CN104064195A - Multidimensional blind separation method in noise environment - Google Patents

Abstract

The invention belongs to the technical field of signal processing, and particularly relates to a multidimensional blind separation method in a noise environment. The invention discloses a denoising FastIVA algorithm well adapted to a noise IVA model. Being different from conventional IVA algorithms, the algorithm employs pseudo-whitening processing and introduces a noise item into an update formula of a separation matrix, so that multidimensional blind separation in a noise environment is achieved. Compared with the conventional FastIVA algorithm, it is verified through simulation that the denoising FastIVA algorithm can achieve excellent separation effects with a relatively wide signal-to-noise ratio range, and as long as the sample number is large enough, the denoising FastIVA algorithm can still achieve good separation effects when the signal-to-noise ratio is low (-10 dB), which cannot be achieved by the conventional FastIVA algorithms.

Description

Multidimensional blind separating method under a kind of noise circumstance

Technical field

The invention belongs to signal processing technology field, relate in particular to the multidimensional blind separating method under a kind of noise circumstance.

Background technology

When solving convolution mixing in functional magnetic resonance signal processing or frequency domain, often need to solve the problems of many group blind signal separation simultaneously.Yet the method for traditional independent component analysis (Independent Component Analysis, ICA) is carried out defection in blind minute to each group and is produced the inconsistent problem of the signal sequence recovering between a plurality of groups.Independent vector analysis (Independent Vector Analysis, IVA), as a kind of method that solves the blind separation of multidimensional, is a kind of expansion of ICA from single argument composition to multivariate composition.IVA has utilized the statistic correlation of statistical independence between multivariate signal and each multivariate signal inside, application to some extent in the arrangement problems that solves the blind separation of multidimensional.Yet, traditional IVA algorithm all proposes based on the muting model of ideal, under the noisy environment of reality, these algorithms can accurately not dock and receive data and carry out albefaction, and do not consider the impact of noise in follow-up fixed-point iteration process yet, thereby performance can non-constant.Nobody proposed the IVA algorithm under noise model so far, so, in conjunction with the IVA model under noise background, propose a kind of separation algorithm effectively and seem particularly important.

IVA is exactly multidimensional independent component analysis in itself, but it has solved not the signal sequence inconsistent problem after ICA separation on the same group.

IVA model under noise background is: z ^k=A ^ks ^k+ n ^k, wherein, 1≤k≤K, $z^k=\left(\begin{array}{c}{z}_1^{\left(k\right)}\\ \·\\ \·\\ \·\\ z_i^{\left(k\right)}\\ \·\\ \·\\ \·\\ z_M^{\left(k\right)}\end{array}\right)$ The observation signal that represents k group, $s^k=\left(\begin{array}{c}{s}_1^{\left(k\right)}\\ \·\\ \·\\ \·\\ s_i^{\left(k\right)}\\ \·\\ \·\\ \·\\ s_N^{\left(k\right)}\end{array}\right)$ The source signal that represents k group, A ^kthe hybrid matrix that represents k group, $n^k=\left(\begin{array}{c}{n}_1^{\left(k\right)}\\ \·\\ \·\\ \·\\ n_i^{\left(k\right)}\\ \·\\ \·\\ \·\\ n_M^{\left(k\right)}\end{array}\right)$ The noise that represents k group, M represents the number of every group of receiving end sensor, N represents the number of every group of information source.Source signal between same group is separate, average be zero and power be normalized, not on the same group between corresponding to the source signal of same component ( with ) be not independently, not the source signal of corresponding different components between on the same group ( with ) be independently, wherein, i the source signal that represents k group, i the source signal that represents l group, j the source signal that represents l group.Hybrid matrix A ^kbe row full ranks, the noise between different components is white Gaussian noise, and meets separate and zero mean characteristic.The object of IVA is exactly to find the separation matrix W of each group ^krecover the source signal of each group, and the order of the source signal recovering between requiring not is on the same group consistent.The quality of separating effect can be weighed by Amari index, and it is defined as: $I_C=\frac{1}{2N(N-1)}\{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\left(\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\right[\frac{\left|c_{\mathrm{ij}}\right|}{{\max }_k\left|c_{\mathrm{ik}}\right|}-1\left]\right)+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\left(\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\right[\frac{\left|c_{\mathrm{ij}}\right|}{{\max }_k\left|c_{\mathrm{kj}}\right|}-1\left]\right)\},$ Wherein, $C=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\left|{\left(W^k\right)}^H{A}^k\right|,$ C _ijthe element of the capable j row of i of representing matrix C, N represents the number of every group of information source, I _cless expression separating effect is better, 10log I _athe separating effect of >-10dB explanation algorithm is bad.

