Hearing aid comprising a noise reduction system

Abstract

A hearing aid comprises a) a multitude of M input transducers each providing an electric input signal representative of environment sound in a time-frequency representation (k, l), and each comprise varying amounts of target (s) and noise (v) signal components; b) a signal processor configured to process said multitude of electric input signals; and comprising a beamformer filter configured to receive said multitude M of electric input signals and to provide a spatially filtered signal and a post-filter configured to receive said spatially filtered signal and to provide an estimate Ŝ(k,l) of a target signal representing said target signal components from said target sound source. The signal processor is configured to provide estimates of power spectral densities λ.sub.s(k,l) of said target signal components in dependence of inter-frequency bin relationships between the spectral components enforced by properties of the electric input signals across at least some of said frequency bins.

Claims

1. A hearing aid configured to compensate for a user's hearing impairment, comprising an input unit comprising a multitude of M input transducers, each configured to convert sound in an environment of the user to an electric input signal representative of said sound, each of the multitude of electric input signals being provided in a time-frequency representation (k, l), where k and l are frequency and time frame indices, respectively, (k, l) defining a time-frequency tile, and k=1, . . . , K, where K is a number of frequency bins, and wherein the electric input signals X.sub.m(k,l), m=1, . . . , M, each comprise varying amounts of target (s) and noise (v) signal components originating from a target sound source and one or more noise sound sources, respectively, in said environment; a signal processor configured to process said multitude of electric input signals and for providing a processed electric signal representative of said sound; and wherein the signal processor comprises a noise reduction system comprising a beamformer filter followed by a post-filter, the beamformer filter being connected to the input unit and configured to receive said multitude M of electric input signals X.sub.m(k,l) and configured to provide a spatially filtered signal, the post-filter being configured to receive said spatially filtered signal and to provide an estimate Ŝ(k,l) of a target signal representing said target signal components from said target sound source; and wherein the signal processor is configured to provide estimates of power spectral densities λ.sub.s(k,l) of said target signal components in dependence of inter-frequency bin relationships between the spectral components of the target signal components and/or of the noise signal components across at least some of said frequency bins.

2. A hearing aid according to claim 1 wherein the estimates of power spectral densities λ.sub.s(k,l) of the target signal components are provided under the constraint that the final target speech power spectral density estimates λ.sub.s(k,l) a) are all non-negative, and b) sum across frequency, for a given frame index, to a less biased a priori estimate of the clean speech estimate for the frequency range in question.

3. A hearing aid according to claim 1 wherein the signal processor comprises or has access to a multitude D of observations of the electric input signals X.sub.m(k,l) at different time frame indices l.

4. A hearing aid according to claim 1 wherein the signal processor is configured to provide first maximum likelihood estimates λ.sub.s.sup.ML(k,l) and λ.sub.v.sup.ML(k,l) of power spectral densities λ.sub.s(k,l) and λ.sub.v(k,l) of said target and noise signal components, respectively, estimated independently in each frequency bin.

5. A hearing aid according to claim 3 wherein the signal processor is configured to provide estimates of power spectral densities λ.sub.s(k,l) of said target signal components in dependence of said multitude of observations of the electric input signals by solving an estimation problem wherein the likelihood of said power spectral densities of said target and noise signal components is maximized, where the likelihood is computed across a multitude of frequency bins for a given time instant l′, under constraints regarding said estimates of power spectral densities λ.sub.s(k,l) of said target signal components.

6. A hearing aid according to claim 5 wherein said constraints comprise a) that a sum of said estimates of power spectral densities λ.sub.s(k,l) over frequency indices, k=k.sub.i.sup.min, . . . , k.sub.i.sup.max, is equal to a corresponding sum of first maximum likelihood estimates λ.sub.s.sup.ML(k,l), and b) that each of said estimates of power spectral densities λ.sub.s(k,l) over frequency indices, k=k.sub.i.sup.min, . . . , k.sub.i.sup.max, are larger than or equal to zero.

7. A hearing aid according to claim 6 wherein frequency bins between k.sub.i.sup.min and k.sub.i.sup.max represent a frequency sub-band of the electric input signals.

8. A hearing aid according to claim 6 wherein k.sub.i.sup.min is equal to 1, and wherein k.sub.i.sup.max is equal to K, whereby index i represents a full-band signal.

9. A hearing aid according to claim 4 wherein said estimates of the power spectral densities λ.sub.v(k,l) of said noise signal components are equal to the first maximum likelihood estimates λ.sub.v.sup.ML(k,l).

10. A hearing aid according to claim 4 wherein said estimates of the power spectral densities λ.sub.s(k,l) of said target signal components is determined in dependence of said first maximum likelihood estimates λ.sub.v.sup.ML(k,l) current beamformer weights w(k,l), and Ĉ.sub.x(k,l) an estimate of a noisy covariance matrix C.sub.x(k,l) computed as a sample covariance matrix of the M electric input signals X.sub.m(k,l), m=1, . . . , M, or a as a recursively updated covariance matrix estimate.

11. A hearing aid according to claim 1 wherein said post-filter is configured to apply post-filter gains to said spatially filtered signal in dependence of said estimates of power spectral densities λ.sub.s(k,l) and λ.sub.v(k,l) of said target and noise signal components to thereby provide said estimate Ŝ(k,l) of the target signal.

