hint at the algorithm issue of minimizing the mismatch (12) more details can be found ....

Dinh-Tuan Pham. Blind separation of instantaneous mixture of sources via the gaussian mutual information criterion. In Proc. EUSIPCO, pages 621--624, 2000.

....(24) and (25) the mutual information appears as a measure of the mean diagonality of (spectral) covariance matrices. They lead to simple separation techniques since an efficient algorithm exists for the joint diagonalization of a set of positive matrices. See [9] for the non stationary case and [8] for the time correlated case. Marginal mismatches The second term of decomposition (20) is a sum (22) of marginal mismatches. Their respective forms in the three models are Yn jP Sn ] T K[P yn jP sn ] 26) Si Yn jP Sn ] K(fEy n (t)gjf Fi Yn jP Sn ] K(fEj y n (l)j gjfDn (l)g) ....

....either in time (37) or in frequency (38) Due to space limitations, most proofs have been omitted paper. However most of the present material revisits other publications. See [3] for the geometry of the non Gaussian i.i.d. case, see [9] for mutual information in non stationary models and [8] for mutual information in temporally correlated models. Diversity This paper emphasizes the structural similarities between three models. The comparison could be pushed further in terms of estimating equations, adaptivity (estimation of the nuisance parameters) and stability conditions. However, ....

D. Pham. Blind separation of instantaneous mixture of sources via the Gaussian mutual information criterion. Signal Processing, (4):855--870, 2001.

....(24) and (25) the mutual information appears as a measure of the mean diagonality of (spectral) covariance matrices. They lead to simple separation techniques since an efficient algorithm exists for the joint diagonalization of a set of positive matrices. See [9] for the non stationary case and [8] for the time correlated case. Marginal mismatches The second term of decomposition (20) is a sum (22) of marginal mismatches. Their respective forms in the three models are T q (26) av u R 7 ) B v Q=R 7 d (27) av uV m 7 )n1 R v r 7 ....

....profiles either in time (37) or in frequency (38) Due to space limitations, most proofs have been omitted paper. However most of the present material revisits other publications. See [3] for the geometry of the non Gaussian i.i.d. case, see [9] for mutual information in non stationary models and [8] for mutual information in temporally correlated models. Diversity This paper emphasizes the structural similarities between three models. The comparison could be pushed further in terms of estimating equations, adaptivity (estimation of the nuisance parameters) and stability conditions. However, ....

D. Pham. Blind separation of instantaneous mixture of sources via the Gaussian mutual information criterion. Signal Processing, (4):855--870, 2001.

....On the other hand, if the source distributions are known, #ML is more appropriate because it expresses directly the fit between data and model. Also, #ML is easier to minimize because its gradient is easily estimated (see eq. 31) while estimating the gradient of #MI is computationally demanding [60]. Even when the source distributions are unknown, one may use #ML with hypothesized source distributions which only need to be close enough to the true distributions: recall sec. II C for a qualitative explanation and see sec. VI A for a quantitative statement and sec. V B about adapting the ....

D.-T. Pham. Blind separation of instantaneous mixture of sources via an independent component analysis. IEEE Trans. on Sig. Proc., 44(11):2768--2779, Nov. 1996.

....# E# (s)Es [#(s)s] 56) Note that the solution of (34) with H = H# then is the ML estimator based on the true model. It follows that the expression of ISR in (55) also is the asymptotic CramerRao bound for source separation i.e. the best achievable ISR rate with T independent samples (see [59], 70] 62] Since the achievable performance depends on the magnitude , this moment characterizes the hardness of the BSS problem with respect to source distribution. Not surprisingly, we can relate it to the non Gaussianity of the sources as follows. As above, denote # the score function for ....

D.-T. Pham. Blind separation of instantaneous mixture of sources via an independent component analysis. Research report RT 119, LMC IMAG, Grenoble, France, 1994.

....other hand, if the source distributions are known, OE ML is more appropriate because it expresses directly the fit between data and model. Also, OE ML is easier to minimize because its gradient is easily estimated (see eq. 31) while estimating the gradient of OE MI is computationally demanding [60]. Even when the source distributions are unknown, one may use OE ML with hypothesized source distributions which only need to be close enough to the true distributions: recall sec. II C for a qualitative explanation and see sec. VI A for a quantitative statement and sec. V B about adapting the ....

D.-T. Pham. Blind separation of instantaneous mixture of sources via an independent component analysis. IEEE Trans. on Sig. Proc., 44(11):2768--2779, Nov. 1996.

