CN104485964A - Relative threshold value-based signal sparseness estimation method in signal compressive transmission process - Google Patents

Abstract

The invention discloses a relative threshold value-based signal sparseness estimation method in a signal compressive transmission process. The method includes the following two steps that: the first step, coefficients with maximum amplitudes are searched from current signals; and the second step, the relative threshold values of the signals are calculated, whether newly-obtained coefficients belong to larger coefficients can be judged through utilizing the relative threshold values of the signals, if the newly-obtained coefficients belong to the larger coefficients, the coefficients are deleted from the current signals, and the current signals are updated, and the method returns to the first step to find coefficients with maximum amplitudes from the current signals, if the newly-obtained coefficients do not belong to the larger coefficients, it is indicated that search for the larger coefficients is completed, and the method terminates; and the sparseness of the signals can be estimated according to the number of the larger coefficients. According to the method, computation complexity is low, and the number of required test values is small; and the relative threshold values are determined according to the amplitudes of the larger coefficients which are searched previously, and therefore, the method is only slightly affected by environmental noises, and has high stability.

Description

Based on the signal degree of rarefication method of estimation of relative threshold in Signal Compression transmitting procedure

Technical field

The present invention relates to Signal Compression transmission field, in a kind of Signal Compression transmitting procedure based on the signal degree of rarefication method of estimation of relative threshold.

Background technology

1.1 compressed sensing

In signals transmission, compressing being transmitted signal, is a kind of effective ways improving efficiency of transmission.

Compressed sensing is the emerging technology of of compressing signal.

For signal at an orthogonal sparse base under, signal can be expressed as:

x＝Ψθ

If in coefficient θ, the number of nonzero value is no more than K, then we claim signal x to be degree of rarefication to be the sparse signal of K.

Pass through calculation matrix we can obtain sparse signal x by the measured value after compressing

y＝Φx＝ΦΨθ

If A=Φ is Ψ, if A meets RIP (Restricted Isometry Property) characteristic, then according to the measured value y after compression, can intactly recover sparse signal x.Most of random matrix can both meet RIP characteristic, such as Bernoulli random matrix and Gaussian random matrix.

In compressed sensing, conventional signal recovery method has two classes, and a class is the method based on convex optimization, and the precision that the method is recovered is higher, but computation complexity is higher, such as BP (Basis Pursuit) method.Another kind of based on greedy algorithm, it is lower that these class methods recover precision, but arithmetic speed is very fast, such as MP (Matching Pursuit) method and OMP (OrthogonalMatching Pursuit) method.

In Signal Compression transmitting procedure, be the signal of N for dimension pass through calculation matrix conversion after, obtain the measured value that dimension is M due to (M<N), therefore signal reality be have compressed, and transmitting terminal is by the measured value after compression send, receiving terminal receives measured value after, by recovery algorithms, can be complete obtain signal

The deficiency of 1.2 classical signal degree of rarefication methods of estimation

The degree of rarefication (Sparsity) of signal refers in a specific base, the number of signal nonzero coefficient.Namely

S＝||θ|| ₀

Due in actual applications, by the impact of ambient noise and accuracy of detection, most of coefficients of signal are not be entirely zero, but equal a less value, and therefore, in practical application, signal degree of rarefication often equals the number of higher value in signal coefficient.Namely

$S=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left(\right|{\mathrm{\&theta;}}_i|>\mathrm{\&gamma;})$

Wherein γ is compare threshold, is used for determining larger coefficient.

In compressed sensing, the degree of rarefication of signal is an important parameter of signal, the design of calculation matrix in Signal Compression transmission, and the quantity of required measured value and recovery algorithms etc. are all relevant with the degree of rarefication of signal.Because the degree of rarefication being transmitted signal is unknown, and time dependent, therefore, the estimation carrying out signal degree of rarefication is quickly and accurately a major issue in Signal Compression transmission.