12. A hearing aid according to claim 11 wherein said post-filter gains G.sub.PF(k,l) are determined from the respective target and noise power spectral densities λ.sub.s(k,l) and λ.sub.v(k,l) as a single-channel Wiener filter gain, given by G.sub.PF(k,l)=λ.sub.s/(λ.sub.s+λ′.sub.v), where λ′.sub.v is a normalized noise power spectral density.

13. A hearing aid according to claim 1 wherein said beamformer filter is or comprises an LCMV beamformer.

14. A hearing aid according to claim 1 comprising an output unit comprising an output transducer for converting said processed electric signal to stimuli perceivable by the user as sound, and/or a transmitter for transmitting processed electric signal to another device or system.

15. A hearing aid according to claim 14 wherein said estimate Ŝ(k,l) of a target signal representing sound from said target sound source may a) be presented to a user of the hearing aid, and/or b) be transmitted to another device or system for use and/or further analysis there.

16. A hearing aid according to claim 1 wherein said target sound source is sound from the user's mouth.

17. A hearing aid according to claim 15 wherein said estimate Ŝ(k,l) of a target signal represents the user's own voice and a) is transmitted to a far end communication partner and/or b) is forwarded to a keyword detector of the hearing aid and/or of another device.

18. A hearing aid according to claim 1 being constituted by or comprising an air-conduction type hearing aid, a bone-conduction type hearing aid, a cochlear implant type hearing aid, or a combination thereof.

19. A method of operating a hearing aid configured to compensate for a user's hearing impairment, the method comprising providing a multitude M of electric input signals representing sound in an environment of the user in a time-frequency representation (k, l), where k and l are frequency and time frame indices, respectively, (k, l) defining a time-frequency tile, and k=1, . . . , K, where K is the number of frequency bins, and wherein the electric input signals X.sub.m(k,l), m=1, . . . , M, each comprise varying amounts of target (s) and noise (v) signal components originating from a target sound source and one or more noise sound sources in said environment; processing said multitude of electric input signals and providing a processed electric signal representative of said sound; and providing a spatially filtered signal by beamforming in dependence the input unit and configured to receive said multitude M of electric input signals X.sub.m(k,l), and providing an estimate Ŝ(k,l) of a target signal representing said target signal components from said target sound source by post-filtering said spatially filtered signal, and providing estimates of power spectral densities λ.sub.s(k,l) of said target signal components in dependence of inter-frequency bin relationships between the spectral components of the target signal and/or of the noise signal components across at least some of said frequency bins.

20. A method according to claim 19 comprising determining post-filter gains in dependence of said estimates of power spectral densities λ.sub.s(k,l) and λ.sub.v(k,l) of said target and noise signal components; and applying said post-filter gains to said spatially filtered signal to thereby provide said estimate Ŝ(k,l) of the target signal.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) The aspects of the disclosure may be best understood from the following detailed description taken in conjunction with the accompanying figures. The figures are schematic and simplified for clarity, and they just show details to improve the understanding of the claims, while other details are left out. Throughout, the same reference numerals are used for identical or corresponding parts. The individual features of each aspect may each be combined with any or all features of the other aspects. These and other aspects, features and/or technical effect will be apparent from and elucidated with reference to the illustrations described hereinafter in which:

(2) FIG. 1 shows an exemplary course of the expression

(3) $\delta \left(\mu \right)-ϛ+\frac{\sqrt{2\mathrm{ϛ\mu }+1}-1}{\mu }$
in dependence of the ‘water level’ μ in the range [0, 10],

(4) FIG. 2A schematically shows (in the top part) a noisy speech signal x.sub.i(n), amplitude versus time (n), as received at an i.sup.th microphone of a hearing aid, and (in the bottom part) overlapping time ranges (Frame #l) for a fast Fourier transform (FFT) algorithm;

(5) FIG. 2B schematically shows a time-frequency (frequency domain) representation X.sub.i(k,l) of the time domain signal x.sub.i(n) of FIG. 2A after an FFT, each frequency bin (time-frequency unit, X.sub.i(k,l)) comprising a complex number representing a magnitude (|X.sub.i(k,l)|) and a phase (∠X.sub.i(k,l)) of the signal at frequency index k and time index l, the values X.sub.i(k,l′), k=1, . . . , K, at time l′ (K being the order of the FFT) representing a spectrum of the noisy x.sub.i signal at microphone i at time l′; and

(6) FIG. 2C schematically shows a spectrum of the noisy input signal at microphone i (X.sub.i(k,l′), and estimates of the corresponding spectra of the clean speech signal S.sub.i(k,l′) according to a prior art method (Ŝ.sub.i,prior(k,l′)) and according to the present disclosure (Ŝ.sub.i(k,l′)),

(7) FIG. 3 schematically shows an embodiment of a hearing aid comprising a noise reduction system according to the present disclosure,

(8) FIG. 4A schematically shows a time variant analogue signal (Amplitude vs time) and its digitization in samples, the samples being arranged in a number of time frames, each comprising a number N.sub.s of samples, and

(9) FIG. 4B schematically illustrates a time-frequency representation of the time variant electric signal of FIG. 4A, in relation to the present disclosure,

(10) The figures are schematic and simplified for clarity, and they just show details which are essential to the understanding of the disclosure, while other details are left out. Throughout, the same reference signs are used for identical or corresponding parts.

(11) Further scope of applicability of the present disclosure will become apparent from the detailed description given hereinafter. However, it should be understood that the detailed description and specific examples, while indicating preferred embodiments of the disclosure, are given by way of illustration only. Other embodiments may become apparent to those skilled in the art from the following detailed description.

