EP1830349B1 - Method of noise reduction of an audio signal - Google Patents

Abstract

The method involves determining a reference signal by applying a process to a noisy audio signal for attenuating voice components in the audio signal by utilizing predictive least mean square (LMS) algorithm. Probability of presence/absence of voice is determined from respective energy levels in a spectral range of the audio and reference signals. A noise spectrum is estimated, and a noise reduction value is derived from the audio signal by utilizing the probability.

Description

BACKGROUND OF THE INVENTION Field of the invention

The present invention relates to the denoising of audio signals picked up by a microphone in a noisy environment.

The invention is advantageously applied, but in a nonlimiting manner, to the speech signals picked up by the hands-free telephones or the like.

These devices include a sensitive microphone not only capturing the voice of the user, but also the surrounding noise, noise that is a disruptive element that can go, in some cases, to make incomprehensible the speaker's words.

It is the same if one wants to implement speech recognition techniques, where it is very difficult to perform a form recognition on words embedded in a high noise level.

This difficulty related to ambient noise is particularly restrictive in the case of devices "hands-free" for motor vehicles. In particular, the large distance between the microphone and the speaker leads to a high relative level of noise which makes it difficult to extract the useful signal embedded in the noise. In addition, the highly noisy environment typical of the automotive environment has non-stationary spectral characteristics, that is to say that evolve unpredictably depending on the driving conditions: passage on deformed or paved roads, car radio operating etc.

Description of the Related Art

Various techniques have been proposed to reduce the noise level of the signal picked up by a microphone.

For example, the WO-A-98/45997 (Parrot SA) uses the push-button activation of a phone (for example when the driver wants to answer an incoming call) to detect the beginning of a speech signal and consider that the signal previously received to this support was essentially a noise signal. This last signal, stored, is analyzed to give a weighted average energy spectrum of the noise, then subtract from the noisy speech signal.

The US-A-5,742,694 describes another technique, implementing a predictive adaptive filter type mechanism. This filter delivers a "reference signal" corresponding to the predictable part of the noisy signal and an "error signal" corresponding to the prediction error, then attenuates these two signals in variable proportions, and recombines them to provide a signal noised.

The major disadvantage of this denoising technique lies in the significant distortion introduced by prefiltering, giving a very degraded signal output in terms of acoustic quality. It is also poorly suited to situations where it would require energetic denoising with a speech signal embedded in a noise of complex and unpredictable nature, with non-stationary spectral characteristics.

Still other techniques, called beamforming or double-phoning , implement two separate microphones. The first is designed and placed to primarily capture the speaker's voice, while the other is designed and placed to capture a larger noise component than the main microphone. The comparison of the signals captured makes it possible to extract the voice of the ambient noise efficiently, and by relatively simple software means.

This technique, based on a spatial coherence analysis of two signals, however, has the disadvantage of requiring two remote microphones, which generally confines it to fixed or semi-fixed installations and does not allow to integrate it into a pre-existing device by simply adding a software module. It also assumes that the speaker's position relative to the two microphones is approximately constant, which is generally the case in a car phone used by its driver. In addition, to achieve a near satisfactory denoising, the signals are subjected to a significant pre-filtering, which again has the disadvantage of introducing distortions that degrade the quality of the denoised signal restored.

The invention relates to a technique for denoising audio signals picked up by a single microphone recording a voice signal in a noisy environment.

1. [1] Y. Ephraim et D. Malah, Speech Enhancement using a Minimum Mean-Square Error Short-Time Spectral Amplitude Estimator, IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-32, No 6, pp. 1109-1121, Dec. 1984 , et
2. [2] Y. Ephraim et D. Malah, Speech Enhancement using a Minimum Mean-Square Error Log-Spectral Amplitude Estimator, IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-33, No 2, pp. 443-445, April 1985 .

A large part of the most efficient methods used in single-microphone systems are based on the statistical model established by D. Malah and Y. Ephraim in:

1. [1] Y. Ephraim and D. Malah, Speech Enhancement Using a Minimum Mean-Square Error Short-Time Spectral Amplitude Estimator, IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-32, No. 6, pp. 1109-1121, Dec. 1984 , and
2. [2] Y. Ephraim and D. Malah, Speech Enhancement Using a Minimum Mean-Square Error Log-Spectral Amplitude Estimator, IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-33, No. 2, pp. 443-445, April 1985 .