Summary of the invention

Main thought of the present invention is by analyzing the singularity of the blind disjunctive model of multidimensional under noise background, first the reception signal of each group is carried out to pseudo-albefaction, and utilize each variance information of organizing noise and pseudo-albefaction matrix information to derive a kind of new point of fixity algorithm and solve the blind separation problem of multidimensional based on noise background.This algorithm can provide more practical application scenarios, and separation efficiency is high, and stable performance can be widely used in voice, image, medical science and signal of communication processing etc.

The object of the invention is the defect for existing IVA algorithm poor-performing under noise background, providing a kind of can better be applicable under noise circumstance, and separating property is better, and speed of convergence is IVA algorithm faster, i.e. denoising FastIVA algorithm.

For achieving the above object, adopt following technical scheme:

S1, systematic parameter is carried out to initialization;

S2, to every group, receive data and carry out pseudo-albefaction processing, obtain the mixed signal after the noise variance of each group, pseudo-albefaction matrix and pseudo-albefaction, specific as follows:

S21, k ← 1 is set, wherein, k represents that k group receives data, symbol ← expression assignment;

S22, calculating k group receive the autocorrelation matrix of data to described autocorrelation matrix do feature decomposition wherein, Λ=diag (λ ₁, λ ₂..., λ _m);

S23, estimation k group receive the noise variance (σ of data _k) ²=(λ _n+1+ ... + λ _m)/(M-N), wherein, M represents the number of every group of sensor, N represents the number of every group of information source;

S24, calculating k group receive the pseudo-albefaction matrix of data obtain the mixed signal x after pseudo-albefaction ^k=V ^kz ^k, wherein, Λ _s=diag (λ ₁-(σ _k) ², λ ₂-(σ _k) ²..., λ _n-(σ _k) ²), U _sthe matrix forming for the front N row of U;

If S25 k < is K, k ← k+1 is set, and returns to S22, if k=K enters S3, wherein, K is the group number of blind separation to be processed altogether;

S3, choose the unit matrix I on N rank _nas the initialization separation matrix of every group, initialization n=1, n _max=1000, wherein, n _maxfor maximum iterations;

S4, the separation matrix of each group is upgraded, specific as follows:

S41, k ← 1 is set, i ← 1;

S42, k is organized to the separation matrix of i row according to following formula, upgrade:

$\begin{array}{c}{w}_i^{k(n+1)}=-E\left\{G^{\&prime;}\left(\underset{m}{\mathrm{\&Sigma;}}{\left|y_i^m\right|}^2\right)y_i^{k^{*}}{x}^k\right\}\\ +[I_N+{\left({\mathrm{\&sigma;}}_k\right)}^2{v}^k{\left(v^k\right)}^H]E\{G^{\&prime;}\left(\underset{m}{\mathrm{\&Sigma;}}{\left|y_i^m\right|}^2\right)+{\left|y_i^k\right|}^2{G}^{\&prime;\&prime;}\left(\underset{m}{\mathrm{\&Sigma;}}{\left|y_i^m\right|}^2\right)\}{w}_i^{k\left(n\right)},\\ +E\left[x^k{\left(x^k\right)}^T\right]E\left\{{\left(y_i^{k^{*}}\right)}^2{G}^{\&prime;}\left(\underset{m}{\mathrm{\&Sigma;}}{\left|y_i^m\right|}^2\right)\right\}{w}_i^{{k\left(n\right)}^{*}}\end{array}$ Wherein, n represents update times, g is nonlinear function, g' and G " are respectively single order and the second derivative of G;

S43, when i < N, i ← i+1 is set, return to S42, when i=N, enter S44;

S44, as k < K, k ← k+1 is set, i ← 1, returns to S42, works as k=K, enters S5;

S5, the separated average of each group after upgrading is carried out to orthogonalization process: W ^k← [W ^k(W ^k) ^h] ^-1/2w ^(k), wherein, k=1,2,3 ..., K;

S6, judge that whether separation matrix restrains, and is specially:

If separation matrix convergence or n=n _max, export separation matrix, signal is separated to be finished;

If separation matrix is not restrained and n < n _max, n ← n+1 is set and returns to S4.