Traditional signal degree of rarefication method of estimation is first restoring signal, again the coefficient of signal is compared with absolute threshold, the degree of rarefication carrying out signal estimates [1Yue Wang, etc.:Sparsity Order Estimation and its Application in CompressiveSpectrum Sensing for Cognitive Radios, IEEE Transactions on Wireless Communications, vol.11, no.6, pp.2116-2124, 2012. Wang Yue etc., degree of rarefication is estimated and it carries out compressing the application of frequency spectrum detection in cognitive radio, IEEE radio communication transactions, 11st volume the 6th phase in 2012, 2116-2124 page.]。

In conventional estimated method, detection threshold is defined as

γ ₁＝(u+δ)/2

Wherein u is the power of detected signal, and δ is the power of ambient noise.

Mainly there is the deficiency of following two aspects in this method:

(1), when carrying out the estimation of signal degree of rarefication, need first to recover by the signal compressed completely, then carry out the estimation of degree of rarefication, computational complexity is higher.

(2) standard using absolute threshold as inspection signal coefficient size, when detected signal power or environmental noise power change, threshold value also can change thereupon, and this will affect the effect of detection.

Chinese invention patent, patent name: a kind of based on degree of rarefication adaptive compressed sensing radio communication channel method of estimation, Authorization Notice No. CN 102497337B, authorized announcement date 2014.08.20, measured value and calculation matrix is utilized to obtain the coefficient of sparse signal, and the signal coefficient obtained carried out descending sequence according to second differnce, then the average amplitude of the coefficient of rear 50% is got as reference threshold value, carry out the estimation of degree of rarefication, but this method chooses Shortcomings part in the determination with threshold value at coefficient:

(1) by measured value and calculation matrix is disposable obtains all coefficients, this method calculates simple, but in computational process, the projection of different coefficients on the multiple vector of calculation matrix, can influence each other, compare the method calculating signal coefficient one by one, the precision of the coefficient that one-time calculation obtains is lower, affects the accuracy that degree of rarefication is estimated.

(2) reference threshold is determined by the average of less coefficient, accuracy and less stable.In sparse signal, only have the amplitude of limited coefficient comparatively large, the amplitude of other coefficients is close to zero, and the amplitude of these coefficients is larger by Environmental Noise Influence.If threshold value is determined according to the average of less coefficient, its value by the impact of ambient noise, must be difficult to the accuracy and the stability that ensure degree of rarefication estimation.

Summary of the invention

Object of the present invention is exactly to solve the problem, signal degree of rarefication method of estimation based on relative threshold in a kind of Signal Compression transmitting procedure is provided, it is in the estimation procedure carrying out signal degree of rarefication, do not need to recover the signal by compressing completely, only need to find out coefficient larger in signal, computational complexity is low, needs the negligible amounts of detected value; Relative threshold is determined according to the amplitude of the larger coefficient that early stage is found, and little by Environmental Noise Influence, stability is high.

To achieve these goals, the present invention adopts following technical scheme:

Based on the signal degree of rarefication method of estimation of relative threshold in Signal Compression transmitting procedure, be referred to as RTSE (RelativeThreshold Sparsity Estimation) method, method is carried out in two steps:

The first step, in the process of Signal Compression transmission, after receiving terminal receives the measured value by compressed signal, find in current demand signal, the coefficient of amplitude maximum:

Utilize the measured value of signal, calculation matrix and sparse base, projection on each vector on the new matrix formed at calculation matrix and sparse base product according to current measurement value, determine the coefficient of amplitude maximum in current demand signal, in described current demand signal, the coefficient of amplitude maximum is the coefficient newly obtained;

Second step, calculates the relative threshold of signal, and utilize comparing of the relative threshold of signal and the coefficient newly obtained, whether the coefficient that judgement newly obtains belongs to larger coefficient; If so, then this coefficient is deleted from current demand signal, upgrade current demand signal, return the coefficient that the first step continues to find amplitude maximum in current demand signal, if not, then illustrate that larger coefficient has been found complete, terminate;

According to the number of the larger coefficient found, the degree of rarefication of estimated signal.