Making the approximation that speech and noise are uncorrelated Gaussian processes and presupposing that the spectral power of noise is a known datum, these two articles give an optimal solution to the problem of noise reduction described above. This solution proposes to cut the noisy signal into independent frequency components by using the discrete Fourier transform, to apply an optimal gain on each of these components and then to recombine the signal thus treated. The two articles differ on the choice of the criterion of optimality. In [1], the applied gain is called the STSA gain and allows to minimize the mean squared distance between the estimated signal (at the output of the algorithm) and the original speech signal (non-noisy). In [2], the application of a gain called gain LSA makes it possible to minimize the mean square distance between the logarithm of the amplitude of the estimated signal and the logarithm of the amplitude of the original speech signal. This second criterion is superior to the first because the distance chosen is much better suited to the behavior of the human ear and therefore qualitatively gives better results. In all cases, the essential idea is to reduce the energy of the very noisy frequency components by applying a low gain while leaving intact (by the application of a gain equal to 1) those that are little or no at all.

Although attractive as supported by a rigorous mathematical demonstration, this method can not however be implemented by itself. Indeed, as indicated above, the spectral power of the noise is unknown and unpredictable ex ante. Moreover, this same process does not propose not to evaluate at what moments the speech of the speaker is present in the captured signal. It simply assumes either that speech is always present, or that it is present a fixed portion of time, which can seriously limit the quality of noise reduction.

It is therefore necessary to use another algorithm whose function is to evaluate the spectral power of the noise as well as the times when the speech of the speaker is present on the raw signal picked up. It even turns out that this estimate is the determining factor of the quality of the noise reduction operated, the algorithm of Ephraim and Malah being only the optimal way to use the information thus obtained.

This is an original solution to this double problem of evaluation of the noise and moments of presence of the speech signal that the present invention provides.

These two questions are in fact intrinsically linked. Indeed, suppose that the raw signal picked up is cut into frames of equal lengths, for which the Fourier transform is calculated for the short term.

For a given frequency component, the knowledge of the indices of the frames where the speech is absent makes it possible to evaluate the power of the noise as well as its evolution over time on this segment of the spectrum. It suffices to measure the energy of the raw signal when the speech is absent and to make an average continuously updated these measurements. The main question is therefore when exactly the speech of the speaker is absent from the signal picked up by the microphone.

If the noise is stationary or pseudo-stationary, this problem can be easily solved by declaring that speech is absent in a spectrum segment of a given frame when the spectral energy of the data for that spectrum segment has not evolved. or has changed little compared to the last frames. Conversely, speech is said to be present in case of non-stationary behavior.

However, in a real environment, a fortiori an automobile environment which has been indicated above that the noise had many non-stationary spectral characteristics, this method is easily faulted, insofar as both speech and noise can present transient behavior. However, if we decide to keep all the transitional components, there will be musical noise residual in the debruised data; conversely, if it is decided to suppress the transient components below a given energy threshold, then the weak components of speech will be erased, whereas these components may be important, both for their informative content and for the general intelligibility. (low distortion) of the denoised signal restored after treatment.

• [3] I. Cohen et B. Berdugo, Speech Enhancement for Non-Stationary Noise Environments, Signal Processing, Elsevier, Vol. 81, pp. 2403-2418,2001 ,

In this regard, various methods have been proposed. Among the most effective, we can mention the one described by:

• [3] I. Cohen and B. Berdugo, Speech Enhancement for Non-Stationary Noise Environments, Signal Processing, Elsevier, Vol. 81, pp. 2403 to 2418.2001 ,

As is frequently the case in the field, the method described in this article is not intended to identify precisely on which frequency components of which frames the speech is absent, but rather to give a confidence index between 0 and 1, a value of 1 indicating that the speech is absent for sure (according to the algorithm) while a value 0 declares the opposite. By its nature, this index is likened to the probability of absence of speech a priori , ie the probability that speech is absent on a given frequency component of the frame considered. This is of course a non-rigorous assimilation in the sense that even if the presence of speech is probabilistic ex ante, the signal picked up by the microphone can at any moment only go through two distinct states. It can either (at the moment considered) include speech or not contain it. However, this assimilation gives good results in practice which justifies its use. To estimate this probability of absence, Cohen and Berdugo use averages on signal-to-noise ratios a priori themselves used and calculated in the algorithm of Ephraim and Malah. These authors also describe the so-called OM-LSA gain technique ( Optimally-Modified Log-Spectral Amplitude ), aimed at improving the LSA gain by integrating this probability of absence of speech.

This estimate of the a priori probability of absence of speech proves to be effective, but depends directly on the statistical model developed by Ephraim and Malah and not on a priori knowledge of the data.