.... Gamma E [ s)s] 56) Note that the solution of (34) with H = H then is the ML estimator based on the true model. It follows that the expression of ISR in (55) also is the asymptotic Cram er Rao bound for source separation i.e. the best achievable ISR rate with T independent samples (see [59], 70] 62] Since the achievable performance depends on the magnitude of fl , this moment characterizes the hardness of the BSS problem with respect to source distribution. Not surprisingly, we can relate it to the non Gaussianity of the sources as follows. As above, denote the score ....

D.-T. Pham. Blind separation of instantaneous mixture of sources via an independent component analysis. Research report RT 119, LMC IMAG, Grenoble, France, 1994.

.... cost function as the criterion to select the so called least statistically dependent basis (LSDB) in the basis dictionary context [9] o , 243 aqp 3 r(ts ( 243 XT ( D (2) Now, we can define the LSDB as uwvVx y o , We were informed that Pham [10] had proposed the minimization of the same cost (2) earlier. We would like to point out the main difference between our work [9] and Pham s. We used the basis libraries such as wavelet packets and local Fourier bases that allow us to deal with datasets with large dimensions such as face images ....

D. T. Pham, "Blind separation of instantaneous mixture of sources via an independent component analysis, " IEEE Trans. Signal Process., vol. 44, no. 11, pp. 2768--2779, 1996.

....among artificial neural networks, information theory and signal processing and neurobiology. Recently, several researchers have focused their attention on this class of stochastic learning theories, with applications to blind separation of sources by the independent component analysis [1, 2, 3, 4, 5, 6, 16, 20], probability density estimation [1, 18, 7] self organizing classification [19] and blind system deconvolution [2, 8, 9] Also, some studies on neurobiological mechanisms have suggested interesting non linear models and information theoretic based learning theories [10, 11, 13, 14, 15] ....

D.T. PHAM, Blind separation of instantaneous mixtures of sources based on order statistics, IEEE Trans. on Signal processing, Vol. 48, No. 2, pp. 363 -- 375, Feb. 2000

....(24) and (25) the mutual information appears as a measure of the mean diagonality of (spectral) covariance matrices. They lead to simple separation techniques since an efficient algorithm exists for the joint diagonalization of a set of positive matrices. See [9] for the non stationary case and [8] for the time correlated case. Marginal mismatches The second term of decomposition (20) is a sum (22) of marginal mismatches. Their respective forms in the three models are ) 9 ) 9 9 ) 9 (26) 9 ) 9 DF 4 ) 27) 9 ) ....

....either in time (37) or in frequency (38) Due to space limitations, most proofs have been omitted paper. However most of the present material revisits other publications. See [3] for the geometry of the non Gaussian i.i.d. case, see [9] for mutual information in non stationary models and [8] for mutual information in temporally correlated models. Diversity This paper emphasizes the structural similarities between three models. The comparison could be pushed further in terms of estimating equations, adaptivity (estimation of the nuisance parameters) and stability conditions. However, ....

D. Pham. Blind separation of instantaneous mixture of sources via the Gaussian mutual information criterion. Signal Processing, (4):855--870, 2001.

No context found.

D. T. Pham, "Blind separation of instantaneous mixture of sources via an independentcomponent analysis," IEEE Trans. Signal Processing, vol. 44, no. 11, pp. 2768--2779, 1996.

....a matrix B which jointly approximately diagonalizes the matrices f X (1) f X (m) relative to the above measure of deviation from diagonality. The contrast (8) and (12) have been introduced in Pham [11] Their Gaussian analogues and the contrast (14) or (15) have been introduced in Pham [13, 14]. Pham [15] also provide an ecient algorithm to solve the associate problem of joint approximate diagonalization of several matrices. 3 Contrast for convolutive mixtures Consider now the case where the sources are mixed through a convolution X(t) A(l)S(t l) A S) t) where X( and ....

Pham, D. T. \Blind Separation of Instantaneous Mixture of Sources via the Gaussian Mutual Information Criterion". Signal Processing, to apear 2001.

....a matrix B which jointly approximately diagonalizes the matrices f X (1) f X (m) relative to the above measure of deviation from diagonality. The contrast (8) and (12) have been introduced in Pham [11] Their Gaussian analogues and the contrast (14) or (15) have been introduced in Pham [13, 14]. Pham [15] also provide an ecient algorithm to solve the associate problem of joint approximate diagonalization of several matrices. 3 Contrast for convolutive mixtures Consider now the case where the sources are mixed through a convolution X(t) A(l)S(t l) A S) t) where X( and ....