The step of the described first step is as follows:

Step (1): initialization, if current demand signal rs ₀equal the measured value after the compression that Signal transmissions receiving terminal obtains, i.e. rs ₀=y, matrix A equals the product of calculation matrix Ψ and sparse base Φ, i.e. A=Ψ Φ, finds number of times t=1, and signal degree of rarefication S=0, A (t) the vector set for selecting from calculation matrix after t time, its initial value is empty set, namely the signal coefficient set of θ (t) for selecting after t time, its initial value is empty set, namely

Step (2): according to current demand signal rs _t-1projection in matrix A, selects the vectorial a in the matrix A making projection maximum _t, this vector is incorporated in set A (t);

Step (3): utilize the vectorial a that step (2) is selected _t, calculate corresponding to the coefficient θ of estimated signal _t, and will newly obtain coefficient θ _tbe incorporated in coefficient sets θ (t), upgrade current demand signal rs _t.

The step of described second step is as follows:

Step (4): calculate relative threshold γ _t, according to relative threshold γ _tjudge newly obtain by the coefficient θ of estimated signal _twhether belong to larger coefficient, if newly obtain by estimated signal coefficient θ _tbe more than or equal to relatively then threshold gamma _t, so newly obtain by the coefficient θ of estimated signal _tbelong to larger coefficient; Then add 1, if be less than γ by by the degree of rarefication S of estimated signal _tthreshold value, then terminate estimation procedure;

Step (5): increase and find number of times t, return step (2), continues estimation procedure.

The formula of described step (2) is:

$a_t=\arg \underset{i=\mathrm{1,2},...,N}{\max }\frac{<{\mathrm{rs}}_{t-1},a_i>}{\left|\right|a_i\left|\right|}$

A(t)＝[A(t-1),a _t]；

Wherein, a _trepresent in the t time searching process, by what choose in matrix A, make current demand signal rs _t-1that vector that projection value is maximum on each vector of matrix A, rs _t-1represent the current demand signal after finding for the t-1 time, a _ivector in representing matrix A, || a _i|| represent vectorial a _imodulus value, A (t) represent the t time find after, by front t searching process, the set of the vector composition chosen in matrix A, after A (t-1) represents the t-1 time searching, by front t-1 searching process, the set of the vector chosen in matrix A composition.

The formula of described step (3) is:

${\mathrm{\&theta;}}_t=\frac{<{\mathrm{rs}}_{t-1},a_t>}{{\left|\right|a_t\left|\right|}^2}$

θ(t)＝[θ(t-1),θ _t]

rs _t＝rs ₀-θ(t)A(t)；

Wherein, θ _texpression obtains in the t time searching process, by the greatest coefficient of estimated signal, and rs _t-1represent the current signal value after the t-1 time searching process, a _trepresent in the t time searching process, by what choose in matrix A, make current demand signal rs _t-1that vector that projection value is maximum on each vector of matrix A, || a _t|| ²represent vectorial a _tmodulus value square, θ (t) represent the t time find after, by front t searching process, the set formed by the coefficient of estimated signal obtained, after θ (t-1) represents the t-1 time searching, by front t-1 searching process, the set formed by the coefficient of estimated signal obtained.

The formula of described step (4) is:

${\mathrm{\&gamma;}}_t=\frac{\underset{i=2}{\overset{t}{\mathrm{\&Sigma;}}}{\mathrm{\&theta;}}_{i-1}}{2(t-1)},({\mathrm{\&gamma;}}_0=0)$

if θ _t≥γ _t,then S＝S+1。

Wherein, γ _trepresent the relative threshold determined in the t time searching process, θ _i-1expression obtains in the i-th-1 time searching process, by the greatest coefficient of estimated signal, and γ ₀represent the relative threshold determined in the 0th searching process, i.e. the initial value of relative threshold, represent what obtain from the 1st searching process to the t-1 time searching process, added up by the value of the coefficient of estimated signal, θ _texpression obtains in the t time searching process, and by the greatest coefficient of estimated signal, S represents by the degree of rarefication of estimated signal.

