CN108710917A - A kind of sparse source signal blind separating method based on grid and Density Clustering - Google Patents
A kind of sparse source signal blind separating method based on grid and Density Clustering Download PDFInfo
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Abstract
The invention discloses a kind of sparse source signal blind separating method based on grid and Density Clustering, the mixed model by two sensor signals is extended to the mixed model of M sensor signal and carries out Short Time Fourier Transform, obtains the instantaneous mixing model of sensor signal；Described finds out cluster centre, as the estimation of mixed coefficint.By the way of being evenly dividing, by α-δ plane discretizations, using the maximum N number of grid of density as mixed coefficint；The recovery source signal；It is described for each time frequency point in time-frequency domain, the value that can have up to M source signal is not zero；It is described with seeking minimum L1The method of Norm Solution determines which M signal is not zero, and then finds out the unique solution of source signal.The present invention solve the problems, such as source signal it is insufficient it is sparse in the case of it is deficient determine blind separation, the application of density and Grid Clustering effectively increases computational efficiency, and in blind signal processing, Sparse Component Analysis field is of great significance to.
Description
Technical field
The present invention relates to blind signal processing field, Sparse Component Analysis fields, and in particular to for owing in the case of determining to dilute
The method that the sensor signal that thin source signal is mixed into carries out blind separation.
Background technology
In owing to determine blind separation algorithm, if it is assumed that thering is more than one source signal to be not zero in a time frequency point, only adopt
Take simply cannot effectively restore source signal by the method that time-frequency domain is classified, and need to consider source signal vector in each time-frequency
Structure on point.At this moment the method for Sparse Component Analysis can be taken to carry out blind separation.
Blind source separation algorithm based on Sparse Component Analysis generally uses the operating mode of second order segmentation：It is calculated first with cluster
Method estimated mixing matrix, then restores source signal.Since the hybrid matrix estimated is not square formation, cannot use simple
The mode inverted obtains the unique solution of source signal.Sparse Component Analysis seeks to obtain one group of most sparse solution of source signal.
General Sparse Component Analysis is directly used in the separation without mixed signal under the environment that echoes, there are problems that two：
1. the sparsity of signal in the time domain is bad；2. signal is preferable in the degree of rarefication of time-frequency domain, but with general hyperplane clustering
When carrying out hybrid matrix estimation, algorithm complexity is high and is affected by isolated point.Therefore the present invention propose one it is new
Blind separation algorithm in the case of owing fixed.Separation process is divided into three steps：The sensor signal of time domain is carried out in Fu in short-term
Leaf transformation, estimated mixing matrix restore source signal.In second step, the amplitude fading and time delay of source signal are utilized
The cluster centre of two features estimates hybrid matrix parameter, can be quickly found out using the method for grid and Density Clustering poly-
Class center.In third step, it is proposed that a looser sparse condition, that is, in the same time frequency point, allow multiple sources
Signal is not zero；By seeking minimum l1Norm Solution determines source signal that each time frequency point is not zero, defines arrays matrix to remember
The information for recording the source signal being not zero in each grid avoids computing repeatedly.
Invention content
The technical problem to be solved by the present invention is in order to overcome in traditional Sparse Component Analysis method, it is desirable that at one
Frequency point can only be not zero there are one signal, the limitation of the necessary silence of other signals, it is proposed that more loose sparse condition；True
Determine to use grid and Density Clustering when cluster centre；When restoring source signal, it is each mesh definition array, improves calculating
Efficiency.
The technical solution adopted by the present invention to solve the technical problems is：
A kind of sparse source signal blind separating method based on grid and Density Clustering, including following steps：
The mixed model of two sensor signals is extended to the mixed model of M sensor signal and carried out short by step 1.
When Fourier transformation.The model of time domain is：
Wherein aijAnd δijAmplitude fading and time delay coefficient of respectively j-th of the source signal to i-th of sensor.It is right
Above formula carries out Short Time Fourier Transform, obtains the instantaneous mixing model of time-frequency domain：
Corresponding cluster feature also becomes：A=[1,a2j,…,aMj]T, δ=s [0,δ2j,…,δMj]T.In each time-frequency
Point (t, f),
Step 2. finds out cluster centre, as the estimation of mixed coefficint.In fact, accurately being clustered in time-frequency domain
It is relatively difficult.The computation complexity of K mean cluster and hyperplane clustering is higher, the combination for each representative point, all
Need to handle in data set it is non-represent a little, and easily influenced by isolated point.In addition, the processing of convergence and data is suitable
Sequence has much relations.Scatterplot distribution due to each time frequency point in a- δ planes has regularity, that is, is formed naturally with true
Elliptical shape centered on mixed coefficint.
The method that the present invention uses grid and Density Clustering, come realize it is described find out cluster centre, as mixed coefficint
Estimation.
By the way of being evenly dividing, a plane, referred to as a- δ planes are defined for each (a (t, f), δ (t, f)), and
It is divided into several grids.
