GB2426167A - Quantile based noise estimation - Google Patents

Abstract

A method of estimating the noise power spectrum <FLA>N Ô </FLA> (k,t) in an observed noisy signal having a power spectrum X(k,t) comprising the steps of: (a) Receiving and storing the noisy signal for T time frames; (b) for a frequency k sorting the frames X(k, t) such that X(k, t0) & X(k,t1) &ÒÒÒ& X(k,tT-1) and obtaining a noise estimate Ç(k,t) wherein the noise estimate is calculated as the quantile <EMI ID=2.1 HE=8 WI=34 LX=1043 LY=816 TI=UI> <PC>; (c) applying a recursive function to Ç(k,t) in order to generate <FLA>N Ô </FLA>(k,t), the recursive function being arranged so as to reduce fluctuations in the noise estimate Ç(k,t). Also, a method of saving processing power by only updating odd frequency bands for one time frame, and only updating even frequency bands for the next time frame.

Description

Noise Estimation Method The present invention relates to signal processing

and in particular to a method of noise estimation.

Elimination of additive noise from a noisy signal is a fundamental problem in signal processing. Signal noise is a problem in many environments, for example speech signals that are transmitted by speech communication devices will often be corrupted to some extent by noise resulting in reduced speech quality and intelligibility. Noise can also interfere with and degrade the performance of coding, detection and recognition algorithms.

A variety of different noise estimation techniques and devices have been developed in order to estimate and ultimately suppress noise in signals which comprise both signal and noise components. Such devices and methods have application in many areas such as speech coding, speech enhancement and speech recognition.

A noise estimation method for use with spectral subtraction and wiener filtering is described in "Quantile Based Noise Estimation for Spectral Subtraction and Wiener Filtering" by Stahl, Fischer and Bippus; ppl8751878, vol. 3, ICASSP 2000.

The quantile based noise estimation (QBNE) method described in Stahl et al is in relation to the estimation and suppression of noise in speech signals. In the QBNE method it is assumed that even in speech sections of an input signal not all frequency bands will be occupied by speech and that, in fact, for a significant percentage of the time the energy in each frequency band will be noise only.

With the above assumption the noise power N(k,t) for frame t and frequency bin k is estimated in Stahl et al's QBNE method using the noisy signal power X(k,t) from T adjacent time frames. Note that X(k,t) for k = 0,.. ,K is obtained via the Short Term Discrete Fourier Transform where 2(K -1) is the DFT size. Any power spectral density (PSD) estimator, for example the periodogram, may then be used to obtain X(k,t). The T frames are maintained and sorted in a First-In-First-Out (FIFO) buffer.

In general, the quantile of a data set {x,i 0, .,T-l} is obtained by sorting the data in ascending order, i.e. x0 = x =* = x7. For a particular q value, the quantile will then be XqTj where [j rounds down to the nearest integer and 0 = q <I. The minimum will be selected if q = 0, the maximum is when q - 1 and the median is obtained with q=0.5.

Tn the QBNE method of Stahl et al the T frames are sorted by the FIFO buffer and the noise estimate obtained by setting q= 0.5.

The above QBNE approach yields good noise estimates but it is noted that the estimation accuracy is highly dependent on the size of the quantile buffers, i.e. the number of frames, T, that are sorted in the buffer. If T is small then the number of frames used will not capture enough signal statistics to provide accurate quantile estimation. If T is large, then rapid changes in the noise power will not be tracked by the QBNE technique. Indeed, the tracking capabilities will be restricted by the size of the quantile buffer.

The above described QBNE approach is also sensitive to the choice of the q value which in turn is usually dependent on the Signal to Noise Ratio (SNR). A fixed q value will in general result in over-estimation of the noise power under high SNR conditions.

Under very noisy conditions, on the other hand, the noise estimate may be under- estimated.