• [4] I. Cohen et B. Berdugo, Two Channel Signal Detection and Speech Enhancement Based on the Transient Beam-to-Reference Ratio, Proc. ICASSP 2003, Hong Kong, pp. 233-236, April 2003 ,

de calculer la probabilité d'absence à partir de signaux captés par deux microphones différemment placés, donnant des signaux respectifs sur deux voies différentes, dont la combinaison permet d'obtenir une voie dite de sortie et une voie dite de bruit de référence. L'analyse est basée sur la constatation que les composantes de parole sont relativement plus faibles sur la voie de bruit de référence, et que les composantes de bruit transitoire présentent à peu près la même énergie sur les deux voies. Une probabilité de présence de parole pour chaque segment de spectre de chaque trame est déterminée en calculant un ratio d'énergie entre les composantes non stationnaires des signaux respectifs des deux voies.To obtain an estimate of the probability of absence that is independent of this statistical model, Cohen and Berdugo proposed in:

• [4] I. Cohen and B. Berdugo, Two Channel Signal Detection and Speech Enhancement Based on the Transient Beam-to-Reference Ratio, Proc. ICASSP 2003, Hong Kong, pp. 233-236, April 2003 ,

calculating the probability of absence from signals picked up by two differently placed microphones, giving respective signals on two different channels, the combination of which makes it possible to obtain a so-called output channel and a so-called reference noise channel. The analysis is based on the finding that the speech components are relatively weaker on the reference noise path, and that the transient noise components have approximately the same energy on both paths. A speech presence probability for each spectrum segment of each frame is determined by computing an energy ratio between the non-stationary components of the respective signals of the two channels.

But, as for beamforming or double-phoning techniques mentioned above, this process is quite restrictive in that it requires two microphones.

SUMMARY OF THE INVENTION

One of the aims of the invention is to overcome the drawbacks of the methods proposed up to now, by means of an improved denoising method applicable to a speech signal considered in isolation, in particular a signal picked up by a single microphone, a method which is based on the analysis of the temporal coherence of the captured signals.

The starting point of the invention lies in the observation that speech generally has a temporal coherence greater than noise and that, as a result, it is clearly more predictable. Essentially, the invention proposes to use this property to calculate a reference signal where the speech has been more attenuated than the noise, by applying in particular a predictive algorithm which may for example be of the LMS ( Least Mean Squares, Least Mean Squares ) type. ). This reference signal derived from the speech signal to be denoised may be used in a manner comparable to that of the signal of the second microphone of beam-forming techniques. two-way, for example techniques similar to those of Cohen and Berdugo [4, supra]. The calculation of a ratio between the respective energy levels of the original signal and the reference signal thus obtained will make it possible to discriminate between the speech components and the nonstationary noise noises, and will provide an estimate of the probability of presence of speech of independently of any statistical model.

In other words, the technique proposed by the invention implements an "intelligent subtraction" implying, after a linear prediction made on the passed samples of the original signal (and not of a prefiltered signal, thus degraded), a registration phase between the original signal and the predicted signal.

The technique of the invention turns out, in practice, sufficiently powerful to provide extremely effective denoising directly on the original signal, freeing distortions introduced by a prefiltering chain, become unnecessary.

1. a) détermination d'un signal de référence par application au signal bruité d'un traitement propre à atténuer de façon plus importante les composantes de parole que les composantes de bruit de ce signal bruité, ledit traitement comprenant : (a1) l'application d'un algorithme de prédiction linéaire adaptatif opérant sur une combinaison linéaire des échantillons antérieurs du signal bruité, et (a2) la détermination dudit signal de référence par une soustraction, avec compensation du déphasage, entre le signal bruité originel, non filtré et le signal délivré par l'algorithme de prédiction linéaire ;
2. b) détermination d'une probabilité de présence/absence de parole a priori à partir des niveaux d'énergie respectifs dans le domaine spectral du signal bruité et du signal de référence ; et
3. c) utilisation de cette probabilité d'absence de parole a priori pour estimer un spectre de bruit et dériver du signal bruité une estimée débruitée du signal de parole.