The formula of described step (5) is:

t＝t+1。

Beneficial effect of the present invention: compared to conventional method, RTSE method mainly contains the advantage of following two aspects:

1, in the estimation procedure carrying out signal degree of rarefication, do not need to recover the signal by compressing completely, only need to find out the coefficient by larger in estimated signal, computational complexity is low, needs the negligible amounts of detected value.It is by the searching of the larger coefficient of estimated signal, obtaining one by one, obtaining all coefficients, improve the precision of obtained coefficient amplitude compared to disposable according to being compressed the projection of rear measuring-signal on calculation matrix and sparse base product.

2, in the estimation procedure carrying out signal degree of rarefication, relative threshold is adopted to carry out the determination of larger coefficient.The power of relative threshold and signal and environmental noise power have nothing to do, and are not subject to environmental change impact, improve the accuracy that signal degree of rarefication is estimated.

RTSE method contributes to the degree of rarefication of estimated signal quickly and accurately, and for the quantity determining the detected value needed for signal recuperation in Signal Compression transmission, there is positive effect the aspects such as the realization of data recovering algorithms.

Accompanying drawing explanation

Fig. 1 is the coefficient amplitude distribution map of sparse signal;

Fig. 2 is the block diagram of RTSE method;

The degree of rarefication of Fig. 3 distinct methods estimates the situation of change of accuracy with detected value quantity;

Fig. 4 represents that the degree of rarefication of distinct methods estimates the situation of change of accuracy with signal to noise ratio.

Embodiment

Below in conjunction with accompanying drawing and embodiment, the invention will be further described.

Find by studying us, the amplitude attenuation speed of sparse signal coefficient is very fast, and the amplitude difference of different coefficient is very large.Fig. 1 is dimension is 128, and degree of rarefication is the coefficient amplitude distribution map of a sparse signal under the sparse base of normal orthogonal of 5, by amplitude order from big to small in figure, shows front 20 coefficients.As seen from Figure 1, the amplitude of 5 larger coefficients, has larger difference with the amplitude of all the other coefficients, and therefore we can the otherness of usage factor amplitude, determines in detected signal, the number of larger coefficient, and then the degree of rarefication of estimated signal.

2.1 the determination of signal coefficient

In compressed sensing, can according to the measured value after compression, the sparse base of calculation matrix and signal, adopts the method for iteration, progressively determines the coefficient of signal.Each coefficient all finding out amplitude maximum in unknowm coefficient.Degree of rarefication due to signal equals the number of larger coefficient in signal, therefore, in the process found, larger coefficient is only needed to find out, whole coefficient need not be determined, namely do not need to recover completely by compressed signal, which reduce the time that signal degree of rarefication is estimated.

The determination of 2.2 relative thresholds

In the process of carrying out the estimation of signal degree of rarefication, the coefficient of signal is determined one by one by the size of amplitude, and what find out is all one maximum in residual coefficient at every turn.(such as signal has 10 coefficients, and first time finds out maximum that in these 10, and then second time is looked in remaining 9 maximum.) therefore, the average of the larger coefficient that early stage can have been found, as threshold value, judges the coefficient whether new-found coefficient belongs to larger, i.e. relative threshold

${\mathrm{\&gamma;}}_t=\frac{\underset{i=2}{\overset{t}{\mathrm{\&Sigma;}}}{\mathrm{\&theta;}}_{i-1}}{2(t-1)}$

Wherein t is the number of times found, θ _iit is the signal coefficient searched out for i-th time.

Visible, the relative threshold in this method is determined by the coefficient amplitude in earlier stage searched out, and has nothing to do, determine larger coefficient by the contrast between different coefficient amplitude with the power of signal and the power of ambient noise, and the precision of its threshold value is affected by environment less.