A periodogram PSD estimator is usually used in the QBNE approach mainly due to its cheap implementation cost. However, this estimator is widely known to suffer from a large variance which can result in large and nontolerable fluctuations in the noise estimate.

If the above QBNE approach is applied to speech enhancement devices in which spectral subtraction, for example, is used then the above estimation errors can result in signal distortions due to over- suppression of the noise. It can also yield the musical noise artefact usually associated with subtractive methods due to the random fluctuations in the noise estimate (see for example RJ. McAulay and M.L. Malpass, Speech enhancement using a soft-decision noise suppression Jilter, IEEE Transactions on Acoustics, Speech and Signal Processing 28 (1980), no. 2, 137-145) It is also noted that the above noise estimation technique requires that T-dimensional quantile buffers are maintained and updated for K+1 frequency bins. The sorting operation and subsequent memory shifting is usually expensive and as either K or T increases the technique will become computationally expensive which will have implications for real time and low resource implementations.

It is therefore an object of the present invention to provide a noise estimation method and apparatus that substantially overcomes or mitigates the above mentioned problems

with the prior art.

According to a first aspect of the present invention there is provided a method of estimating the noise power spectrum N(k,t) in an observed noisy signal having a power spectrum X(k,t) comprising the steps of a. Receiving and storing the noisy signal for Ttime frames; b. For a frequency k sorting the frames X(k, t) such that X(k,t0) =X(k,t) =... =x(k,t1) (1) and obtaining a noise estimate N(k,t) wherein the noise estimate is calculated as the quantile N(k,t) X(k,tLqTj); (2) c. applying a recursive function to N(k,t) in order to generate N(k,t), the recursive function being arranged so as to reduce fluctuations in the noise estimate N(k,t).

Correspondingly there is provided an apparatus for estimating the noise power spectrum N(k,t) in an observed noisy signal having a power spectrum X(k,t) comprising a. input and storage means for receiving and storing the noisy signal for T time frames; b. first means arranged for a frequency k to sort the frames X(k,t) such that X(k,to) =X(k,t1) =.. =X(k,t) and to calculate a noise estimate N(k), wherein I(k,t)=X(k,t [qi] c. second means to apply a recursive function to N(k, t) in order to generate N(k, t), the recursive function being arranged so as to reduce fluctuations in the noise estimate 7V(k,t) In the present invention a noise estimate, N(/c), is obtained by a quantile based noise estimation method and the noise estimate so obtained is further processed by smoothing the estimate by means of a recursive function to calculate a smoothed noise estimate N(k,t).

The T frames of the received signal may conveniently be stored in a Firstin-First-Out Buffer (FIIFO). The T frames stored within the buffer may represent the past T frames or alternatively the buffer may be filled with frames from the past (relative to the current frame t) and the future (e.g. the buffer may store frames t - T/2 to t + T/2-1).

The value of q used is preferably the median (i.e. =0.5).

It is noted that noise estimation methods arc often utilised in systems in such a manner that requires the analysis of the input signal over multiple frequency bands (K+1 bands).

Furthermore, in the present invention the noise estimate is obtained by processing a T- dimensional buffer at each frequency band. This equates to K+1 times the cost of sorting one buffer (this cost depends on I) that needs to be performed in order to produce an updated noise estimate over all frequency bands. This can be computationally expensive and so conveniently only a subset of the K+1 frequencies may be updated at any one time frame t. The noise estimate at the remaining frequencies may be derived by interpolation from the sub-set of values that have just been updated.

Conveniently, the estimates that have been derived by interpolation may further be averaged with previously calculated values for those frequencies that are stored within the buffer.

At the following frame, i.e. frame t+ 1, a different subset of the frequency range of interest is updated.

Conveniently the noise estimate, N(k,t), obtained by the quantile based method is smoothed by a first order recursive function wherein N(k, t) = p(k, t)N(k, I -1) + (1 - p(k, t))N(k, t) (3) where p(k,t) is a smoothing (forgetting) factor with values between 0 and 1. p(k,t) can be fixed or can be frequency and time dependent and updated according to the signalto-noise (SNR) ratio in the observed signal at the current frame.