Step 2.1 is turned to a- δ planes are discrete using Δ a and Δ δ as the small rectangle of step-length, and a and δ after discretization are denoted as respectively
(a0,...,aK) and (δ0,…,δL), K, L are the number of segmentation, and have
Step 2.2 is to each grid (a in a- δ planesk,δl) (wherein k ∈ 1 ..., K, l ∈ 1 ..., L), define M
(ak,δl), it is used in combination zero to be initialized.For (a (t, f), the δ (t, f)) of each time frequency point, with following rule to M (ak,
δl) be updated：
M(ak,δl)=M (ak,δl)+1
if|a(t,f)-ak|< Δ a and|δ(t,f)-δl|< Δs δ
Wherein l=0,1 ..., L.M(ak,δl) value be exactly grid (ak,δl) in include data point (a (t, f), δ (t, f))
Number, i.e. the density of data point.The amplitude fading and time delay parameter generated in each time frequency point (t, f) is distributed in very
Around real mixed coefficint.N number of peak so centered on will produce by actual parameter in a- δ planes, that is, cluster centre.
It can be using the maximum N number of grid of density as mixed coefficint.
The recovery of step 3. source signal
Owing fixed, hybrid matrix is sequency spectrum.In this case, inverse of a matrix is not unique, i.e., enabled
Estimated mixing matrix well can not also acquire solution hybrid matrix with inverse of a matrix.Common method is to ask in Sparse Component Analysis
Minimum l1Norm Solution.
In DUET methods, a source signal is only allowed to be not zero in each time frequency point.In most of signals, this vacation
If excessively stringent.The present invention proposes a more loose sparsity condition, i.e.,：For each time-frequency in time-frequency domain
Point, the value that can have up to M source signal are not zero.
The estimation of the mixed coefficint obtained by step 2 is denoted as：Have
The time-frequency domain representation of mixed signal can be denoted as：
Hybrid matrix is write as to the form of column vector：
WhereinIt is the column vector of hybrid matrix, and has：
According to assumed condition, if in each time frequency point, at most only M source signal is not equal to zero, then in formula (1)
MatrixFor the square formation of M × M, the unique solution of source signal can be obtained with inverse matrix.
The minimum l of source signal is acquired by the way of following1Norm Solution：In matrixMiddle selection
M Column vector groups are at square formation：
If the source signal obtained with Φ (f)
It can meetSo just enableAs the time frequency point
Non-zero source signal, and be approximately zero by other source signals.
In a- δ planes, the time frequency point M source signal having the same for falling into the same grid is not zero, in order to avoid
It computes repeatedly, is one array of each mesh definition in estimated mixing matrix on the basis of grid division：
When reading in sample point (a (t, f), a δ (t, f)) for the first time, to the grid H where (a (t, f), δ (t, f))
(ak,δl) be updated：H(ak,δl)=(1, j1,…,jM).At this moment, H (ak,δl) in store be：First value indicates current
Whether sample point reads in for the first time, is otherwise 1 if it is, being 0；That subsequent M value indicates successively is current sample point (a
(t, f), δ (t, f)) selected hybrid matrix column vector number.A sample point is often read in, is required for first determining whether its institute
Whether the grid at place is to read in for the first time.In this way, we need not calculate each sample point the column vector selected by it, but use
Column vector selected by each grid represents sample point therein.
Description of the drawings
Fig. 1 is flow chart of the present invention.
Specific implementation mode
A kind of sparse source signal blind separating method based on grid and Density Clustering, as shown in Figure 1, including following step
Suddenly,
Specific implementation mode is as follows：
The mixed model of two sensor signals is extended to the mixed model of M sensor signal and carried out short by step 1.
When Fourier transformation.Obtain the instantaneous mixing model of time-frequency domain.
Step 2. finds out cluster centre, as the estimation of mixed coefficint using the method for grid and Density Clustering.Using equal
The mode of even division defines an a- δ plane for each (a (t, f), δ (t, f)).
Step 2.1 is turned to a- δ planes are discrete using Δ a and Δ δ as the small rectangle of step-length, and a and δ after discretization remember respectively
For (a0,…,aK) and (δ0,…,δL), K, L are the number of segmentation, and have
Step 2.2 is to each grid (a in a- δ planesk,δl) (wherein k ∈ 1 ..., K, l ∈ 1 ..., L), define M
(ak,δl), it is used in combination zero to be initialized.For (a (t, f), the δ (t, f)) of each time frequency point, with following rule to M (ak,
δl) be updated：
M(ak,δl)=M (ak,δl)+1
if|a(t,f)-ak|< Δ a and|δ(t,f)-δl|< Δs δ
Wherein l=0,1 ..., L.M(ak,δl) value be exactly grid (ak,δl) in include data point (a (t, f), δ (t, f))
Number, i.e. the density of data point.
The recovery of step 3. source signal.The estimation of the mixed coefficint obtained by step 2 is denoted as：
Have
The time-frequency domain representation of mixed signal can be denoted as：
Hybrid matrix is write as to the form of column vector：
WhereinIt is the column vector of hybrid matrix, and has：
Step 3.1 is according to assumed condition, if in each time frequency point, at most only M source signal is not equal to zero, matrixFor the square formation of M × M.The minimum l of source signal is acquired by the way of following1Norm Solution：In square
Battle arrayMiddle M Column vector groups of selection are at square formation
If the source signal obtained with Φ (f)
It can meetSo just enableAs the time frequency point
Non-zero source signal, and be approximately zero by other source signals.