More specifically, the present invention proposes, for the denoising of an original noisy audio signal comprising a speech component combined with a noise component comprising itself a transient noise component and a pseudo-stationary noise component, to operate temporal coherence analysis of the noisy signal by the steps of:

1. a) determining a reference signal by applying to the noisy signal a processing adapted to more significantly attenuate the speech components than the noise components of this noisy signal, said processing comprising: (a1) the application of an adaptive linear prediction algorithm operating on a linear combination of the previous noisy signal samples, and (a2) determining said reference signal by subtracting, with phase shift compensation, between the original, unfiltered noisy signal and the delivered signal by the linear prediction algorithm;
2. b) determining a probability of presence / absence of speech a priori from the respective energy levels in the spectral range of the noisy signal and the reference signal; and
3. c) using this probability of absence of speech a priori to estimate a noise spectrum and derive from the noisy signal a denoised estimate of the speech signal.

où X(k,l) et Y(k,l) sont les transformées de Fourier à court terme de chaque segment de spectre k de chaque trame l, respectivement du signal bruité originel et du signal délivré par l'algorithme de prédiction linéaire.The reference signal may in particular be determined by applying in step a2) a relation of the type: $$\mathit{Ref}\left(kl\right)=X\left(kl\right)-X\left(kl\right)\frac{\left|Y\left(kl\right)\right|}{\left|X\left(kl\right)\right|}$$

where X ( k , l ) and Y ( k , l ) are the short-term Fourier transforms of each spectrum segment k of each frame 1 , respectively of the original noisy signal and the signal delivered by the linear prediction algorithm.

The predictive algorithm is advantageously a recursive adaptive algorithm of LMS mean least squares type.

• [5] I. Cohen et B. Berdugo, Noise Estimation by Minima Controlled Recursive Averaging for Robust Speech Enhancement, IEEE Signal Processing Letters, Vol. 9, No 1, pp. 12-15, Jan. 2002 ,

Step b) advantageously comprises the application of an algorithm for estimating the energy of the pseudo-stationary noise component in the reference signal and in the noisy signal, in particular a recursive averaging type algorithm by control MRCA minima as described in:

• [5] I. Cohen and B. Berdugo, Noise Estimation by Minima Controlled Recursive Averaging for Robust Speech Enhancement, IEEE Signal Processing Letters, Vol. 9, No. 1, pp. 12-15, Jan. 2002 ,

Step c) advantageously comprises the application of a variable gain algorithm depending on the probability of presence / absence of speech, in particular an OM-LSA optimized modified log-spectral amplitude gain type algorithm.

SUMMARY DESCRIPTION OF THE DRAWINGS

• La figure 1 est un diagramme schématique illustrant les différentes opérations effectuées par un algorithme de débruitage conformément au procédé de l'invention.
• La figure 2 est un diagramme schématique illustrant plus particulièrement l'algorithme prédictif LMS adaptatif.

An embodiment of the invention will now be described with reference to the appended drawings in which the same reference numerals designate elements that are identical or functionally similar from one figure to another.

• The figure 1 is a schematic diagram illustrating the various operations performed by a denoising algorithm according to the method of the invention.
• The figure 2 is a schematic diagram illustrating more particularly the predictive algorithm LMS adaptive.

DETAILED DESCRIPTION OF THE PREFERRED MODE OF IMPLEMENTATION

The signal that we want to denoise is a sampled digital signal x (n) , where n denotes the number of the sample ( n is the temporal variable).

The captured signal x (n) is a combination of a speech signal s (n) and an additional noise, uncorrelated, d (n) : $$x\left(\mathrm{not}\right)=s\left(\mathrm{not}\right)+d\left(\mathrm{not}\right)$$

This noise d (n) has two independent components, namely a transient component d _t (n) and a pseudo-stationary component d _ps (n) : $$d\left(\mathrm{not}\right)=d_t\left(\mathrm{not}\right)+d_{\mathit{ps}}\left(\mathrm{not}\right)$$

As illustrated on the figure 1 , the noisy signal x (n) is applied as input to a predictive LMS algorithm schematized by block 10, including the application of appropriate delays 12. The operation of this LMS algorithm will be described below, with reference to FIG. figure 2 .

The short-term Fourier transform of the captured signal x (n) (block 16) and the signal y (n) delivered by the predictive LMS algorithm (block 14) are then calculated. From these two transforms is calculated a reference signal (block 18), which is one of the input variables of an algorithm for calculating the probability of absence of speech (block 24). Meanwhile, the noisy signal transform x (n), from block 16, is also applied to the probability calculation algorithm.

Blocks 20 and 22 estimate the pseudo-stationary noise of the reference signal and the noisy signal transform is estimated, and the result is also applied to the probability calculation algorithm.

The result of the speech absence probability calculation, as well as the noisy signal transform, are inputted to an OM-LSA gain processing algorithm (block 26), the result of which is subjected to an inverse transformation of Fourier (block 28) to give an estimate of speech de-noiseed.