The instantaneous signal-to-noise ratio (SNR), y(k,z'), may be defined as the ratio between the input noisy speech spectrum and the current QBNE estimate, i.e. r(k,t)t) (4) Alternatively, the noise estimate at the previous frame can also be used as follows = X(k,t) (5) N(k,t-l) The smoothing factor p(k,i) may be selected to satisfy the following criteria: If the SNR increases, the most recent noise estimate N(k,t) calculated by the QBNE method will become less reliable since it is likely to be over-estimated. This most recent estimate of N(k,t) should therefore be given less weight when updating the noise estimate IcT(k,t). Hence p(k,t) should approach I. As the SNR decreases, howcver, the noise will dominate at a given frequency bin and the current QBNE estimate will become more reliable as far as calculating an updated cstimate is concerned. p(k,t) should then be closer to zero.

A function satisfying the above criteria could be p(k,t)= (k,t) (6) The sensitivity of the prcsent invention may conveniently be controlled by the parameter,u. As u -O then p(k,t)- 1 and N(k,t) will have less of an effect on the smoothed noise estimate (hence reducing the tracking capability of QBNE) regardless of the SNR value. As i increases N(k,t) can have a greater effect, depending on the SNR, on the smoothed noise estimate.

The present invention may be used for example to estimate noise in signals comprising speech and noise components. This noise estimator will be useful for many applications including speech enhancement and voice activity detection.

In a further aspect of the present invention there is provided a method of estimating the noise power spectrum N(k,t) at frequencies k = 0,. ,K in an observed noisy signal having a power spectrum X(k,t) comprising the steps of i) Receiving and storing the noisy signal for Ttime frames; ii) for each frequency of a subset of the total K+1 frequency bands, sorting the frames X(k, t) such that X(k,t0) = X(k,t1) =... = X(k,t) and obtaining a noise estimate N(k,t) wherein the noise estimate is calculated as the quantile N(k,t) = X(k,t[TJ); iii) calculating N(k,t) over all remaining frequencies by interpolation from the values derived in step (ii) The skilled person will recognise that the above-described equalisers and methods may be embodied as processor control code, for example on a carrier medium such as a disk, CD- or DVD-ROM, programmed memory such as read only memory (Firmware), or on a data carrier such as an optical or electrical signal carrier.

These and other aspects of the invention will now be further described, by way of example only, with reference to the accompanying figures in which: Figure 1 shows a plot of signal power versus frequency for a noisy speech signal Figure 2 shows a frequency versus time plot for a signal over Ttime frames Figure 3 shows an unsorted buffer of power spectrum values versus time Figure 4 shows the results of an objective test comparing the conventional QBNE technique with aspects of the present invention.

The quantile based noise estimation method described in Stahl et al estimates the noise power spectrum continuously (i.e. even during periods of speech activity) by utilising the assumption that the speech signal is not stationary and will not occupy the same frequency band permanently. The noise signal on the other hand is assumed to be slowly varying compared to the speech signal such that it can be considered relatively constant for several consecutive analysis frames (time periods).

Working under the above assumptions it is possible to sort, at each frequency band under consideration, the received signal power spectrum into a buffer and to retrieve a noise estimate from the so constructed buffers.

The prior art implementation of this quantile based noise estimation (QBNE) approach is illustrated in Figures 1 to 3.

Figure 1 shows a plot of signal power (power spectrum) versus frequency for a noise signal 1 and a speech signal at two different times, tj and t2 (in the Figure the speech signal at time tj is labelled 3 and at time t2 it is labelled 5). It can be seen that the speech signal does not occupy the same frequencies at each time and so the noise, at a particular frequency, can be estimated when speech does not occupy that particular frequency band. In the Figure, for example, the noise at frequencies fj and f2 can be estimated at time r1 and the noise at frequenciesf andf4 can be estimated at time t2.

