Underdetermined blind source separation in a time-varying environment

Vielva, Luis; Erdoğmuş, Deni̇z; Pantaleón, C.; Santamarı́a, Ignacio; Pereda, José Antonio Martín; Prı́ncipe, José C.

doi:10.1109/icassp.2002.5745292

Cited by 27 publications

(23 citation statements)

References 4 publications

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“…Hence, when they are strictly positive, they may be assumed to be equal to 1 so that (65) becomes (66) Then, if is the symmetric Schur decomposition of defined for as in (18), we define by . Then, since we defined by (49), we can prove as in (24) that (67) which implies, using the same approach as in (25) but now with (51) (68) 6 Convolutive mixtures entail a slight approximation concerning which points of this sphere may be reached, as explained in Section III-E. so that due to (66) (69) Therefore, varying so that yields a simple method in the underdetermined convolutive case to constrain our vector to be on the unit sphere (64). The optimization of the absolute value of defined in (63) under the constraint (64), therefore, belongs to the same generic problem as in (13)- (14), with a set of variables here denoted instead of .…”

Section: Extension Of Convolutive Approach To Underdetermined Mixtmentioning

confidence: 85%

“…of them are now assumed to be long-term nonstationary (i.e., not identically distributed) and correspond to the sources of interest, while the other are stationary and correspond to the "noise sources." Using the multilinearity of the kurtosis for independent random variables, we derive from (6) and (59) (60) where (61) is defined as in (6). As in the linear instantaneous case, let us denote by the set containing the indices of the unknown nonstationary sources.…”

Section: Extension Of Convolutive Approach To Underdetermined Mixtmentioning

confidence: 99%

“…The previous hypotheses of our differential concept mean that only the processes with are assumed to have the same kurtosis for different times, i.e., (62) Thus, we have (63) Hence, we see that the noise sources (whose indices do not belong to the set ) are invisible in our differential extraction criterion. As an extension of the linear instantaneous case, we here consider the values of (63) on the dimensional unit sphere 6 where , i.e., such that (64) First, it may be shown easily that the differential power of , again defined by (15), here reads (65) Each process with is assumed to exhibit nonstationarity from time to . However, it is here assumed to be identically distributed for all times when is varied from to .…”

Section: Extension Of Convolutive Approach To Underdetermined Mixtmentioning

confidence: 99%

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Differential Fast Fixed-Point Algorithms for Underdetermined Instantaneous and Convolutive Partial Blind Source Separation

Thomas

Deville

Hosseini

2007

IEEE Trans. Signal Process.

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Abstract-This paper concerns underdetermined linear instantaneous and convolutive blind source separation (BSS), i.e., the case when the number of observed mixed signals is lower than the number of sources. We propose partial BSS methods, which separate supposedly nonstationary sources of interest (while keeping residual components for the other , supposedly stationary, "noise" sources). These methods are based on the general differential BSS concept that we introduced before. In the instantaneous case, the approach proposed in this paper consists of a differential extension of the FastICA method (which does not apply to underdetermined mixtures). In the convolutive case, we extend our recent time-domain fast fixed-point C-FICA algorithm to underdetermined mixtures. Both proposed approaches thus keep the attractive features of the FastICA and C-FICA methods. Our approaches are based on differential sphering processes, followed by the optimization of the differential nonnormalized kurtosis that we introduce in this paper. Experimental tests show that these differential algorithms are much more robust to noise sources than the standard FastICA and C-FICA algorithms.

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Section: Extension Of Convolutive Approach To Underdetermined Mixtmentioning

confidence: 85%

Section: Extension Of Convolutive Approach To Underdetermined Mixtmentioning

confidence: 99%

Section: Extension Of Convolutive Approach To Underdetermined Mixtmentioning

confidence: 99%

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Differential Fast Fixed-Point Algorithms for Underdetermined Instantaneous and Convolutive Partial Blind Source Separation

Thomas

Deville

Hosseini

2007

IEEE Trans. Signal Process.

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“…The columns of the mixing matrix A assign each observed data point to only one source based on some measure of proximity to those columns [182], i.e., at each instant only one source is considered active. Therefore the mixing system can be presented as:…”

Section: Sparse Component Analysis (Sca)mentioning

confidence: 99%

A unified approach to sparse signal processing

Marvasti

Amini

Haddadi

et al. 2012

EURASIP J. Adv. Signal Process.

101

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A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common potential benefits of significant reduction in sampling rate and processing manipulations through sparse signal processing are revealed. The key application domains of sparse signal processing are sampling, coding, spectral estimation, array processing, component analysis, and multipath channel estimation. In terms of the sampling process and reconstruction algorithms, linkages are made with random sampling, compressed sensing, and rate of innovation. The redundancy introduced by channel coding in finite and real Galois fields is then related to over-sampling with similar reconstruction algorithms. The error locator polynomial (ELP) and iterative methods are shown to work quite effectively for both sampling and coding applications. The methods of Prony, Pisarenko, and MUltiple SIgnal Classification (MUSIC) are next shown to be targeted at analyzing signals with sparse frequency domain representations. Specifically, the relations of the approach of Prony to an annihilating filter in rate of innovation and ELP in coding are emphasized; the Pisarenko and MUSIC methods are further improvements of the Prony method under noisy environments. The iterative methods developed for sampling and coding applications are shown to be powerful tools in spectral estimation. Such narrowband spectral estimation is then related to multi-source location and direction of arrival estimation in array processing. Sparsity in unobservable source signals is also shown to facilitate source separation in sparse component analysis; the algorithms developed in this area such as linear programming and matching pursuit are also widely used in compressed sensing. Finally, the multipath channel estimation problem is shown to have a sparse formulation; algorithms similar to sampling and coding are used to estimate typical multicarrier communication channels.

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“…On the basis that the source distribution is assumed sparse, another algorithm which jointly estimates the mixing matrix and the sources is proposed in [1]. Alternatively, by noticing that the received signals will be colinear with the corresponding steering vector if only a single source is present at a given time instant, an approach is proposed in [5]. Recently, the techniques of t-f analysis have been suggested in the BSS literature, as they are able to reveal the information embedded within the nonstationary signals and are advantageous in the environment of low signal to noise ratio.…”

Section: Introductionmentioning

confidence: 99%

A new block based time-frequency approach for underdetermined blind source separation

Luo

Lambotharan

Chambers

2004 IEEE International Conference on Acoustics, Speech, and Signal Processing

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The problem of underdetermined blind source separation is addressed. The sparse assumption which is commonly required in the current underdetermined blind source separation literature is relaxed. By introducing an advanced clustering technique based upon self-splitting competitive learning, the time-frequency plane is partitioned into appropriate blocks where the number of active sources is no more than the number of sensors, resulting in a novel robust block based algorithm. Simulation studies are presented to support the proposed approach for the separation of GMSK sources.

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Underdetermined blind source separation in a time-varying environment

Cited by 27 publications

References 4 publications

Differential Fast Fixed-Point Algorithms for Underdetermined Instantaneous and Convolutive Partial Blind Source Separation

Differential Fast Fixed-Point Algorithms for Underdetermined Instantaneous and Convolutive Partial Blind Source Separation

A unified approach to sparse signal processing

A new block based time-frequency approach for underdetermined blind source separation

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