The different phases of this treatment will now be described in more detail.

The predictive algorithm LMS (block 10) is schematized on the figure 2 .

Insofar as the signals in the presence are globally non-stationary but locally pseudo-stationary, one can advantageously use an adaptive system, which can take into account the variations of energy of the signal over time and converge towards the various local optima.

qui minimise l'erreur quadratique moyenne de l'erreur de prédiction : $$ϵ\left(n\right)=x\left(n\right)-y\left(n\right)$$

Essentially, if we apply successive delays Δ, the linear prediction y (n) of the signal x (n) is a linear combination of the earlier samples { x ( n - Δ - i + 1)} 1 i i _{M M} : $$\mathrm{there}\left(\mathrm{not}\right)={\displaystyle \underset{i=1}{\overset{M}{\Sigma }}}{\omega }_{i}x\left(\mathrm{not}-\mathrm{\Delta }-\mathrm{<figure-callout\; id="1"\; label="i\; +"\; filenames="imgf0001.png"\; state="\{\{state\}\}">i\; </figure-callout>}+1\right)$$

which minimizes the mean squared error of the prediction error: $$\epsilon \left(\mathrm{not}\right)=x\left(\mathrm{not}\right)-\mathrm{there}\left(\mathrm{not}\right)$$

Minimization involves finding: $$\underset{{\omega }_{}}{\mathrm{<figure-callout\; id="1"\; label="min\; \omega "\; filenames="imgf0001.png"\; state="\{\{state\}\}">min\; </figure-callout>}}E{\left[x\left(\mathrm{not}\right)-{\displaystyle \underset{i=1}{\overset{M}{\Sigma }}}{\omega }_{i}x\left(\mathrm{not}-\mathrm{\Delta }-\mathrm{<figure-callout\; id="1"\; label="i\; +"\; filenames="imgf0001.png"\; state="\{\{state\}\}">i\; </figure-callout>}+1\right)\right]}^2$$

• [6] B. Widrow, Adaptative Filters, Aspect of Network and System Theory, R. E. Kalman and N. De Claris (Eds). New York: Holt, Rinehart and Winston, pp. 563-587, 1970 , et
• [7] B. Widrow et al., Adaptative Noise Cancelling: Principles and Applications, Proc. IEEE, Vol. 63, No 12 pp. 1692-1716, Dec 1975 .

To solve this problem, it is possible to use an algorithm LMS, which is an algorithm in itself known, described for example in:

• [6] B. Widrow, Adaptative Filters, Aspect of Network and System Theory, RE Kalman and N. De Claris (Eds). New York: Holt, Rinehart and Winston, pp. 563-587, 1970 , and
• [7] B. Widrow et al., Adaptive Noise Canceling: Principles and Applications, Proc. IEEE, Vol. 63, No. 12 pp. 1692-1716, Dec 1975 .

µ étant une constante de gain qui permet d'ajuster la vitesse et la stabilité de l'adaptation.It is possible to define a recursive method for adapting weights. $${\omega }_i\left(\mathrm{not}+1\right)={\omega }_i\left(\mathrm{not}\right)+2\mathrm{\mu \epsilon }\left(\mathrm{not}\right)x\left(\mathrm{not}-\mathrm{\Delta }-\mathrm{<figure-callout\; id="1"\; label="i\; +"\; filenames="imgf0001.png"\; state="\{\{state\}\}">i\; </figure-callout>}+1\right)$$

μ being a gain constant which makes it possible to adjust the speed and the stability of the adaptation.

• [8] B. Widrow et S. Stearns, Adaptative Signal Processing, Prentice-Hall Signal Processing Series, Alan V. Oppenheim Series Editor, 1985 .

General information on these aspects of the LMS algorithm can be found in:

• [8] B. Widrow and S. Stearns, Adaptative Signal Processing, Prentice-Hall Signal Processing Series, Alan V. Oppenheim Series Editor, 1985 .

It can be shown that such an adaptive linear prediction makes it possible to discriminate effectively between noise and speech because the samples containing speech will be much better predicted (smaller quadratic errors between the prediction and the raw signal) than those containing only noise.