For a noisy signal, X(k,t) is the power spectrum of the noisy signal where k is the frequency tone and t is the tirne(frame) index. If T fl- ames around frame t are stored in a buffer then for frame 1, these T frames X(k, t) can be sorted at each frequency bin in an ascending order such that X(k,i0) = X(k,t1) = - -. = X(k,t1) (7) rT where t.EIt-- t±- l L 2 2 It is noted that in this case the T frames that are stored in the buffer comprise frames from both before and after time frame t. As an alternative the T frames could all be taken from before time t.

The above equation is illustrated in Figures 2 and 3. Turning to Figure 2 a frequency versus time plot is shown for a number of time frames (for the sake of clarity only 5 of the total T frames are shown). At each frame the power spectrum of the signal is a vector represented by the vertical boxes (2 1,23,25,27,29).

For a particular frequency, k, (illustrated by the horizontal box 31 in Figure 2) the power spectrum values over a window of T frames may be stored in a FIFO buffer as illustrated in Figure 3. The stored frames can then be sorted in ascending order (as described in relation to Equation 7 above) using any fast sorting technique.

The noise estimate, N(k,t), for the k" frequency may be taken as the qth quantile of the sorted values in the buffer. In other words, N(k,t) = X(ktqj) (8) where 0 = q <1 and [ ] denotes rounding down to the nearest integer. The noise estimate may be worked out for each frequency band.

If q is set equal to 0.5 then the median value will be selected as the noise estimate. By selecting that value it is then assumed that, for T frames, one particular frequency will be occupied by a speech component for at most 50% of the time. It is thought that the median quantile value will give better performance than other quantile values as it is less vulnerable to outliers.

It is noted that conventional speech analysis systems often analyse input signals in more than one hundred frequency bands. If 30 frames (i.e. if T=30) are also stored and sorted in order to derive the noise estimate then it may become computationally prohibitively expensive to maintain and update a noise estimate at every frequency for every frame.

The noise estimate may therefore only be updated over a sub-set of the total frequency bands under analysis. For example, if there are 10 frequency bands then for a first frame t the quantile buffers may be updated and sorted only for the odd frequency bands (1,3,5,7,9). During the next frame t', only buffers for the even frequency bands (2,4,6,8,10) are updated.

For frame t, the noise estimate on the even frequency bands (the quantile of which has not been altered) may be calculated by interpolation from the odd frequency values. For frame t', the noise estimate on the odd frequency bands may be calculated by interpolation from the even frequency values.

To improve the accuracy, the noise estimates which were obtained solely by interpolation can also be adjusted by a weighted linear combination with the quantile estimate for that particular frequency from the previous time frame. The two weights should add up to one.

In the present invention it is noted that the QBNE derived noise estimate can be improved by smoothing the value obtained from Equation (8) above using a recursive function which preferably is a first order recursive function, wherein I/(k, t) = p(k, t)I(k, t -1) + (1 - p(k, t)) N(k, t) (9) where N(k,t) is the noise estimate derived in Equation (8) above, N(k,t) is the smoothed noise estimate and p(k,t) is a smoothing parameter. p(k,t) may be fixed or alternatively may be time and frequency dependent and updated at every frame t according to the signal-to-noise ratio (SNR).

The instantaneous SNR may be defined as the ratio between the input noisy speech spectrum and the current QBNE noise estimate, i.e. (10) Alternatively, the noise estimate from the previous frame may also be used such that X(k,t) (11) N(k,t-1) In either case the smoothing parameter may be obtained as p(k,t) = y(k,t) (12) Where 1u is a parameter that controls the sensitivity to the QBNE estimate.

Figure 4 shows the performance of aspects of the present invention in an objective test.

In the test, car noise was artificially added to originally clean recordings from 3 female and 3 male speakers at different SNR levels. The experiments were performed on a speech enhancement task where classical spectral subtraction was used. A buffer of size 33 frames was used (T=33).