Further, described in S6, judge that the criterion whether separation matrix restrains is $|{\left|\right|\sqrt{\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|W^{k(n+1)}\right|}^2}\left|\right|}_F-{\left|\right|\sqrt{\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|W^{k\left(n\right)}\right|}^2}\left|\right|}_F|<\mathrm{\&epsiv;},$ Wherein, ε=10 ^-6.

The invention has the beneficial effects as follows:

The present invention can provide more practical application scenarios, and separation efficiency is high, and stable performance can be widely used in voice, image, medical science and signal of communication processing etc., can better be applicable to the blind separation under noise circumstance.

Accompanying drawing explanation

The denoising FastIVA algorithm flow chart that Fig. 1 is proposed by the invention.

When Fig. 2 denoising FastIVA algorithm is fixed (T=1000) in number of samples, performance is with signal to noise ratio (S/N ratio) change curve.

When Fig. 3 denoising FastIVA algorithm is fixed (SNR=-10dB) in signal to noise ratio (S/N ratio), performance is with hits change curve.

Embodiment

Below in conjunction with embodiment and accompanying drawing, describe technical scheme of the present invention in detail.

Embodiment 1 is denoising FastIVA algorithm of the present invention and traditional FastIVA algorithm in the number of samples emulation that separating property changes with signal to noise ratio (S/N ratio) fixedly time:

The method of denoising FastIVA algorithm is as shown in attached 1, simulated conditions is: the mixing under K=10 group noise circumstance, every group of N=2 source signal, the hits of mixed signal is fixed as T=1000, the number of every group of receiving end sensor is M=5, the variation range of signal to noise ratio (S/N ratio) (SNR) is-10dB is to 10dB, carries out 100 Monte Carlo experiments.The source signal in does not on the same group produce in the following manner, s _n(t)=M _n(|| b _n(t) || _fb _n(t)).Wherein, n=1,2, t=1,2 ... T, $s_n\left(t\right)=\left(\begin{array}{c}{s}_n^{\left(1\right)}\left(t\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ s_n^{\left(k\right)}\left(t\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ s_n^{\left(10\right)}\left(t\right)\end{array}\right),b_n\left(t\right)=\left(\begin{array}{c}{b}_n^{\left(1\right)}\left(t\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_n^{\left(k\right)}\left(t\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_n^{\left(10\right)}\left(t\right)\end{array}\right),$ B _n(t) each element in is zero-mean variance to be 1 white Gaussian noise and to meet m _nbe the invertible matrix of 10 * 10 dimensions, be used for producing not the nonindependence between the source signal of identical dimension on the same group, its each element is obeyed the Gaussian distribution that zero-mean variance is 1, || || _frepresent frobenius norm.Mixed signal does not on the same group produce in the following manner, z ^k=A ^ks ^k+ n ^k, 1≤k≤10, wherein $s^k=\left(\begin{array}{c}{S}_1^{\left(k\right)}\\ S_2^{\left(k\right)}\end{array}\right),$ 1≤k≤10, A ^kbe the row non-singular matrix of 5 * 2 dimensions, be used for producing the mixed signal of each group, the real part of its each element and imaginary part are all obeyed zero-mean variance and are gaussian distribution, $n^k=\left(\begin{array}{c}{n}_1^{\left(k\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ n_i^{\left(k\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ n_M^{\left(10\right)}\end{array}\right),$ Wherein, n ^kin each element to be zero-mean variance be σ _k ²white Gaussian noise and meet σ _k ²by signal to noise ratio (S/N ratio), determined.The concrete steps of denoising FastIVA algorithm are as follows:

S1, systematic parameter is carried out to initialization, K=10, N=2, M=5, n=1, n _max=1000, ε=10 ^-6;