More precisely, the respective signals x (n) and y (n) (noisy speech signal and linear prediction) are split into frames of identical lengths, and their short-term Fourier transform (denoted respectively X and Y ) is calculated for each frame. To avoid the effects of precision errors, the algorithm predicts a 50% overlap between consecutive frames, and the samples are multiplied by the coefficients of the Hanning window so that the addition of even and odd fields corresponds to the signal of origin itself. For the spectrum segment k of a frame 1 pair, we have: $$X\left(kl\right)={\displaystyle \underset{p=1}{\overset{R}{\Sigma }}}h\left(p\right)x\left(\mathit{Services}+p\right)e^{-j2\mathit{\pi }\frac{\mathit{pk}}{R}}$$

h étant la fenêtre de Hanning.And for the spectrum segment k of an odd l- frame: $$X\left(kl\right)={\displaystyle \underset{p=1}{\overset{R}{\Sigma }}}h\left(p\right)x\left(\frac{\mathit{R}}{2}\mathit{l}+p\right)e^{-j2\mathit{\pi }\frac{\mathit{pk}}{R}}$$

h being the Hanning window.

A first possibility is to define the reference signal by taking the Fourier transform of the prediction error: $$\hat{\epsilon }\left(kl\right)=X\left(kl\right)-Y\left(kl\right)$$

However, there is in practice a certain phase shift between X and Y due to an imperfect convergence of the LMS algorithm, preventing good discrimination between speech and noise. It is therefore preferred to adopt for the reference signal another definition that compensates for this phase difference, namely: $$\mathit{Ref}\left(kl\right)=X\left(kl\right)-X\left(kl\right)\frac{\left|Y\left(kl\right)\right|}{\left|X\left(kl\right)\right|}$$

où $${\alpha }_S\left(k\right)<{\alpha }_{D_t}\left(k\right)<{\alpha }_{D_{\mathit{ps}}}\left(k\right)$$

représentent l'atténuation sur le signal de référence des trois signaux dans chaque segment de spectre.It is assumed that the spectral energy of the reference signal can be described as: $$E{\left[\mathit{Ref}\left(kl\right)\right]}^2=E{\left[S\left(kl\right)\right]}^2{\alpha }_S\left(k\right)+E{\left[D_t\left(kl\right)\right]}^2{\alpha }_{D_t}\left(k\right)+E{\left[D_{\mathit{ps}}\left(kl\right)\right]}^2{\alpha }_{D_{\mathit{ps}}}\left(k\right)$$

or $${\alpha }_S\left(k\right)<{\alpha }_{D_t}\left(k\right)<{\alpha }_{D_{\mathit{ps}}}\left(k\right)$$

represent the attenuation on the reference signal of the three signals in each spectrum segment.

H₀(k,l) indiquant l'absence de parole (et H₁(k,l) la présence de parole) dans le k ^ième segment de spectre de la l ^ième trame.The next step consists in delivering an estimate q (k, l) of the probability of absence of speech in the noisy signal: $$q\left(kl\right)=\mathit{Pr}\left\{H_0\left(kl\right)\right\}$$

H ₀ (k, l) indicating the absence of speech (and H ₁ (k, l) the presence of speech) in the k ^th spectrum segment of the 1 ^th frame.

The discrimination between transient noise and speech can be made by a technique comparable to that of Cohen and Berdugo [5, cited above]. More precisely, the algorithm of the invention evaluates a ratio of the transient energies on the two paths, given by: $$\mathit{\Omega }\left(\mathit{k}\mathit{l}\right)\mathit{=}\frac{\mathit{SX}\left(\mathit{k}\mathit{l}\right)\mathit{-}\mathit{MX}\left(\mathit{k}\mathit{l}\right)}{\mathit{SRef}\left(\mathit{k}\mathit{l}\right)\mathit{-}\mathit{MRef}\left(\mathit{k}\mathit{l}\right)}$$

b étant une fenêtre dans le domaine temporel et M étant un estimateur de l'énergie pseudo-stationnaire, qui peut être obtenu par exemple par une méthode MCRA (Minima Controlled Recursive Averaging) du même type que celle décrite par Cohen et Berdugo [5, précité] (cependant plusieurs alternatives existent dans la littérature). S being a smoothed estimate of the instantaneous energy: $$\mathit{SX}\left(\mathit{k}\mathit{l}\right)=\mathit{SX}\left(\mathit{k}\mathit{,}\mathit{l}-1\right)+{\displaystyle \underset{i=-\omega }{\overset{\omega }{\Sigma }}}b\left(i\right){\left|X\left(kl\right)\right|}^2$$

b being a window in the time domain and M being an estimator of the pseudo-stationary energy, which can be obtained for example by a method MCRA ( Minima Controlled Recursive Averaging ) of the same type as that described by Cohen and Berdugo [5, supra] (however, several alternatives exist in the literature).