In the objective test 6 recordings from every speaker were used. Each speaker had just a couple of sentences shared with at least one other speaker. In total there were 27 different sentences in the 36 recordings used.

The sentences were enhanced using the conventional QBNE technique (as taught by Stahl et al) and compared to enhancement using aspects of the present invention. The objective measure used was the cepstral distance between the original clean recording and the enhanced signal after noise has been artificially added to it.

In Figure 4, the conventional QBNE enhancement is shown as the solid black line (labelled ORIG). The results of enhancement using two embodiments of the present invention are also shown in Figure 4.

In the first embodiment of the present invention tested, the noise estimate was recursivcly smoothed and updated at each time frame for every frequency band. The results of this enhancement are shown by the dashed line with A symbols (labelled SMTII in Figure 4). It can be seen that the present invention outperforms the conventional QBNE technique across all SNR values.

In the second embodiment of the present invention tested, the noise estimate was recursively smoothed and updated for a sub-set of the available frequency bands only at each time frame. Interpolation was used to obtain a full noise estimate. The results of this enhancement are shown by the dashed line with 0 symbols (labelled SMTH_RUIR in Figure 4). It can be seen that the second version of the present invention (smoothing of the noise estimate with a reduced update rate) also outperforms the conventional QBNE technique. It is also note that the Reduced Update Rate technique used without recursive smoothing is also found to improve performance. The size of the quantile buffers in this second embodiment was 7 frames and the rate at which they were updated was 8 frames per second.

The present invention was also assessed in a further subjective test. For each of the 6 speakers, two sentences were selected and concatenated together. The concatenated recordings were then enhanced using the ORIG and the SMTH RUR methods. Subjects were asked to listen to a pair of recordings, each enhanced with one different method, and asked to choose the one they preferred (they were also allowed to choose not to have any preference). Note that a few pairs with a slight but obvious differences were also inserted in the test. The results of this test are shown in Table 1 below for three different SNIR values: 0, 5 and 20 dB. From these results it can be seen that, as desired, the subjects were unable to perceive any difference between the two approaches and that, at an SNR of 20dB, subjects preferred the results achieved using the present invention.

Ornc Same SMTH_RUR 0dB 6.25 % - 87.5 % 6.25 % dB 6.25 % 85.4 % 8.35 dB 10.4 % 43.75 % 45.85 % Table 1 Results of the subjective test to evaluate the original QBNE technique with the new technique.

The same recordings used in the subjective test were used to assess the computational

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load. The algorithms were implemented on Matlab and no special effort was put to optimise the processing speed. The speed was measured using the Matlab profiler which gives the total processing time in seconds. Despite the overhead incurred due to the additional processing steps the new algorithm was found to be about 2.23 times faster than the original approach. As shown in Figure 4 and Table I the gain in computational efficiency is obtained at no performance degradation cost.

Claims (19)