DETAILED DESCRIPTION OF EMBODIMENTS

(12) The detailed description set forth below in connection with the appended drawings is intended as a description of various configurations. The detailed description includes specific details for the purpose of providing a thorough understanding of various concepts. However, it will be apparent to those skilled in the art that these concepts may be practiced without these specific details. Several aspects of the apparatus and methods are described by various blocks, functional units, modules, components, circuits, steps, processes, algorithms, etc. (collectively referred to as “elements”). Depending upon particular application, design constraints or other reasons, these elements may be implemented using electronic hardware, computer program, or any combination thereof.

(13) The electronic hardware may include micro-electronic-mechanical systems (MEMS), integrated circuits (e.g. application specific), microprocessors, microcontrollers, digital signal processors (DSPs), field programmable gate arrays (FPGAs), programmable logic devices (PLDs), gated logic, discrete hardware circuits, printed circuit boards (PCB) (e.g. flexible PCBs), and other suitable hardware configured to perform the various functionality described throughout this disclosure, e.g. sensors, e.g. for sensing and/or registering physical properties of the environment, the device, the user, etc. Computer program shall be construed broadly to mean instructions, instruction sets, code, code segments, program code, programs, subprograms, software modules, applications, software applications, software packages, routines, subroutines, objects, executables, threads of execution, procedures, functions, etc., whether referred to as software, firmware, middleware, microcode, hardware description language, or otherwise.

(14) The present application relates to the field of hearing aids, e.g. hearing instruments configured to compensate for a user's hearing impairment, or similar devices. The present disclosure relates to noise reduction in hearing aids.

(15) One of the challenges with the implementation of multi-microphone noise reduction systems in practical applications lies in the need for the knowledge of the speech and noise covariance matrices. A method based on Maximum Likelihood (ML) estimation has been proposed to address the problem. Despite its relative success in practical setups, this method may suggest (physically impossible) negative spectral components for the clean speech due to noise influences.

(16) The present disclosure proposes a new estimation technique that tackles this issue by enforcing a power constraint on the estimation problem.

(17) Poor performance in noise is one of the most common points of dissatisfaction for the users of hearing-assistive devices (HADs). A noise reduction system is for this reason an integral part of most modern HADs. One of the most well-known noise reduction techniques is the multi-channel Wiener filter (MWF). Despite offering simple closed-form solutions, implementation of MWFs in practical setups such as in HADs tangles with practicalities, among which estimation of the generally time-varying inter-microphone statistics of speech and noise is particularly challenging.

(18) The MWF can be decomposed as a cascade of an MVDR beamformer and a single-channel postfilter. Several methods have been proposed for estimating the signal statistics necessary to implement the MWF beamformer in general and the speech and noise power spectral densities (PSD) for implementing the postfilter in particular. A Maximum Likelihood (ML) scheme has been proposed for estimating the speech and noise PSDs. This method has been successfully used for scientific as well as industrial applications (cf. e.g. US20180359572A1, or U.S. Pat. No. 10,165,373B2). However, typically there are some frequency bins where the ML estimation scheme suggests negative values for the speech spectrum. Rounding these components up to zero, which is often done in practical speech enhancement systems, leads to an overall tendency to overestimate the speech power (cf. below for more details). In this disclosure, an estimation technique that alleviates this issue is proposed. Although the proposed method can be applied for speech and noise PSD estimation in a broader context, we focus in the present disclosure on noise reduction using the MWF.

(19) Maximum Likelihood Estimation of Speech and Noise Spectra:

(20) In the short-time Fourier transform (STFT) domain, we use the following model for the noisy speech X acquired by M microphones:
X(k,l)=S(k,l)d(k,l)+V(k,l),  (1)
where the M-dimensional vectors X(k,l) and V(k,l), respectively. represent noisy speech and noise signals at the M microphones at frequency bin k and time frame l. The clean speech signal at the reference microphone is denoted by S(k,l), and the M-dimensional vector d(k,l) is the relative transfer function for the M microphones; i.e. the transfer function from the target speech source to the M microphones normalized by the one for the reference microphone (cf. e.g. US20180359572A1). Assuming that the noise and speech signals are uncorrelated and using (1), the covariance matrix of the noisy speech is given by:
C.sub.x(k,l)=λ.sub.s(k,l)d(k,l)d.sup.H(k,l)+λ.sub.v(k,l)Γ(k,l),  (2)
Where λ.sub.s(k,l)=|S(k,l)|.sup.2 and λ.sub.v(k,l) are, respectively, the clean speech and noise spectra at the reference microphone, and Γ(k,l) is the noise covariance matrix normalized by the noise variance at the reference microphone. One can say that Γ(k,l) represents the structure of the noise covariance matrix. Using a voice activity detector, the noise covariance matrix can be estimated directly during the speech absence intervals. Assuming that the structure of the covariance matrix remains unchanged during speech activity intervals, (2) can be written as:
C.sub.x(k,l)=λ.sub.s(k,l)d(k,l)d.sup.H(k,l)+λ.sub.v(k,l)Γ(k,l.sub.0),  (3)
where l.sub.0 indexes the most recent frame with no speech activity. Given that the relative transfer functions d(k,l) are known, the only unknown parameters left in (3) are λ.sub.s(k,l) and λ.sub.v(k,l). Assume that X(k,l) follows a zero-mean complex circularly symmetric Gaussian distribution with the covariance matrix given in (3); i.e.
f.sub.X(X(k,l); λ.sub.s(k,l), λ.sub.v(k,l)=(0,C.sub.x(k,l)),  (4)
Also suppose that D independent observations of the noisy speech are available; e.g. D consecutive frames X.sub.D(k,l)=[X(k,l−D+1) . . . X(k,l)] assuming independence across the frames. The joint probability density function (pdf) of X.sub.D(k,l) is simply given by the product of the density functions of the individual frames, and the ML estimation of λ.sub.s(k,l) and λ.sub.v(k,l) can be obtained by maximizing the resultant joint pdf; i.e.