In the presence of speech but in the absence of transient noise, this ratio is approximately: $$\mathrm{\Omega }\left(kl\right)=\frac{1}{{\alpha }_{D_t}\left(k\right)}={\mathrm{\Omega }}_{\mathit{max}}\left(k\right)$$

Conversely, in the absence of speech but in the presence of transient noises: $$\mathrm{\Omega }\left(kl\right)=\frac{1}{{\alpha }_S\left(k\right)}={\mathrm{\Omega }}_{\mathit{min}}\left(k\right)$$

une procédure d'estimation de q(k,l) est donnée par l'algorithme en métalangage suivant :If we assume that in general: $${\mathrm{\Omega }}_{\mathit{min}}\left(k\right)\le \mathrm{\Omega }\left(kl\right)\le {\mathrm{\Omega }}_{\mathit{max}}\left(k\right)$$

a procedure for estimating q (k, l) is given by the following metalanguage algorithm:

For each frame l and for each spectrum segment k,

1. (i) Calculate SX ( k , l ), MX ( k , l ), SRef ( k , l ) and MRef ( k , l ). Go to (ii)
2. (ii) If SX ( k , l )> L _X MX ( k , l ) (transient detection on the noisy speech path), then go to (iii) otherwise $$q\left(kl\right)=1$$
   
3. (iii) If SRef ( k, l )> L _Ref MRef ( k, l ) (transient detection on the reference path), then go to (iv) otherwise $$q\left(kl\right)=0$$
   
4. (iv) Calculate Ω ( k , l ). go to (v)
5. (v) Calculate: $$q\left(kl\right)=\max \left(\min \left(\frac{{\mathrm{\Omega }}_{\mathit{max}}\left(k\right)-\mathrm{\Omega }\left(kl\right)}{{\mathrm{\Omega }}_{\mathit{max}}\left(k\right)-{\mathrm{\Omega }}_{\mathit{min}}\left(k\right)}1\right),0\right)$$
   

The constants L _x and L _Ref are transient detection thresholds. Ω _min (k) and Ω _{m ax} (k) are the upper and lower limits for each spectrum segment. These various parameters are chosen so as to correspond to typical situations, close to reality.

The next step (corresponding to block 26 of the figure 1 ) consists in operating the denoising itself (reinforcement of the speech component). The estimator just described will be applied to the statistical model described by Ephraim and Malah [2, supra], which assumes that the noise and speech in each spectrum segment are independent Gaussian processes of respective variances λ _x ( k, l) and λ _d (k, l) .

This step may advantageously implement the OM-LSA gain algorithm ( Optimally Modified Log-Spectral Amplitude Gain ) described by Cohen and Berdugo [3, cited above]. The signal / noise ratio a priori is defined by: $$\xi \left(kl\right)=\frac{{\lambda }_x\left(kl\right)}{{\lambda }_d\left(kl\right)}$$

The signal-to-noise ratio a posteriori is defined by: $$\gamma \left(kl\right)=\frac{{\left|X\left(kl\right)\right|}^2}{{\lambda }_d\left(kl\right)}$$

The conditional probability of signal presence is: $$p\left(kl\right)=\mathit{Pr}\left(H_1\left(kl\right)|X\left(kl\right)\right)$$

avec : $$\upsilon \left(kl\right)=\frac{\gamma \left(kl\right)\xi \left(kl\right)}{1+\xi \left(kl\right)}$$

With the Gaussian Hypothesis and the parameters above, it comes: $$p\left(kl\right)={\left\{1+\frac{q\left(kl\right)}{1-q\left(kl\right)}\left(1+\xi \left(kl\right)\right)\mathit{exp}\left(-\upsilon \left(kl\right)\right)\right\}}^{-1}$$

with: $$\upsilon \left(kl\right)=\frac{\gamma \left(kl\right)\xi \left(k\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="imgf0001.png"\; state="\{\{state\}\}">l</figure-callout>}\right)}{1+\xi \left(kl\right)}$$

The optimal estimate of speech de-noiseed S (k, l) is given by: $$\hat{S}\left(kl\right)={\mathrm{<figure-callout\; id="1"\; label="BOY\; WUT\; H"\; filenames="imgf0001.png"\; state="\{\{state\}\}">BOY\; WUT\; </figure-callout>}}_{H_{}}{\left(kl\right)}^{p\left(kl\right)}{\mathrm{BOY\; WUT}}_{\min }^{1-p\left(kl\right)}X\left(kl\right)$$

G _H1 being the gain in the hypothesis where speech is present, which is defined by: $${\mathrm{BOY\; WUT}}_{H_1}\left(kl\right)=\frac{\xi \left(k\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="imgf0001.png"\; state="\{\{state\}\}">l</figure-callout>}\right)}{1+\xi \left(kl\right)}\mathit{exp}\left(\frac{1}{2}{\displaystyle {\int }_{\upsilon \left(kl\right)}^{\infty }}\frac{e^{-t}}{t}dt\right)$$

The G _min gain in the absence of speech hypothesis is a lower limit for noise reduction, in order to limit the distortion of speech.

