Robust Estimation of Noise Standard Deviation in Presence of Signals With Unknown Distributions and Occurrences

Contribution of statistical tests to sparseness-based blind source separation

“…Based on a weak-sparseness model for the signal sources in noise, it begins by estimating the noise standard deviation via the DATE introduced in [22]. Then, the noise standard deviation estimate is used instead of the unknown true value in the expression of http://asp.eurasipjournals.com/content/2012/1/169 a statistical test, also designed for noisy sparse signal representations.…”

“…Therefore, the noisy time-frequency points are not very few and cannot play the role of outliers with respect to the main core data distribution. In a recent article [22], a new noise standard deviation estimator called the DATE has been proposed. This estimator relies on the weak-sparseness model presented before.…”

“…This estimator relies on the weak-sparseness model presented before. An exhaustive presentation of the theoretical background on which this estimator is based is beyond the scope of the present article and the reader is asked to refer to [22] for an heuristic presentation and a complete mathematical description of the DATE. In the context addressed in the present article, this algorithm applies as follows.…”

“…, M, we assume that the L time-frequency components S x j (t, f ) for the jth sensor are independent and that each time-frequency component obeys the binary hypothesis model of (5) with α = σ log(2ML). According to [22] and setting κ = 2 (3/2) where is the standard Gamma function, there exists a specific convergence criterion, for which we have:…”

“…Then, Section "Statistical tests for sparseness-based UBSS" is the main core of the article because it introduces the statistical tests for the selection of the time-frequency points needed by source recovery and mixing matrix estimation. For source recovery, the selection of the timefrequency points relies on a weak notion of sparseness, exploited through an estimate-and-plug-in detector: We begin by estimating the noise standard deviation via the d-dimensional amplitude trimmed estimator (DATE), recently introduced in [22], especially designed for coping with noisy representations of weakly-sparse signals; then, the noise standard deviation estimate is used instead of the unknown true value in the expression of a statistical test, specifically designed for noisy representations of weakly-sparse signals as well. For the mixing matrix estimation, the physics of the signal suggest introducing a novel strategy.…”