Contribution of statistical tests to sparseness-based blind source separation

Aziz-Sbaï, Si Mohamed; Bey, Abdeldjalil Aïssa El; Pastor, Dominique

doi:10.1186/1687-6180-2012-169

Cited by 13 publications

(10 citation statements)

References 35 publications

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“…The more difficult case is clearly the underdetermined case, where the number of sources is more than the number of observed signals and for which solutions cannot be derived without additional assumptions. For instance, the sources can be separated thanks to their sparse representation in the time-frequency domain [5], [6], a source being said to be sparse in a given signal representation domain if most of its samples are close to zero. Another approach can be based on geometric properties of signals as in [7].…”

Section: Introductionmentioning

confidence: 99%

Sparsity-Based Recovery of Finite Alphabet Solutions to Underdetermined Linear Systems

Bey

Pastor

Sbai

et al. 2015

IEEE Trans. Inform. Theory

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We consider the problem of estimating a deterministic finite alphabet vector f from underdetermined measurements y = Af , where A is a given (random) n × N matrix. Two new convex optimization methods are introduced for the recovery of finite alphabet signals via 1-norm minimization. The first method is based on regularization. In the second approach, the problem is formulated as the recovery of sparse signals after a suitable sparse transform. The regularization-based method is less complex than the transform-based one. When the alphabet size p equals 2 and (n, N) grows proportionally, the conditions under which the signal will be recovered with high probability are the same for the two methods. When p > 2, the behavior of the transform-based method is established. Experimental results support this theoretical result and show that the transform method outperforms the regularization-based one.

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Section: Introductionmentioning

confidence: 99%

Sparsity-Based Recovery of Finite Alphabet Solutions to Underdetermined Linear Systems

Bey

Pastor

Sbai

et al. 2015

IEEE Trans. Inform. Theory

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“…be confirmed by the application to speech processing of Sections IV and V. Another means to choose the minimal SNR required by the DATE is to resort to the notion of universal threshold [17], as proposed in [18]. Indeed, the coordinates of all the [17] where the universal threshold is utilized to discriminate noisy signal wavelet coefficients from wavelet coefficients of noise alone, the trick proposed in [22] and [18] is to consider λ u (N × d ) as the minimum amplitude that a signal must have to be distinguishable from noise. The minimal SNR can then be defined as ρ…”

Section: The Datementioning

confidence: 78%

“…The presence or the absence of this source is modeled by a Bernoulli random variable ε(m, k). This Bernoulli model is tantamount to and justified by the concept of ideal binary masking in the time-frequency domain, as used in audio source separation [18], [23]. The probability of presence is assumed to be less than or equal to 1/2.…”

Section: Weak-sparseness Model Of Noisy Speechmentioning

confidence: 99%

“…Let us further denote by Θ(m, k) the underlying atomic audio source. Then, under the previous assumptions, the noisy speech signal at timefrequency point (m, k) can be modeled as: We recognize here the weak-sparseness model [24] applied to speech processing, in the continuation of [18]. In summary, our model essentially assumes that the STFT of noisy speech signals satisfies the following three key properties in each time-frequency bin (m, k): (A'1): the presence/absence of speech ε(m, k) and the atomic speech audio source Θ(m, k) are independent, (A'2): the speech-presence probability does not exceed 1/2, (A'3): the instantaneous power of the random clean speech signal is upper-bounded by a finite value.…”

Section: Weak-sparseness Model Of Noisy Speechmentioning

confidence: 99%

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Robust Estimation of Non-Stationary Noise Power Spectrum for Speech Enhancement

Mai

Pastor

Bey

et al. 2015

IEEE/ACM Trans. Audio Speech Lang. Process.

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International audienceWe propose a novel method for noise power spectrum estimation in speech enhancement. This method called extended-DATE (E-DATE) extends the d-dimensional amplitude trimmed estimator (DATE), originally introduced for additive white gaussian noise power spectrum estimation, to the more challenging scenario of non-stationary noise. The key idea is that, in each frequency bin and within a sufficiently short time period, the noise instantaneous power spectrum can be considered as approximately constant and estimated as the variance of a complex gaussian noise process possibly observed in the presence of the signal of interest. The proposed method relies on the fact that the Short-Time Fourier Transform (STFT) of noisy speech signals is sparse in the sense that transformed speech signals can be represented by a relatively small number of coefficients with large amplitudes in the time-frequency domain. The E-DATE estimator is robust in that it does not require prior information about the signal probability distribution except for the weak-sparseness property. In comparison to other state-of-the-art methods, the E-DATE is found to require the smallest number of parameters (only two). The performance of the proposed estimator has been evaluated in combination with noise reduction and compared to alternative methods. This evaluation involves objective as well as pseudo-subjective criteria

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“…In fact, BSS has become a very important topic of research and development in many areas, especially biomedical engineering and medical imaging [6,10], speech and audio processing [2,3], remote sensing [8], communications systems [1,7] and radar processing [11].…”

Section: Introductionmentioning

confidence: 99%

An analytical derivation for second-order blind separation of two signals

et al. 2018

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In this paper, we propose analytical formulas that involve second-order statistics for separating two signals. The method utilizes source decorrelation and correlation function diversity. In particular, the proposed SOBAS (Second-Order Blind Analytical Separation) algorithm differs from the ASOBI (Analytical Second-Order Blind Identification) algorithm in that it does not require prior knowledge or estimation of the noise variance. Computer simulations demonstrate the effectiveness of the proposed method.

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Contribution of statistical tests to sparseness-based blind source separation

Cited by 13 publications

References 35 publications

Sparsity-Based Recovery of Finite Alphabet Solutions to Underdetermined Linear Systems

Sparsity-Based Recovery of Finite Alphabet Solutions to Underdetermined Linear Systems

Robust Estimation of Non-Stationary Noise Power Spectrum for Speech Enhancement

An analytical derivation for second-order blind separation of two signals

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