(21) $\begin{array}{cc}\underset{{\lambda }_s\left(k,l\right),{\lambda }_v\left(k,l\right)}{\max }\ln f_{{\underset{\_}{X}}_D}\left({\underset{\_}{X}}_D\left(k,l\right);{\lambda }_s\left(k,l\right),{\lambda }_v\left(k,l\right)\right)& \left(5\right)\end{array}$
which can be solved in closed-form, yielding the following (cf. e.g. [Jensen & Pedersen; 2015]):

(22) $\begin{array}{cc}{\lambda }_v^{\mathrm{ML}}\left(k,l\right)=\frac{1}{M-1}\mathrm{tr}\left(\frac{1}{D}{\underset{¯}{X}}_D^H\left(k,l\right)B\left(k,l\right){\left(B^H\left(k,l\right)\Gamma \left(k,l_0\right)B\left(k,l\right)\right)}^{-1}{B}^H\left(k,l\right){\underset{¯}{X}}_D\left(k,l\right)\right)& \left(6\right)\\ {\lambda }_s^{\mathrm{ML}}\left(k,l\right)=w^H\left(k,l\right)\left({\hat{C}}_x\left(k,l\right)-{\lambda }_v^{\mathrm{ML}}\left(k,l\right)\Gamma \left(k,l_0\right)\right)w\left(k,l\right),& \left(7\right)\end{array}$
where ‘tr’ is the trace operator, and where the M×M−1 blocking matrix B(k,l) can be calculated as the first M−1 columns of I.sub.M−d(k,l)d.sup.H(k,l)/d.sup.H(k,l)d(k,l), I.sub.M being theM×M identity matrix, and Ĉ.sub.x(k,l) (the sample covariance matrix) and w(k,l) (the MVDR beamformer weight vector) are defined as:

(23) $\begin{array}{cc}{\hat{C}}_x\left(k,l\right)\frac{1}{D}\underset{j=l-D+1}{\overset{l}{.Math.}}X\left(k,j\right)X^H\left(k,j\right)& \left(8\right)\\ w\left(k,l\right)\frac{{\Gamma }^{-1}\left(k,l_0\right)d\left(k,l\right)}{d^H\left(k,l\right){\Gamma }^{-1}\left(k,l_0\right)d\left(k,l\right)}& \left(9\right)\end{array}$
respectively.

(24) The estimator given by eq. (6) and (7) is the minimum-variance unbiased estimator, thus achieving the Cram{acute over ( )}er-Rao lower bound (cf. e.g. [Jensen & Pedersen; 20156]).

(25) However, when the noise level is large compared to the speech level at a certain frequency bin k, λ.sub.s.sup.ML(k,l) in eq. (7) may become negative. This can happen even at high global SNRs at frequency bins where the speech power is low. The typical treatment in such cases is to round up the negative values to zero (equivalent to adding a nonnegativity constraint to eq. (5)). However, one can argue that as the negative values of λ.sub.s.sup.ML(k,l) are due to the noise influence, there is no reason to believe that the positive ones are not, especially taking into account that the estimator is unbiased. Getting rid of the negative values by trimming them to zero at some frequency bins, leaves us with spurious positive estimates at some other frequency bins, which give rise to a net effect of overestimating the speech power. Consequently, when used in an MWF context, the noise in the resulting enhanced speech signal would be under-suppressed.

(26) The Problem to be Solved:

(27) Suppose that ={1, . . . , K} is the set of all frequency bins. The optimization problem of eq. (5) is defined over individual frequency bins, and one needs to solve it separately for each and every λ. Equivalently, one can write the joint pdf for all frequency bins as the product of the individual pdfs in eq. (4), and obtain the same solution as in eq. (6)-(7) by solving the following problem:

(28) $\begin{array}{cc}\underset{{\lambda }_s\left(1,l\right),\mathrm{.Math.},{\lambda }_s\left(K,l\right),{\lambda }_v\left(1,l\right),\mathrm{.Math.},{\lambda }_v\left(K,l\right)}{\max }\ln \underset{k=1}{\overset{K}{.Math.}}{f}_{{\underset{\_}{X}}_D}\left({\underset{\_}{X}}_D\left(k,l\right);{\lambda }_s\left(k,l\right),{\lambda }_v\left(k,l\right)\right)& \left(10\right)\end{array}$

(29) As argued above, when the noise influence is significant, λ.sub.s.sup.ML(k,l) resulting from eq. (10) may take negative or positive spurious values depending on the frequency bin. Let us denote the ML estimate of the speech power in frame l by P.sub.s.sup.ML(l), i.e.