Pham, D. T. \Blind Separation of Instantaneous Mixture of Sources via the Gaussian Mutual Information Criterion". In Signal Processing X, 3-6, Proceeding of EUSIPCO 2000.

....unless RX or RY equal 0. Thus the resulting criterion k=1 log RYk log j det Bj is a discriminating contrast (we assume implicitly that no source can have support reduced to a single point, otherwise such source clearly cannot be extracted) It has in fact been introduced and proved to be so in [12]. Example 4: Suppose that the sources are sub Gaussian, that is they admit fourth order cumulant: cum 4 (S k ) def = E[ S k ES k ) 3fE[ S k ES k ) g ; k = 1; K; which are non positive. Since the cumulant of a sum of independent random variables is the sum of their ....

Pham, D. T. \Blind Separation of Instantaneous Mixture of Sources via Order Statistics. IEEE Trans. Signal Processing, 48, 2, 363-375, 2000.

....for any positive definite matrix , with equality if and only if this matrix is diagonal. Thus, the contrast (9) is a joint diagonalization criterion. The contrast (6) and (7) have been introduced in Pham [10] Their Gaussian analogues and the contrast (8) or (9) have been introduced in Pham [11, 12]. Pham [13] also provides an efficient algorithm to solve the associated problem of joint approximate diagonalization of several matrices. 3. CONTRAST FOR CONVOLUTIVE MIXTURES Consider now the case where the sources are mixed through a convolution 548 R ....

D. T. Pham, "Blind separation of instantaneous mixture of sources via the Gaussian mutual information criterion," Signal Processing, 2001, To appear.

....for any positive definite matrix , with equality if and only if this matrix is diagonal. Thus, the contrast (9) is a joint diagonalization criterion. The contrast (6) and (7) have been introduced in Pham [10] Their Gaussian analogues and the contrast (8) or (9) have been introduced in Pham [11, 12]. Pham [13] also provides an efficient algorithm to solve the associated problem of joint approximate diagonalization of several matrices. 3. CONTRAST FOR CONVOLUTIVE MIXTURES Consider now the case where the sources are mixed through a convolution 548 R ....

D. T. Pham, "Blind separation of instantaneous mixture of sources via the Gaussian mutual information criterion," in Signal Processing X (Proceeding of EUSIPCO 2000.

....by piecewise constant functions. All algorithms require only the estimation of the score functions of the reconstructed sources. A new method for score function estimation is presented for this purpose. 1. INTRODUCTION Blind source separation has been well studied in the case of linear mixtures [1, 2, 3, 4], but only begins to attract attention in the case of nonlinear mixtures. Yet in many situations, it is more realistic to assume a nonlinear rather than a linear mixture. The main difficulty in using this class of mixtures is that they are too broad and thus lead to the problem of identifiability. ....

D.-T. Pham, "Blind separation of instantaneous mixture of sources via an independent component analysis, " IEEE Transactions on Signal Processing, vol. 44, no. 11, pp. 2768--2779, Nov. 1996.

No context found.

D.-T. Pham. Blind separation of instantaneous mixture of sources based on order statistics. IEEE Transactions on Signal Processing, 48(2):363--375, 2000.

No context found.

D.-T. Pham. Blind separation of instantaneous mixtures of sources via the Gaussian mutual information criterion. Signal Processing, 81:855--870, 2001.

No context found.

D.-T. Pham, "Blind separation of instantaneous mixture of sources based on order statistics," IEEE Transactions on Signal Processing, vol. 48, no. 2, pp. 363-- 375, 2000.

No context found.

D.-T. Pham. Blind separation of instantaneous mixture of sources via an independent component analysis. IEEE Transactions on Signal Processing, 44(11):27682779, 1996.

No context found.

D.-T. Pham. Blind separation of instantaneous mixture of sources via an independent component analysis. IEEE Trans. on Sig. Proc., 44(11)) Nov. 1996.

No context found.

D.-T. Pham. Blind separation of instantaneous mixture of sources via an independent component analysis. ResearchreportRT 119, LMC IMAG, Grenoble, France, 1994.

No context found.

Pham, D.T. (1996) Blind separation of instantaneous mixture of sources via an Independent Component Analysis. IEEE Trans. on Signal Processing 44 2768 - 2779.

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D.-T. Pham. Blind separation of instantaneous mixture of sources via the Gaussian mutual information criterion. In Proc. EUSIPCO 2000.

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