Step 3.2 is one array of each mesh definition：When for the first time read in a sample point
When (a (t, f), δ (t, f)), to the grid H (a where (a (t, f), δ (t, f))k,δl) be updated：H(ak,δl)=(1,
j1,…,jM)。H(ak,δl) in store be：First value indicates whether current sample point reads in for the first time, if it is, be 0,
Otherwise it is 1；If it is reading in for the first time, then formula (2) is utilized to calculateAnd update H (ak,δl), with
Record which source signal is not zero.H (a are then utilized if not reading in for the first timek,δl)=(1, j1,…,jM) value that has preserved is straight
Connect calculating
The present invention solve the problems, such as source signal it is insufficient it is sparse in the case of it is deficient determine blind separation, density and Grid Clustering are answered
With computational efficiency is effectively increased, in blind signal processing, Sparse Component Analysis field is of great significance to.
Claims (3)
1. a kind of sparse source signal blind separating method based on grid and Density Clustering, it is characterized in that the method includes following several
A step：
The mixed model of two sensor signals is extended to the mixed model of M sensor signal and carries out Fu in short-term by step 1.
In leaf transformation, obtain the instantaneous mixing model of sensor signal.
Step 2. finds out cluster centre, as the estimation of mixed coefficint.By the way of being evenly dividing, by a- δ plane discretizations,
Several grids are divided into, using the maximum N number of grid of density as mixed coefficint.
Step 3. restores source signal using the mixed coefficint that step 2 obtains.A more loose sparsity condition is proposed,
I.e.：For each time frequency point in time-frequency domain, the value that can have up to M source signal is not zero.With seeking minimum l1Norm Solution
Method determine which M signal is not zero, then find out the unique solution of source signal.
2. a kind of sparse source signal blind separating method based on grid and Density Clustering as described in claim 1, it is characterized in that
In step 2, cluster centre is found using grid and Density Clustering, and as the estimation of mixed coefficint.Specific method includes as follows
Step：In step 2, by the way of being evenly dividing, a plane is defined for each (a (t, f), δ (t, f)), referred to as a- δ are flat
Face, by its it is discrete turn to using Δ a and Δ δ as the small rectangle of step-length, to each grid (a in a- δ planesk,δl) (wherein k ∈
1 ..., K, l ∈ 1 ..., L), define M (ak,δl), it is used in combination zero to be initialized.For each time frequency point (a (t, f), δ (t,
F)), with following rule to M (ak,δl) be updated：
M(ak,δl)=M (ak,δl)+1
if|a(t,f)-ak|<Δa and|δ(t,f)-δl|< Δs δ
Wherein l=0,1 ..., L.M(ak,δl) value be exactly grid (ak,δl) in comprising data point (a (t, f), δ (t, f))
Number, the i.e. density of data point.The amplitude fading and time delay parameter generated in each time frequency point (t, f) is distributed in really
Around mixed coefficint.N number of peak so centered on will produce by actual parameter in a- δ planes, that is, cluster centre.It can incite somebody to action
The maximum N number of grid of density is as mixed coefficint.
3. a kind of muscle damage ultrasonic contrast image segmentation side greatly decomposed based on structured message as described in claim 1
Method, it is characterized in that two methods proposed in step 3：One be source signal it is insufficient it is sparse in the case of blind separation.It relates to herein
And in existing DUET methods, it is desirable that only allow a source signal to be not zero in each time frequency point.It is this in most of signals
Assuming that excessively stringent.This paper presents a more loose sparsity conditions, i.e.,：For each time-frequency in time-frequency domain
Point, the value that can have up to M source signal are not zero.Secondly being each mesh definition array, it is not zero to avoid computing repeatedly
Source signal.Specific method includes the following steps：
Step 3.1 is according to assumed condition, if in each time frequency point, at most only M source signal is not equal to zero, matrixFor the square formation of M × M.The minimum l of source signal is acquired by the way of following1Norm Solution：In square
Battle arrayMiddle M Column vector groups of selection are at square formationIf using Φ
(f) source signal obtained
It can meetSo just enableAs the non-of the time frequency point
Zero source signal, and be approximately zero by other source signals.
Step 3.2 is one array of each mesh definition：When read in for the first time sample point (a (t,
F), δ (t, f)) when, to the grid H (a where (a (t, f), δ (t, f))k,δl) be updated：H(ak,δl)=(1, j1,…,
jM)。H(ak,δl) in store be：First value indicates whether current sample point reads in for the first time, if it is, be 0, otherwise for
1.If it is reading in for the first time, then calculateAnd update H (ak,δl) which source signal recorded
It is not zero；H (a are then utilized if not reading in for the first timek,δl)=(1, j1,…,jM) value that has preserved directly calculates
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| CN112201274A (en) * | 2020-08-21 | 2021-01-08 | 西安交通大学 | Underdetermined blind source separation method, system and device based on minimization and maximization |
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