(30) $\begin{array}{cc}{P}_s^{\mathrm{ML}}\left(l\right)\underset{k=1}{\overset{K}{.Math.}}{\lambda }_s^{\mathrm{ML}}\left(k,l\right)& \left(11\right)\end{array}$

(31) Note that P.sub.s.sup.ML(l) averages the noise influence over the individual spectral components, and is therefore likely to be less noisy than he individual estimates λ.sub.s.sup.ML(k,l). Based on this rationale, we introduce a power constraint to (10) to formulate a new estimation problem as follows:

(32) $\underset{{\lambda }_s\left(1,l\right),\mathrm{.Math.},{\lambda }_s\left(K,l\right),{\lambda }_v\left(1,l\right),\mathrm{.Math.},{\lambda }_v\left(K,l\right)}{\max }\ln \underset{k=1}{\overset{K}{.Math.}}{f}_{{\underset{\_}{X}}_D}\left({\underset{\_}{X}}_D\left(k,l\right);{\lambda }_s\left(k,l\right),{\lambda }_v\left(k,l\right)\right)$
subject to the constraints

(33) $\begin{array}{cc}\underset{k=1}{\overset{K}{.Math.}}{\lambda }_s\left(k,l\right)=P_S^{\mathrm{ML}}\left(l\right)\mathrm{and}{\lambda }_s\left(k,l\right)\ge 0\mathrm{for}\mathrm{all}k\in 𝒦& \left(12\right)\end{array}$
Solution of the Problem:

(34) It can be shown that the solution to the problem of eq. (12) for λ.sub.v(k,l) is the same as λ.sub.v.sup.ML(k,l) as expected (since the constraint in eq. (12) does not depend on λ.sub.v(k,l), and for λ.sub.s(k,l) it is given in the following ‘water-filling form’:

(35) $\begin{array}{cc}{\lambda }_s^{*}\left(k,l\right)={\left({\lambda }_s^{\mathrm{ML}}\left(k,l\right)-ϛ\left(k,l\right)+\frac{\sqrt{2ϛ\left(k,l\right)\mu \left(l\right)+1}-1}{\mu \left(l\right)}\right)}^{+}& \left(13\right)\end{array}$
where (⋅).sup.+max(⋅,ç(k,l)w.sup.H(k,l)Ĉ.sub.x(k,l)w(k,l), and the water level μ(l)≥0 is adjusted so that the following is fulfilled:

(36) 0$\begin{array}{cc}\underset{k=1}{\overset{\overline{K}}{.Math.}}{\lambda }_s^{*}\left(k,l\right)=P_s^{\mathrm{ML}}\left(l\right)& \left(14\right)\end{array}$

(37) The water level μ(l)≥0 can be calculated using any available efficient algorithm (cf. e.g. [Palomar & Fonollosa; 2005]) or simply using bisection. The graph of the term

(38) $\delta \left(\mu \right)-ϛ+\frac{\sqrt{2\mathrm{ϛ\mu }+1}-1}{\mu }$
is shown in FIG. 1 FIG. 1 shows an exemplary course of the expression

(39) $\delta \left(\mu \right)-ϛ+\frac{\sqrt{2\mathrm{ϛ\mu }+1}-1}{\mu }$
in dependence of the ‘water level’ μ in the range [0, 10]. When λ.sub.s.sup.ML(k,l)≥0 for all kϵ, the water level is μ(l)=0, yielding λ*.sub.s(k,l)=λ.sub.s.sup.ML(k,l). When λ.sub.s.sup.ML(k,l)<0 for at least one k, δ(μ) is always negative, implying that λ*.sub.s(k,l)<λ.sub.s.sup.ML(k,l). This, however, is only the case in frequency bins where λ.sub.s.sup.ML(k,l)>0. In other bins, the (⋅).sup.+ operator in eq. (13) sets λ*.sub.s(k,l) equal to 0. In summary, to calculate λ*.sub.s(k,l) from λ.sub.s.sup.ML(k,l), all negative components are trimmed to 0, and each positive one is reduced by an amount that depends on its corresponding ζ(k,l).

(40) Sub-Band Implementation:

(41) The MWF is optimal in sense of mean-squared error (MSE). The proposed method may lead to an implementation that is closer to the ideal MWF, yielding a lower MSE. This, however, may not necessarily translate into perceptual improvements. To optimize the performance in a more perceptual-oriented manner, it is proposed implement (12) in frequency sub-bands. Suppose that k.sub.i.sup.min and k.sub.i.sup.max index the lowest and highest frequencies in sub-band i, respectively. The ML estimation of the speech power in sub-band i is given by:

(42) $\begin{array}{cc}{P}_s^{\mathrm{ML}}\left(l\right)\stackrel{k=k_i^{\max }}{\underset{k=k_i^{\min }}{.Math.}}{\lambda }_s^{\mathrm{ML}}\left(k,l\right)& \left(15\right)\end{array}$

(43) Obviously, λ*.sub.s(k,l) will still be given by eq. (13), but the sub-band dependent water level μ.sub.i(l) should be adjusted such that the following holds:

(44) $\begin{array}{cc}\stackrel{k=k_i^{\max }}{\underset{k=k_i^{\min }}{.Math.}}{\lambda }_s^{*}\left(k,l\right)=P_{s,i}^{\mathrm{ML}}\left(l\right)& \left(16\right)\end{array}$

(45) Further details of the proposed scheme are discussed in [Zahedi et al.; 2020].