S2, to every group, receive data and carry out pseudo-albefaction processing, obtain the mixed signal after the noise variance of each group, pseudo-albefaction matrix and pseudo-albefaction, specific as follows:

S21, k ← 1 is set, wherein, k represents that k group receives data, symbol ← expression assignment;

S22, calculate the mixed signal z of given Noise ^k, k=1,2 ... K, calculates the autocorrelation matrix that k organizes the mixed signal of Noise to described autocorrelation matrix do feature decomposition wherein, Λ=diag (λ ₁, λ ₂..., λ _m);

Noise variance (the σ of the mixed signal of k group Noise described in S23, estimation S22 _k) ²=(λ _n+1+ ... + λ _m)/(M-N), wherein, M represents the number of every group of sensor, N represents the number of every group of information source;

The pseudo-albefaction matrix of the mixed signal of k group Noise described in S24, calculating S22 obtain the mixed signal x after pseudo-albefaction ^k=V ^kz ^k, wherein, Λ _s=diag (λ ₁-(σ _k) ², λ ₂-(σ _k) ²..., λ _n-(σ _k) ²), U _sthe matrix forming for the front N row of U;

If S25 k < is K, k ← k+1 is set, and returns to S22, if k=K enters S3, wherein, K is the group number of blind separation to be processed altogether;

S3, choose the unit matrix I on N rank _nas the initialization separation matrix of every group, initialization n=1, n _max=1000, wherein, n _maxfor maximum iterations;

S4, the separation matrix of each group is upgraded, specific as follows:

S41, k ← 1 is set, i ← 1;

S42, k is organized to the separation matrix of i row according to following formula, upgrade:

$\begin{array}{c}{w}_i^{k(n+1)}=-E\left\{G^{\&prime;}\left(\underset{m}{\mathrm{\&Sigma;}}{\left|y_i^m\right|}^2\right)y_i^{k^{*}}{x}^k\right\}\\ +[I_N+{\left({\mathrm{\&sigma;}}_k\right)}^2{v}^k{\left(v^k\right)}^H]E\{G^{\&prime;}\left(\underset{m}{\mathrm{\&Sigma;}}{\left|y_i^m\right|}^2\right)+{\left|y_i^k\right|}^2{G}^{\&prime;\&prime;}\left(\underset{m}{\mathrm{\&Sigma;}}{\left|y_i^m\right|}^2\right)\}{w}_i^{k\left(n\right)},\\ +E\left[x^k{\left(x^k\right)}^T\right]E\left\{{\left(y_i^{k^{*}}\right)}^2{G}^{\&prime;}\left(\underset{m}{\mathrm{\&Sigma;}}{\left|y_i^m\right|}^2\right)\right\}{w}_i^{{k\left(n\right)}^{*}}\end{array}$ Wherein, n represents update times, g is nonlinear function, g' and G " are respectively single order and the second derivative of G;

S43, when i < N, i ← i+1 is set, return to S42, when i=N, enter S44;

S44, as k < K, k ← k+1 is set, i ← 1, returns to S42, works as k=K, enters S5;

S5, the separated average of each group after upgrading is carried out to orthogonalization process: W ^k← [W ^k(W ^k) ^h] ^-1/2w ^(k), wherein, k=1,2,3 ..., K;

S6, judge that whether separation matrix restrains, and is specially:

If separation matrix convergence or n=n _max, export separation matrix, signal is separated to be finished;

If separation matrix is not restrained and n < n _max, n ← n+1 is set and returns to S4

The described criterion that judges whether separation matrix restrains is wherein, ε=10 ^-6.

Fig. 2 represents denoising FastIVA algorithm and the traditional FastIVA algorithm separating property curve under different signal to noise ratio (S/N ratio)s.Therefrom can find out, the relatively traditional FastIVA algorithm of denoising FastIVA algorithm can reach good separating effect within the scope of wider signal to noise ratio (S/N ratio).

Embodiment 2 is our denoising FastIVA algorithm of proposing and traditional FastIVA algorithm in the signal to noise ratio (S/N ratio) emulation that separating property changes with hits fixedly time.In this case, the producing method of information source and the producing method of mixed signal are all identical with case 1, be fixed as-10dB of signal to noise ratio (S/N ratio) (SNR), and the variation range of hits T is 10 ²～10 ⁵.

