CN104064195A

CN104064195A - Multidimensional blind separation method in noise environment

Info

Publication number: CN104064195A
Application number: CN201410307957.0A
Authority: CN
Inventors: 钱国兵; 李立萍; 廖红舒; 刘亮
Original assignee: University of Electronic Science and Technology of China
Current assignee: University of Electronic Science and Technology of China
Priority date: 2014-06-30
Filing date: 2014-06-30
Publication date: 2014-09-24

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 separation method in noise environment

Technical Field

The invention belongs to the technical field of signal processing, and particularly relates to a multi-dimensional blind separation method in a noise environment.

Background

When convolution mixing is solved in functional magnetic resonance signal processing or frequency domain, the problem of blind separation of multiple groups of signals is often needed to be solved simultaneously. However, blind separation of each group by conventional Independent Component Analysis (ICA) methods can result in inconsistent recovered signal order among groups. Independent Vector Analysis (IVA), a method to solve multi-dimensional blind separation, is an extension of ICA from univariate to multivariate components. IVA has been applied to solve the problem of permutation of multidimensional blind separation, using statistical independence between multivariate signals and statistical correlation within each multivariate signal. However, the conventional IVA algorithms are all proposed based on an ideal noise-free model, and these algorithms cannot accurately whiten the received data in an actually noisy environment, and also do not take the influence of noise into consideration in the subsequent fixed-point iteration process, so that the performance is very poor. No one has proposed the IVA algorithm under the noise model so far, so it is important to propose an effective separation algorithm in combination with the IVA model under the noise background.

IVA is essentially a multi-dimensional independent component analysis, but it solves the problem of inconsistent signal order after separation of different sets of ICAs.

The IVA model on a noise background is: z is a radical of^k＝A^ks^k+n^kWherein K is more than or equal to 1 and less than or equal to K,

the observed signals of the k-th group are represented,

source signals representing the k-th group, A^kA mixing matrix representing the k-th group,

the noise of the kth group is represented, M represents the number of sensors at the receiving end of each group, and N represents the number of sources of each group. Source signals of the same group are independent of each other, mean value is zero and power is normalized, source signals corresponding to the same component between different groups: (And) Source signals of different components corresponding between different groups, which are not independent: (And) Is independent of, wherein,the ith source signal representing the kth group,the ith source signal representing the ith group,representing the jth source signal of the ith group. Mixing matrix A^kIs column full rank, the noise between different components is white gaussian noise, and satisfies the characteristics of mutual independence and zero mean. The purpose of IVA is to find the separation matrix W for each group^kTo recover the source signal of each group and require a differenceThe order of the recovered source signals between groups is consistent. The separation performance can be measured by Amari index, which is defined as:

wherein,

C_ijthe elements of the ith row and the jth column of the matrix C are represented, N represents the number of the sources in each group, I_CSmaller means better separation, 10log I_A>10dB indicates that the separation effect of the algorithm is poor.

Disclosure of Invention

The main idea of the invention is to perform pseudo-whitening on the received signal of each group by analyzing the particularity of a multi-dimensional blind separation model under a noise background, and to deduce a new fixed point algorithm by using the variance information and the pseudo-whitening matrix information of each group noise to solve the problem of multi-dimensional blind separation based on the noise background. The algorithm can provide a more practical application scene, has high separation efficiency and stable performance, and can be widely used for processing voice, images, medicine, communication signals and the like.

The invention aims to provide an IVA algorithm, namely a de-noising FastIVA algorithm, which is better suitable for a noise environment, has better separation performance and higher convergence rate, aiming at the defect that the existing IVA algorithm has poorer performance under a noise background.

In order to realize the purpose, the following technical scheme is adopted:

s1, initializing system parameters;

s2, performing pseudo-whitening processing on each group of received data to obtain a noise variance, a pseudo-whitening matrix, and a pseudo-whitened mixed signal of each group, which are as follows:

s21, setting k ← 1, where k denotes the kth group receiving data, and symbol ← denotes assignment;

s22, calculating the autocorrelation matrix of the kth group of received dataFor the autocorrelation matrixFeature decompositionWherein Λ ═ diag (λ)₁,λ₂,…,λ_M)；

S23, estimating the noise variance (sigma) of the kth group of received data_k)²＝(λ_N+1+…+λ_M) (M-N), wherein M represents the number of sensors per group and N represents the number of sources per group;

s24, calculating the pseudo-whitening matrix of the kth group of received dataObtaining a pseudo-whitened mixed signal x^k＝V^kz^kWherein, Λ_s＝diag(λ₁-(σ_k)²,λ₂-(σ_k)²,…,λ_N-(σ_k)²)，U_sA matrix composed of the first N columns of U;

s25, if K < K, setting K ← K +1, and returning to S22, if K ═ K, then proceeding to S3, where K is the number of blind separated groups to be processed in total;

s3, selecting an N-order identity matrix I_NAs the initialization separation matrix for each set, n is initialized to 1, n_max1000, where n_maxThe maximum number of iterations;

s4, updating the separation matrix of each group, specifically as follows:

s41, setting k ← 1, i ← 1;

s42, separating matrix for ith column of kth groupThe updating is performed according to the following formula:

wherein n represents the number of updates,g is a non-linear function, and G is a linear function,g 'and G' are the first and second derivatives of G, respectively;

s43, if i < N, setting i ← i +1, returning to S42, and if i ═ N, entering S44;

s44, when K is less than K, setting K ← K +1, i ← 1, returning to S42, when K is K, proceeding to S5;

and S5, performing orthogonalization processing on the updated separation mean value of each group: w^k←[W^k(W^k)^H]^-1/2W^(k)Wherein, K is 1,2, 3.