(46) The top part of FIG. 2A shows a noisy (time-domain) speech signal x.sub.i(n), amplitude (‘Ampl.’) versus time (‘Time’) (represented by time sample index n), as received at an i.sup.th microphone of a hearing aid. The noisy speech signal x.sub.i(n) is a mixture (sum) of a target signal s.sub.i(n) and a noise signal v.sub.i(n) (x.sub.i(n)=s.sub.i(n)+v.sub.i(n)). The target signal s.sub.i(n) may originate from a (localized) target sound source and the noise signal v.sub.i(n) may originate from one or more (localized or diffuse) sound sources. The bottom part of FIG. 2A schematically illustrates overlapping time ranges (‘Frame #l’) for from which time samples (e.g. 64 or 128 audio data samples per frame) of the noisy input signal x.sub.i(n) are taken as input to a Fourier transform algorithm, e.g. a fast Fourier transform (FFT) algorithm, such as a STFT algorithm (cf. arrow ‘FFT’ in FIG. 2A). In FIG. 2A, an overlap of approximately 50% is shown. The overlap may be smaller (e.g. 25%) or larger (e. g. 75%). FIG. 2B schematically shows a time-frequency (frequency domain) representation X.sub.i(k,l) of the time domain signal x.sub.i(n) of FIG. 2A after an FFT, each frequency tile (time-frequency unit, X.sub.i(k,l)) comprising a complex number (indicated by .circle-solid.) representing a magnitude (|X.sub.i(k,l)|) and a phase (∠X.sub.i(k,l)) of the signal at frequency index k and time frame index l, the values X.sub.i(k,l′), k=1, . . . , K, at time l′ (K being the order of the FFT) representing a spectrum of the noisy x.sub.i signal at microphone i at time frame l′. In FIG. 2B, the number frequency bins of a given time frame is indicated by K. K may take on any number larger than 1, 8 as shown in FIG. 2B, or 16, or 24 or 64 or more. A number (D−1) of previous time frames of the signal, X.sub.i(k,l′), are, together with the current timeframe l′ enclosed by a bold rectangle in FIG. 2B. The D time frames may represent the ‘context’ of estimation algorithms of the present disclosure, cf. e.g. eq. (5).

(47) FIG. 2C schematically shows a spectrum (magnitude (‘|.circle-solid.|’) versus frequency (‘Frequency (k)’)) of the noisy input signal (X.sub.i(k,l′)) at microphone i, at time index l′ (solid line in FIG. 2C). Likewise, estimates of the corresponding spectra of the clean speech signal S.sub.i(k,l′) according to a prior art method (Ŝ.sub.i,prior(k,l′)) (dashed line in FIG. 2C, based on eq. (5), (7)) and according to the present disclosure (Ŝ.sub.i(k,l′)) (dotted line in FIG. 2C, based on eq. (12)), are shown. As schematically illustrated in FIG. 2C, the estimated spectrum, Ŝ.sub.i,prior(k,l′) according to a prior art method exhibits negative values of magnitude at some (here higher) frequencies, whereas the estimated spectrum, Ŝ.sub.i(k,l′) according to the method of the present disclosure does not.

(48) FIG. 3 shows an embodiment of a hearing aid (HD) comprising a noise reduction system (NRS) according to the present disclosure. The hearing aid, e.g. a hearing instrument, comprises an input unit (IU) comprising a multitude of M input transducers (IT.sub.1, . . . , IT.sub.M), each configured to convert sound in an environment of the user to an electric input signal (x′.sub.1, . . . , x′.sub.M) representative of said sound. The input unit comprises respective analysis filter banks (FB-A) for providing each of the multitude of electric input signals in a time-frequency representation (X.sub.1(k,l), . . . , X.sub.M(k,l), k=1, . . . , K, where K is the number of frequency bins of a Fourier transformation algorithm). The electric input signals X.sub.m(k,l), m=1, . . . , M, each comprise varying amounts of target (s) and noise (v) signal components originating from a target sound source and one or more noise sound sources in said environment. The hearing aid (HD) comprises a signal processing unit (SPU) configured to process said multitude of electric input signals (X.sub.1(k,l), . . . , X.sub.M(k,l)) and to provide a processed electric signal (OUT) representative of said sound. The signal processor (SPU) comprises a noise reduction system (NRS) comprising a beamformer filter (TM-BF, TC-BF) followed by a post-filter (PF). The beamformer filter (TM-BF, TC-BF) is connected to the input unit (IU) and configured to receive the multitude M of electric input signals X.sub.m(k,l), m=1, . . . , M, and configured to provide a spatially filtered signal (Y). The post-filter (PF) is configured to receive the spatially filtered signal (Y) and to provide an estimate Ŝ(k,l) of a target signal representing sound from the target sound source. The hearing aid further comprises a signal processor (PRO) for applying one or more processing algorithms to the estimate Ŝ(k,l) of the target signal, e.g. including a compressive amplification algorithm for applying a level and frequency dependent gain to compensate for the user's hearing impairment (and/or to otherwise enhance the estimate Ŝ(k,l)). The signal processor (PRO) provides processed electric signal (OUT). The hearing device further comprises an output unit (OU) comprising a synthesis filter bank (FB-S) for converting the processed electric signal (OUT) from a time-frequency representation to a time domain signal (out) and an output transducer (OT) for converting said processed electric (time domain) signal (out) to stimuli perceivable by the user as sound. The output transducer may comprise a loudspeaker for providing an air-borne acoustic signal or a vibrator for providing a structure-borne or liquid-borne acoustic signal. In some hearing aids, the output transducer may comprise one or more output electrodes for providing electric signals (e.g. to a multi-electrode array) for electrically stimulating the cochlear nerve (cochlear implant type hearing aid).

(49) In the embodiment of FIG. 3, the beamformer filter comprises a target-maintaining beamformer (TM-BF), e.g. an MVDR beamformer and a target-canceling beamformer (TC-BF) (also termed ‘blocking matrix B(k,l)’, cf. e.g. eq. (6) above). Other beamformer structures may be used.