As shown in Figure 1, the step of again carrying out embodiment 1 after change simulated conditions can obtain the performance curve of the denoising FastIVA algorithm that in Fig. 3, we propose to the method for embodiment 2.As can be seen from Figure 3, as long as hits is abundant, the algorithm of carrying still can reach good separating effect in compared with low signal-to-noise ratio (10dB) situation, and this to be traditional IVA algorithm be beyond one's reach.

Claims (2)

1. the multidimensional blind separating method under noise circumstance, is characterized in that, comprises the following steps:

S1, systematic parameter is carried out to initialization;

S2, to every group, receive data and carry out pseudo-albefaction processing, obtain the mixed signal after the noise variance of each group, pseudo-albefaction matrix and pseudo-albefaction, specific as follows:

S21, k ← 1 is set, wherein, k represents that k group receives data, symbol ← expression assignment;

S22, calculating k group receive the autocorrelation matrix of data to described autocorrelation matrix do feature decomposition wherein, Λ=diag (λ ₁, λ ₂..., λ _m);

S23, estimation k group receive the noise variance (σ of data _k) ²=(λ _n+1+ ... + λ _m)/(M-N), wherein, M represents the number of every group of sensor, N represents the number of every group of information source;

S24, calculating k group receive the pseudo-albefaction matrix of data obtain the mixed signal x after pseudo-albefaction ^k=V ^kz ^k, wherein, Λ _s=diag (λ ₁-(σ _k) ², λ ₂-(σ _k) ²..., λ _n-(σ _k) ²), U _sthe matrix forming for the front N row of U;

If S25 k < is K, k ← k+1 is set, and returns to S22, if k=K enters S3, wherein, K is the group number of blind separation to be processed altogether;

S3, choose the unit matrix I on N rank _nas the initialization separation matrix of every group, initialization n=1, n _max=1000, wherein, n _maxfor maximum iterations;

S4, the separation matrix of each group is upgraded, specific as follows:

S41, k ← 1 is set, i ← 1;

S42, k is organized to the separation matrix of i row according to following formula, upgrade:

$\begin{array}{c}{w}_i^{k(n+1)}=-E\left\{G^{\&prime;}\left(\underset{m}{\mathrm{\&Sigma;}}{\left|y_i^m\right|}^2\right)y_i^{k^{*}}{x}^k\right\}\\ +[I_N+{\left({\mathrm{\&sigma;}}_k\right)}^2{v}^k{\left(v^k\right)}^H]E\{G^{\&prime;}\left(\underset{m}{\mathrm{\&Sigma;}}{\left|y_i^m\right|}^2\right)+{\left|y_i^k\right|}^2{G}^{\&prime;\&prime;}\left(\underset{m}{\mathrm{\&Sigma;}}{\left|y_i^m\right|}^2\right)\}{w}_i^{k\left(n\right)},\\ +E\left[x^k{\left(x^k\right)}^T\right]E\left\{{\left(y_i^{k^{*}}\right)}^2{G}^{\&prime;}\left(\underset{m}{\mathrm{\&Sigma;}}{\left|y_i^m\right|}^2\right)\right\}{w}_i^{{k\left(n\right)}^{*}}\end{array}$ Wherein, n represents update times, g is nonlinear function, g' and G " are respectively single order and the second derivative of G;

S43, when i < N, i ← i+1 is set, return to S42, when i=N, enter S44;

S44, as k < K, k ← k+1 is set, i ← 1, returns to S42, works as k=K, enters S5;

S5, the separated average of each group after upgrading is carried out to orthogonalization process: W ^k← [W ^k(W ^k) ^h] ^-1/2w ^(k), wherein, k=1,2,3 ..., K;

S6, judge that whether separation matrix restrains, and is specially:

If separation matrix convergence or n=n _max, export separation matrix, signal is separated to be finished;

If separation matrix is not restrained and n < n _max, n ← n+1 is set and returns to S4.

2. the multidimensional blind separating method under a kind of noise circumstance according to claim 1, is characterized in that: described in S6, judge that the criterion whether separation matrix restrains is wherein, ε=10 ^-6.