Based on the signal degree of rarefication method of estimation of relative threshold in Signal Compression transmitting procedure, we are referred to as RTSE (RelativeThreshold Sparsity Estimation) method and divide, and this method is carried out in two steps:

The first step, finds by current demand signal, the coefficient of amplitude maximum.

Utilize measured value and calculation matrix and sparse base, calculate the projection of current measurement value on each vector of matrix, determine the coefficient of amplitude maximum in current demand signal.

Second step, utilizes relative threshold, judges whether the coefficient newly obtained belongs to larger coefficient.If so, then this coefficient is deleted from current demand signal, upgrade measured value, return the coefficient that the first step continues to find amplitude maximum in current demand signal, if not, then illustrate that larger coefficient has been found complete, terminate this algorithm.

According to the number of the larger coefficient found, the degree of rarefication of estimated signal.

As shown in Figure 2, a kind of method of estimation of the signal degree of rarefication based on relative threshold, step is as follows:

Step (1): initialization, if current demand signal rs ₀equal the measured value after the compression that receiving terminal obtains, i.e. rs ₀=y, matrix A equals the product of calculation matrix Ψ and sparse base Φ, i.e. A=Ψ Φ, finds number of times t=1, and signal degree of rarefication S=0, A (t) the vector set for selecting from calculation matrix after t time, its initial value is empty set, namely , the signal coefficient set of θ (t) for selecting after t time, its initial value is empty set, namely ;

Step (2): according to current demand signal rs _t-1projection in matrix A, selects the vectorial a in the matrix A making projection maximum _t, be incorporated in set A (t); Namely

$a_t=\arg \underset{i=\mathrm{1,2},...,N}{\max }\frac{<{\mathrm{rs}}_{t-1},a_i>}{\left|\right|a_i\left|\right|}$

A(t)＝[A(t-1),a _t]

Wherein, a _trepresent in the t time searching process, by what choose in matrix A, make current demand signal rs _t-1that vector that projection value is maximum on each vector of matrix A, rs _t-1represent the current demand signal after finding for the t-1 time, a _ivector in representing matrix A, || a _i|| represent vectorial a _imodulus value, A (t) represent the t time find after, by front t searching process, the set of the vector composition chosen in matrix A, after A (t-1) represents the t-1 time searching, by front t-1 searching process, the set of the vector chosen in matrix A composition.

Step (3): utilize the vectorial a that step (2) is selected _t, calculate corresponding to estimated signal coefficient θ _t, and will newly obtain coefficient θ _tbe incorporated in coefficient sets θ (t), upgrade current demand signal rs _t.Namely

${\mathrm{\&theta;}}_t=\frac{<{\mathrm{rs}}_{t-1},a_t>}{{\left|\right|a_t\left|\right|}^2}$

θ(t)＝[θ(t-1),θ _t]

rs _t＝rs ₀-θ(t)A(t)；

Wherein, θ _texpression obtains in the t time searching process, by the greatest coefficient of estimated signal, and rs _t-1represent current signal value after the t-1 time searching process, a _trepresent in the t time searching process, by what choose in matrix A, make current demand signal rs _t-1that vector that projection value is maximum on each vector of matrix A, || a _t|| ²represent vectorial a _tmodulus value square, θ (t) represent the t time find after, by front t searching process, the set formed by the coefficient of estimated signal obtained, after θ (t-1) represents the t-1 time searching, by front t-1 searching process, the set formed by the coefficient of estimated signal obtained.

Step (4): calculate relative threshold γ _t, according to relative threshold γ _tjudge newly obtain by estimated signal coefficient θ _twhether belong to larger coefficient, if newly obtain by estimated signal coefficient θ _tbe more than or equal to relatively then threshold gamma _t, so newly obtain by estimated signal coefficient θ _tbelong to larger coefficient; Then add 1, if be less than γ by by the degree of rarefication S of estimated signal _tthreshold value, then terminate estimation procedure; Namely