(50) The signal processing unit (SPU) comprises a control unit (CONT) configured to provide inputs to the noise reduction system. The control unit (CONT) may e.g. comprise a voice activity detector for determining a speech presence probability at a given point in time (and corresponding a probability of absence of speech). The voice activity detector may be configured to provide a binary estimate of whether or not a human voice is present in a sound signal. The voice activity detector may be adapted to estimate—at a given point in time—whether or not or with what probability a human voice is present in a sound signal at a given frequency. This may have the advantage of allowing the determination of parameters related to noise or speech during time segments where noise or speech, respectively, is (estimated to be) present. A voice signal is in the present context taken to include a speech signal from a human being. The control unit (CONT) may further comprise of have access to a memory storing pre-determined and possibly later updated filter weights for the beamformer filter (e.g. for the target-maintaining beamformer (TM-BF) and/or for the target-canceling beamformer (TC-BF). Additionally or alternatively, the control unit may be configured to estimate a current look vector d during target speech activity based on the multitude of electric input signals and/or to estimate a noise covariance matrix C.sub.v during speech pauses. Based thereon, beamformer weights may be determined. An estimate of the look vector is generally used as an input to the beamformer filter (as e.g. illustrated in FIG. 3 by arrows denoted d). Alternatively these estimations may be performed in the respective beamformer blocks (TM-BF, TC-BF).

(51) The M electric input signals (X.sub.1(k, l), . . . , X.sub.M(k, l)) are connected to the target maintaining beamformer (TM-BF), and to the target-canceling beamformer (TC-BF) and possibly to the control unit (CONT). The beamformer filter processes the M electric input signals and provides an estimate Y of a target signal s from a target sound source represented in the M electric input signals (based on the M electric input signals and the estimate of the look vector d, and possibly on further control or sensor signals). The (currently relevant) target sound source may e.g. be selected by the user, e.g. via a user interface or by looking in the direction of such sound source. Alternatively, it may be selected by an automatic procedure, e.g. based on prior knowledge of potential target sound sources (e.g. frequency content information, modulation, etc.).

(52) The characteristics (e.g. spatial fingerprint) of the target signal is represented by the look vector d whose elements (d.sub.m(k,l), m=1, . . . , M) may define the (frequency (and possibly time) dependent) absolute acoustic transfer function from a target signal source to each of the M input transducers (e.g. microphones), or the relative acoustic transfer function from the m.sup.th input transducer to a reference input transducer (among the M input transducers). The vector element d.sub.m(k,l) is typically a complex number for a specific frequency (k) and time unit (l). The look vector d may be predetermined, e.g. measured (or theoretically determined) in an off-line procedure or estimated in advance of or during use. The look vector may be estimated in an off-line calibration procedure. This can e.g. be relevant, if the target source is at a fixed location (or direction) compared to the input unit(s), if e.g. the target source is (assumed to be) in a particular location (or direction) relative to (e.g. in front of) the user (i.e. relative to the device (worn or carried by the user) wherein the input transducers are located). One or more predetermined look vectors may be stored in the memory, e.g. corresponding to different directions to (and possibly distances to) a target sound source.

(53) The target-maintaining beamformer (TM-BF) may be configured to leave all signal components from all directions (of the M electric input signals) essentially un-attenuated in the resulting all-pass signal Y(k,l). The target-canceling beamformer (TC-BF) may be configured to maximally attenuate signal components from the target direction in the resulting target-canceled signal. The target-canceling beamformer (TC-BF) may be configured to determine estimates of power spectral densities λ.sub.s(k,l) and λ.sub.v(k,l) of said target and noise signal components, respectively, according to the present disclosure. The target-canceling beamformer (TC-BF) provides respective post-filter gains G.sub.PF(k,l) for attenuating remaining noise components in the spatially filtered signal Y in dependence of the estimates of power spectral densities λ.sub.s(k,l) and λ.sub.v(k,l). The post-filter gains G.sub.PF(k,l) may e.g. be determined as a single-channel Wiener filter gain, given by G.sub.PF(k,l)=λ.sub.s/(λ.sub.s+λ.sub.v/(d.sup.HΓ.sub.−1d)). The post-filter gains G.sub.PF(k,l) are applied to the spatially filtered signal Y in the post-filter (PF), thereby providing the (improved) estimate Ŝ(k,l) of the target signal, which is fed to the signal processor (PRO) for optional further processing.

(54) FIG. 4A schematically shows a time variant analogue signal (‘Amplitude’ vs ‘time’) and its digitization in samples, the samples being arranged in a number of time frames, each comprising a number N.sub.s of samples. FIG. 4A shows an analogue electric signal (solid graph), e.g. representing an acoustic input signal, e.g. from a microphone, which is converted to a digital audio signal in an analogue-to-digital (AD) conversion process, where the analogue signal is sampled with a predefined sampling frequency or rate f.sub.s, f.sub.s being e.g. in the range from 8 kHz to 40 kHz (adapted to the particular needs of the application) to provide digital samples x(n) at discrete points in time n, as indicated by the vertical lines extending from the time axis with solid dots at its endpoint coinciding with the graph, and representing its digital sample value at the corresponding distinct point in time n. Each (audio) sample x(n) represents the value of the acoustic signal at n by a predefined number N.sub.b of bits, N.sub.b being e.g. in the range from 1 to 16 bits. A digital sample x(n) has a length in time of 1/f.sub.s, e.g. 50 μs, for f.sub.s=20 kHz. A number of (audio) samples N.sub.s are arranged in a time frame, as schematically illustrated in the lower part of FIG. 4A, where the individual (here uniformly spaced) samples (1, 2, . . . , N.sub.s) are grouped in time frames (1, . . . , L). As also illustrated in the lower part of FIG. 4A, the time frames may be arranged consecutively to be non-overlapping (time frames 1, 2, . . . , l, . . . , L) or overlapping (here 50%, time frames 1, 2, . . . , l, . . . , M′), where l is a time frame index. A time frame may e.g. comprise 64 audio data samples. Other frame lengths may be used depending on the practical application.