S6, determining whether the separation matrix converges, specifically:

if the separation matrix converges or n ═ n_maxIf so, outputting a separation matrix, and finishing signal separation;

if the separation matrix does not converge and n < n_maxThen set n ← n +1, and return to S4.

Further, the criterion for determining whether the separation matrix converges in S6 is

Wherein ε is 10^-6。

The invention has the beneficial effects that:

the invention can provide a more practical application scene, has high separation efficiency and stable performance, can be widely used for processing voice, image, medical and communication signals and the like, and can be better suitable for blind separation in a noise environment.

Drawings

FIG. 1 is a flow chart of the de-noising FastIVA algorithm proposed by the present invention.

Fig. 2 is a graph of the performance of the de-noising FastIVA algorithm as a function of signal-to-noise ratio with a fixed number of samples (T1000).

Fig. 3 is a graph of the performance of the de-noising FastIVA algorithm as a function of the number of samples with a fixed signal-to-noise ratio (SNR-10 dB).

Detailed Description

The technical solution of the present invention will be described in detail below with reference to the embodiments and the accompanying drawings.

Embodiment 1 is a simulation of the separation performance of the denoising FastIVA algorithm and the conventional FastIVA algorithm varying with the signal-to-noise ratio when the sampling number is fixed:

the method for denoising the FastIVA algorithm is shown as attached 1, the simulation conditions are that K is 10 groups of mixed signals under the noise environment, each group of N is 2 source signals, the sampling number of the mixed signals is fixed to T is 1000, the number of the sensors at the receiving end of each group is M is 5, the variation range of the signal-to-noise ratio (SNR) is-10 dB to 10dB, and 100 Monte Carlo experiments are carried out. The source signals in the different groups are generated as follows, s_n(t)＝M_n(||b_n(t)||_Fb_n(t)). Wherein n is 1,2, T is 1,2 … T,

b_n(t) each element is white Gaussian noise with zero mean variance of 1 and satisfiesM_nA reversible matrix of 10 x 10 dimensions for generating non-independence between different sets of source signals of the same dimension, each element of which obeys a Gaussian distribution with a zero mean variance of 1, | · | |_FRepresenting the frobenius norm. The mixed signals of the different groups are generated in such a way that z^k＝A^ks^k+n^kK is not less than 1 and not more than 10, wherein

s^{k} = (\begin{matrix} S_{1}^{(k)} \\ S_{2}^{(k)} \end{matrix}),

1≤k≤10，A^kA column full rank matrix of 5 x 2 dimensions for generating a mixed signal for each group, the real and imaginary parts of each element of which obey a zero mean variance ofThe distribution of the gaussian component of (a) is,

wherein n is^kEach element in (a) is zero mean variance σ_k ²White Gaussian noise and satisfiesσ_k ²Determined by the signal-to-noise ratio. The specific steps of the de-noising FastIVA algorithm are as follows:

s1, initializing system parameters, K is 10, N is 2, M is 5, N is 1, N is_max＝1000，ε＝10^-6；

s22, calculating the given noiseMixed signal z of sound^kK is 1,2 … K, and an autocorrelation matrix of the K-th group of noise-containing mixed signals is calculatedFor the autocorrelation matrixFeature decompositionWherein Λ ═ diag (λ)₁,λ₂,…,λ_M)；

S23, estimating the noise variance (sigma) of the k-th group of mixed signals containing noise S22_k)²＝(λ_N+1+…+λ_M) (M-N), wherein M represents the number of sensors per group and N represents the number of sources per group;

s24, calculating the pseudo-whitening matrix of the k-th group of mixed signals containing noise S22Obtaining a pseudo-whitened mixed signal x^k＝V^kz^kWherein, Λ_s＝diag(λ₁-(σ_k)²,λ₂-(σ_k)²,…,λ_N-(σ_k)²)，U_sA matrix composed of the first N columns of U;

s4, updating the separation matrix of each group, specifically as follows:

s41, setting k ← 1, i ← 1;

S6, determining whether the separation matrix converges, specifically:

if the separation matrix does not converge and n < n_maxThen set n ← n +1, return to S4

The criterion for judging whether the separation matrix is converged isWherein ε is 10^-6。

FIG. 2 shows the separation performance curves of the denoised FastIVA algorithm and the conventional FastIVA algorithm at different signal-to-noise ratios. It can be seen that the denoising FastIVA algorithm can achieve a good separation effect within a wider signal-to-noise ratio range than the conventional FastIVA algorithm.

Example 2 is a simulation of the separation performance as a function of the number of samples for a fixed signal-to-noise ratio for our proposed de-noised FastIVA algorithm and the conventional FastIVA algorithm. In this case, the generation of the source and the generation of the mixed signal are the same as in case 1, the signal-to-noise ratio (SNR) is fixed to-10 dB, and the variation range of the sampling number T is 10²～10⁵。

The method of embodiment 2 is shown in fig. 1, and the performance curve of the de-noising FastIVA algorithm proposed in fig. 3 can be obtained by performing the steps of embodiment 1 again after changing the simulation conditions. It can be seen from fig. 3 that the proposed algorithm can still achieve better separation effect at lower signal-to-noise ratio (-10dB), which cannot be achieved by the conventional IVA algorithm, as long as the number of samples is sufficiently large.

Claims

1. A multidimensional blind separation method under a noise environment is characterized by comprising the following steps:

s1, initializing system parameters;

s4, updating the separation matrix of each group, specifically as follows:

s41, setting k ← 1, i ← 1;

s42, separating matrix for ith column of kth groupAccording to the following formulaNew:

S6, determining whether the separation matrix converges, specifically:

2. The method of claim 1, wherein the method comprises: s6 the criterion for determining whether the separation matrix converges isWherein ε is 10^-6。