${\mathrm{\&gamma;}}_t=\frac{\underset{i=2}{\overset{t}{\mathrm{\&Sigma;}}}{\mathrm{\&theta;}}_{i-1}}{2(t-1)},({\mathrm{\&gamma;}}_0=0)$

if θ _t≥γ _t,then S＝S+1。

Wherein, γ _trepresent the relative threshold determined in the t time searching process, θ _i-1expression obtains in the i-th-1 time searching process, by the greatest coefficient of estimated signal, and γ ₀represent the relative threshold determined in the 0th searching process, the initial value namely relatively predicted, represent what obtain from the 1st searching process to the t-1 time searching process, added up by the value of the greatest coefficient of estimated signal, θ _texpression obtains in the t time searching process, and by the greatest coefficient of estimated signal, S represents by the degree of rarefication of estimated signal.

Step (5): increase and find number of times t, return step (2), continues estimation procedure.Namely

t＝t+1,goto step2

The present invention Matlab carries out emulation testing to the performance of RTSE method, and test environment is set as: sparse signal n=128, degree of rarefication K=5, sparse base is unit orthogonal basis, i.e. Ψ=Ι ^{n × N}, calculation matrix obtain compressing measured value

Fig. 3 represents that the degree of rarefication of distinct methods estimates the situation of change of accuracy with number of measurement values, to fix in signal to noise ratio as seen, calculation matrix be Bernoulli random matrix and Gaussian random matrix time, under the measured value of varying number, the degree of rarefication of RTSE method estimates that accuracy rate is all higher than traditional method.

Fig. 4 represents that the degree of rarefication of distinct methods estimates the change feelings of accuracy with signal to noise ratio, to fix in number of measurement values as seen, calculation matrix be Bernoulli random matrix and Gaussian random matrix time, under different state of signal-to-noise, the degree of rarefication of RTSE method estimates that accuracy rate is all higher than traditional method.

By reference to the accompanying drawings the specific embodiment of the present invention is described although above-mentioned; but not limiting the scope of the invention; one of ordinary skill in the art should be understood that; on the basis of technical scheme of the present invention, those skilled in the art do not need to pay various amendment or distortion that creative work can make still within protection scope of the present invention.

Claims (6)

1. in Signal Compression transmitting procedure based on the signal degree of rarefication method of estimation of relative threshold, it is characterized in that, method is carried out in two steps:

The first step, in the process of Signal Compression transmission, after receiving terminal receives the measured value by compressed signal, find in current demand signal, the coefficient of amplitude maximum:

Utilize the measured value of signal, calculation matrix and sparse base, projection on each vector on the new matrix formed at calculation matrix and sparse base product according to current measurement value, determine the coefficient of amplitude maximum in current demand signal, in described current demand signal, the coefficient of amplitude maximum is the coefficient newly obtained;

Second step, calculates the relative threshold of signal, and utilize comparing of the relative threshold of signal and the coefficient newly obtained, whether the coefficient that judgement newly obtains belongs to larger coefficient; If so, then this coefficient is deleted from current demand signal, upgrade current demand signal, return the coefficient that the first step continues to find amplitude maximum in current demand signal, if not, then illustrate that larger coefficient has been found complete, terminate;

According to the number of the larger coefficient found, the degree of rarefication of estimated signal.

2. in Signal Compression transmitting procedure as claimed in claim 1 based on the signal degree of rarefication method of estimation of relative threshold, it is characterized in that, the step of the described first step is as follows:

Step (1): initialization, if current demand signal rs ₀equal the measured value after the compression that Signal transmissions receiving terminal obtains, i.e. rs ₀=y, matrix A equals the product of calculation matrix Ψ and sparse base Φ, i.e. A=Ψ Φ, finds number of times t=1, and signal degree of rarefication S=0, A (t) the vector set for selecting from calculation matrix after t time, its initial value is empty set, namely the signal coefficient set of θ (t) for selecting after t time, its initial value is empty set, namely

Step (2): according to current demand signal rs _t-1projection in matrix A, selects the vectorial a in the matrix A making projection maximum _t, this vector is incorporated in set A (t);

Step (3): utilize the vectorial a that step (2) is selected _t, calculate corresponding to the coefficient θ of estimated signal _t, and will newly obtain coefficient θ _tbe incorporated in coefficient sets θ (t), upgrade current demand signal rs _t.