(55) FIG. 4B schematically illustrates a time-frequency representation of the (digitized) time variant electric signal x(n) of FIG. 2A. The time-frequency representation comprises an array or map of corresponding complex or real values of the signal in a particular time and frequency range. The time-frequency representation may e.g. be a result of a Fourier transformation converting the time variant input signal x(n) to a (time variant) signal X(k,l) in the time-frequency (or filter bank) domain. The Fourier transformation comprises a discrete Fourier transform algorithm (DFT), or a Short Time Fourier Transform (STFT), or similar algorithm. The frequency range considered by a typical hearing aid (e.g. a hearing aid) from a minimum frequency f.sub.min to a maximum frequency f.sub.max comprises a part of the typical human audible frequency range from 20 Hz to 20 kHz, e.g. a part of the range from 20 Hz to 12 kHz. In FIG. 4B, the time-frequency representation X(k,l) of signal x(n) comprises complex values of magnitude and/or phase of the signal in a number of DFT-bins (or tiles) defined by indices (k,l), where k=1, . . . , K represents a number K of frequency values (cf. vertical k-axis in FIG. 4B) and l=1, . . . , L (L′) represents a number L (L′) of time frames (cf. horizontal l-axis in FIG. 4B). A time frame is defined by a specific time index l and the corresponding K DFT-bins (cf. indication of Time frame l in FIG. 4B). A time frame l represents a frequency spectrum of signal x at time l. A DFT-bin or tile (k,l) comprising a (real) or complex value X(k,l) of the signal in question is illustrated in FIG. 4B by hatching of the corresponding field in the time-frequency map. Each value of the frequency index k corresponds to a frequency range Δf.sub.k, as indicated in FIG. 4B by the vertical frequency axis f. Each value of the time index l represents a time frame. The time Δt.sub.l spanned by consecutive time indices depend on the length of a time frame (e.g. Δt.sub.l=3.2 ms, e.g. for f.sub.s=20 kHz and N.sub.s=64) (cf. horizontal t-axis in FIG. 4B).

(56) In the present application, a number I of (non-uniform) frequency sub-bands with sub-band indices i=1, 2, . . . , I is defined, each sub-band comprising one or more DFT-bins (cf. vertical Sub-band i-axis in FIG. 4B). The i.sup.th sub-band (indicated by Sub-band i (X′.sub.i(l) in the right part of FIG. 4B) comprises DFT-bins (or tiles) with lower and upper indices k.sub.i.sup.min and k.sub.i.sup.max, respectively, defining lower and upper cut-off frequencies of the i.sup.th frequency sub-band, respectively. A specific time-frequency unit (i,l) is defined by a specific time index l and the DFT-bin indices k.sub.i.sup.min-k.sub.i.sup.max, as indicated in FIG. 4B by the bold framing around the corresponding DFT-bins (or tiles). A specific time-frequency unit (i,l) contains complex or real values of the i.sup.th sub-band signal X′.sub.i(l) at time l. The frequency sub-bands may be third octave bands.

(57) It is intended that the structural features of the devices described above, either in the detailed description and/or in the claims, may be combined with steps of the method, when appropriately substituted by a corresponding process.

(58) As used, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well (i.e. to have the meaning “at least one”), unless expressly stated otherwise. It will be further understood that the terms “includes,” “comprises,” “including,” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will also be understood that when an element is referred to as being “connected” or “coupled” to another element, it can be directly connected or coupled to the other element but an intervening element may also be present, unless expressly stated otherwise. Furthermore, “connected” or “coupled” as used herein may include wirelessly connected or coupled. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. The steps of any disclosed method is not limited to the exact order stated herein, unless expressly stated otherwise.

(59) It should be appreciated that reference throughout this specification to “one embodiment” or “an embodiment” or “an aspect” or features included as “may” means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the disclosure. Furthermore, the particular features, structures or characteristics may be combined as suitable in one or more embodiments of the disclosure. The previous description is provided to enable any person skilled in the art to practice the various aspects described herein. Various modifications to these aspects will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other aspects.

(60) The claims are not intended to be limited to the aspects shown herein but are to be accorded the full scope consistent with the language of the claims, wherein reference to an element in the singular is not intended to mean “one and only one” unless specifically so stated, but rather “one or more.” Unless specifically stated otherwise, the term “some” refers to one or more.

(61) The scheme for determining improved maximum-likelihood estimates of power spectral densities λ.sub.s(k,l) and λ.sub.v(k,l) of target and noise signal components, respectively, has been presented in the framework of hearing aids. The scheme may be used in connection with other audio processing devices wherein noise reduction is desirable, e.g. in headsets (for reducing noise in sound transmitted to a far-end device), active ear protection devices (where sound from a noisy environment should be enhanced, by suppressing noise while presenting target speech to the user), or other listening devices.

(62) Accordingly, the scope should be judged in terms of the claims that follow.

REFERENCES

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