1. I. A method of estimating the noise power spectrum N(k,t) in an observed noisy signal having a power spectrum X(k,t) comprising the steps of a Receiving and storing the noisy signal for Ttime frames; b. For a frequency k sorting the frames X(k,t) such that X(k,t0) = X(k,t) =*** = X(k,t1) and obtaining a noise estimate N(k,t)wherein the noise estimate is calculated as the quantile N(k,t) = X(k,t[qrj); c. applying a recursive function to N(k,t) in order to generate N(k,t), the recursive function being arranged so as to reduce fluctuations in the noise estimate N(k,t).
2. 2. A method as claimed in claim 1 wherein q = 0.5.
3. 3. A method as claimed in any preceding claim wherein N(k,t) is estimated at frequencies, k = 0, K and method step (h) comprises the sub-steps of i) calculating the quantile noise estimate N(k,t) over a subset of the total number of frequencies k = 0,. *,K, and; ii) calculating N(k,t) over all remaining frequencies by interpolation from the values derived in step (i).
4. 4. A method as claimed in claim 3 wherein interpolation in step (ii) is by linear interpolation.
5. 5. A method as claimed in any preceding claim wherein the recursive function is a first order recursive function defined as N(k, t) = p(k, t) lcr(k, t -1) + (1 - p(k, t))N(k, t) (13) where p(k,t) is a frequency dependent parameter which is updated at every time t according to the signal-to-noise ratio (SNIR) in the observed signal.
6. 6. A method as claimed in claim 5 wherein p(k,t) is defined as p(k,t) = and y(k,t) = X(k,t) N(k,t) where 1u is a parameter that can be used to alter the sensitivity of p(k,t) to the SNR y(k,t).
7. 7. A method as claimed in claim 5 wherein p(k,t) is defined as p(k,t) = and y(k,t) = X(k,t) N(k,t-1) where 1u is a parameter that can be used to alter the sensitivity of p(k,t) to the SNR
8. 8. An apparatus for estimating the noise power spectrum N(k,t) in an observed noisy signal having a power spectrum X('k,t) comprising a. input and storage means for receiving and storing the noisy signal for Ttime frames; b. first means arranged for a frequency k to sort the frames X(k, t,) such that X(k,t0) =X(k,t1) =.. =X(k,t7) and to calculate a noise estimate N(k), wherein N(k,t)=X(k,t [qi] c. second means to apply a recursive function to N(k,t) in order to generate N(k,t), the recursive function being arranged so as to reduce fluctuations in the noise estimate N(k,t).
9. 9. An apparatus as claimed in claim 8 wherein q 0.5.
10. 10. An apparatus as claimed in claims 8 or 9 wherein the noise estimate 1(k,t) is calculated at frequencies k = 0,..., K and the first means calculates the noise estimate N(k, t) over a subset of the total number of frequencies k = 0,. *, K, the apparatus further comprising interpolation means for calculating N(k, t) over all frequencies by interpolation from the values derived by the first means.
11. II An apparatus as claimed in claim 10 wherein the interpolation means uses linear interpolation
12. 12. An apparatus as claimed in any preceding claim wherein the recursive function applied by the second means is a first order recursive function defined as N(k,t) = p(k,t)I(k,t -1)+(l -p(k,t))N(k,t) where p(k,t,) is a frequency dependent parameter which is updated at every frame t according to the signal-to-noise (SNR) ratio in the observed signal.
13. 13. An apparatus as claimed in claim 12 wherein p(k,t) is defined as p(k, t)= 1(k,t) and 1(k,t)= X(k,t) r(k,t)+,u N(k,t) where i is a parameter that can be used to alter the sensitivity of the noise estimate to N(k,t)
14. 14. An apparatus as claimed in claim 12 wherein p(k,t) is defined as p(k, t)= y(k,t) and y(k,t)= X(k,t) N(k,t-1) where j is a parameter that can he used to alter the sensitivity of the noise estimate to N(k,t)
15. 15. A method of estimating the noise power spectrum N(k,t) at frequencies k = 0,**, K in an observed noisy signal having a power spectrum X(k,t) comprising the steps of i) Receiving and storing the noisy signal for Ttime frames; ii) for each frequency of a subset of the total K+] frequency bands, sorting the frames X(k,1) such that X(k, t0) = X(k, t) =... = X(k, t1) and obtaining a noise estimate N(k, t) wherein the noise estimate is calculated as the quantile N(k,s) X(/ctqj); iii) calculating N(k,t) over all remaining frequencies by interpolation from the values derived in step (ii)
16. 16. Processor control code to, when running, implement the method of any one of claims Ito 7 or claim 15.
17. 17. A carrier carrying the processor control code of claim 16.
18. 18. Processor control code to, when running, implement the apparatus of any of claims 8 to 14.
19. 19. A carrier carrying the processor control code of claim 18.