3. in Signal Compression transmitting procedure as claimed in claim 1 based on the signal degree of rarefication method of estimation of relative threshold, it is characterized in that, the step of described second step is as follows:

Step (4): calculate relative threshold γ _t, according to relative threshold γ _tjudge newly obtain by the coefficient θ of estimated signal _twhether belong to larger coefficient, if newly obtain by estimated signal coefficient θ _tbe more than or equal to relatively then threshold gamma _t, so newly obtain by the coefficient θ of estimated signal _tbelong to larger coefficient; Then add 1, if be less than γ by by the degree of rarefication S of estimated signal _tthreshold value, then terminate estimation procedure;

Step (5): increase and find number of times t, return step (2), continues estimation procedure.

4. in Signal Compression transmitting procedure as claimed in claim 2 based on the signal degree of rarefication method of estimation of relative threshold, it is characterized in that, the formula of described step (2) is:

$a_t=\begin{array}{cc}\arg & \underset{i=\mathrm{1,2},...,N}{\max }\frac{<{\mathrm{rs}}_{t-1},a_i>}{\left|\right|a_i\left|\right|}\end{array}$

A(t)＝[A(t-1),a _t]；

Wherein, a _trepresent in the t time searching process, by what choose in matrix A, make current demand signal rs _t-1that vector that projection value is maximum on each vector of matrix A, rs _t-1represent the current demand signal after finding for the t-1 time, a _ivector in representing matrix A, || a _i|| represent vectorial a _imodulus value, A (t) represent the t time find after, by front t searching process, the set of the vector composition chosen in matrix A, after A (t-1) represents the t-1 time searching, by front t-1 searching process, the set of the vector chosen in matrix A composition.

5. in Signal Compression transmitting procedure as claimed in claim 2 based on the signal degree of rarefication method of estimation of relative threshold, it is characterized in that, the formula of described step (3) is:

${\mathrm{\&theta;}}_t=\frac{<{\mathrm{rs}}_{t-1},a_t>}{{\left|\right|a_t\left|\right|}^2}$

θ(t)＝[θ(t-1),θ _t]

rs _t＝rs ₀-θ(t)A(t)；

Wherein, θ _texpression obtains in the t time searching process, by the greatest coefficient of estimated signal, and rs _t-1represent the current signal value after the t-1 time searching process, a _trepresent in the t time searching process, by what choose in matrix A, make current demand signal rs _t-1that vector that projection value is maximum on each vector of matrix A, || a _t|| ²represent vectorial a _tmodulus value square, θ (t) represent the t time find after, by front t searching process, the set formed by the coefficient of estimated signal obtained, after θ (t-1) represents the t-1 time searching, by front t-1 searching process, the set formed by the coefficient of estimated signal obtained.

6. in Signal Compression transmitting procedure as claimed in claim 3 based on the signal degree of rarefication method of estimation of relative threshold, it is characterized in that, the formula of described step (4) is:

${\mathrm{\&gamma;}}_t=\frac{\underset{i=2}{\overset{t}{\mathrm{\&Sigma;}}}{\mathrm{\&theta;}}_{i-1}}{2(t-1)},({\mathrm{\&gamma;}}_0=0)$

if θ _t≥γ _t,then S＝S+1；

Wherein, γ _trepresent the relative threshold determined in the t time searching process, θ _i-1expression obtains in the i-th-1 time searching process, by the greatest coefficient of estimated signal, and γ ₀represent the relative threshold determined in the 0th searching process, i.e. the initial value of relative threshold, represent what obtain from the 1st searching process to the t-1 time searching process, added up by the value of the coefficient of estimated signal, θ _texpression obtains in the t time searching process, and by the greatest coefficient of estimated signal, S represents by the degree of rarefication of estimated signal.