The classical formula for estimating the signal / noise ratio a priori is: $$\hat{\xi }\left(kl\right)=\mathrm{at}{\mathrm{<figure-callout\; id="1"\; label="BOY\; WUT\; H"\; filenames="imgf0001.png"\; state="\{\{state\}\}">BOY\; WUT\; </figure-callout>}}_{H_{}}^{{}_1}\left(k,l-1\right)\gamma \left(k,l-1\right)+\left(1-\mathrm{at}\right)\max \left(\gamma \left(kl\right)-1,0\right)$$

The noise energy estimate is given by: $${\hat{\lambda }}_d\left(k,l+1\right)={\widetilde{\mathrm{at}}}_d\left(kl\right){\hat{\lambda }}_d\left(kl\right)+\beta \left(1-{\widetilde{\mathrm{at}}}_d\left(kl\right)\right){\left|X\left(kl\right)\right|}^2$$

β étant un facteur de surestimation qui compense le biais en l'absence de signal.The smoothing parameter ã _d evolves between a lower limit of _d and 1, depending on the probability of conditional presence: $${\widehat{\mathrm{at}}}_d\left(kl\right)={\mathrm{at}}_d+\left(1-{\mathrm{at}}_d\right)p\left(kl\right)$$

β being an overestimation factor that compensates for bias in the absence of a signal.

The signal obtained at the end of this treatment is subjected to an inverse Fourier transform (block 28) to give the final estimate of the denoised speech.

The algorithm of the present invention is particularly effective in noisy environments, parasitized by both mechanical noises, vibrations, etc. as well as by musical noises, characteristic situations encountered in the interior of a car. Spectrograms show that the attenuation of the noise is not only effective, but is done without significant distortion of speech after denoising.

Claims (8)

1. A method for processing an audio signal, for the denoising of an original noisy signal comprising a speech component combined with a noise component, this noise component itself comprising a transient noise component and a pseudo-stationary noise component, characterized in that this method is a method of analyzing the temporal coherence of the sampled noisy signal comprising the steps of:

   a) determination of a reference signal by application to the noisy signal of a processing (10, 18) suitable for more significantly attenuating the speech components than the noise components of this noisy signal, the said processing comprising:

   a1) the application of an adaptive linear prediction algorithm operating on a linear combination of the earlier samples of the noisy signal, and

   a2) the determination of the said reference signal by a subtraction, with phase-shift compensation, between the original, non-prefiltered noisy signal and the signal delivered by the linear prediction algorithm;

   b) determination (24) of an a priori probability of presence/absence of speech on the basis of the respective energy levels in the spectral domain of the noisy signal and of the reference signal; and

   c) use of this a priori probability of absence of speech to estimate a noise spectrum and to derive (26) from the noisy signal a denoised estimate of the speech signal.
2. The method of Claim 1, in which the said reference signal is determined by application in step a2) of a relation of the type: $$\mathit{Ref}\left(k,l\right)=X\left(k,l\right)-X\left(k,l\right)\left|\frac{Y\left(k,l\right)}{X\left(k,l\right)}\right|$$

   

   
   where X(k,l) and Y(k,l) are the short-term Fourier transforms of each spectrum segment k of each frame l, respectively of the original noisy signal and of the signal delivered by the linear prediction algorithm.
3. The method of Claim 1, in which the linear prediction algorithm (10) is an algorithm of least mean squares, LMS, type.
4. The method of Claim 1, in which the linear prediction algorithm (10) is a recursive adaptive algorithm.
5. The method of Claim 1, in which step b) comprises the application of an algorithm for estimating the energy of the pseudo-stationary noise component in the reference signal and in the noisy signal.
6. The method of Claim 5, in which the algorithm for estimating the energy of the pseudo-stationary noise component is an algorithm of minima controlled recursive averaging, MCRA, type.
7. The method of Claim 1, in which step c) comprises the application of a variable gain algorithm dependent on the probability of presence/absence of speech.
8. The method of Claim 7, in which the variable gain algorithm is an algorithm of optimally modified log-spectral amplitude, OM-LSA, gain type.

Images