CN106301384A - A kind of signal reconfiguring method based on splits' positions perception - Google Patents
A kind of signal reconfiguring method based on splits' positions perception Download PDFInfo
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- CN106301384A CN106301384A CN201610736095.2A CN201610736095A CN106301384A CN 106301384 A CN106301384 A CN 106301384A CN 201610736095 A CN201610736095 A CN 201610736095A CN 106301384 A CN106301384 A CN 106301384A
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
- H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
- H03M7/3059—Digital compression and data reduction techniques where the original information is represented by a subset or similar information, e.g. lossy compression
- H03M7/3062—Compressive sampling or sensing
Abstract
A kind of signal reconfiguring method based on splits' positions perception, belongs to signal processing field, and the method includes: primary signal is uniformly divided into L block subsignal；Calculate each subsignal sparse signal x' in complete base ΨiI.e. expansion coefficient；It is filtered L sparse signal processing, obtains rebuilding subsignal；Structure calculation matrix Φ, and each reconstruction subsignal is carried out splits' positions perception process, obtain each piece of observation vector y corresponding to subsignali；Utilize expansion coefficient, observation vector yiAnd calculation matrix, calculate each subsignal x respectivelyiReconstruct subsignal；Reconstruct subsignal is carried out linear combination and obtains reconstruction signal.The present invention makes full use of the method that the characteristic proposition of feature base carries out signal reconstruction based on splits' positions perception, improves signal recovery performance；Avoid the matrix inversion process of complexity, particularly, when the length of signal is long, and order of matrix number is the biggest, it is possible to efficiently reduce signal and recover computational complexity.
Description
Technical field
The invention belongs to signal processing field, be specifically related to a kind of signal reconfiguring method based on splits' positions perception.
Background technology
The twice that sampling rate is signal highest frequency of traditional sampling theory calls signal, i.e. sampling process must expire
Foot nyquist sampling theorem, could recover original signal accurately；In recent years it has been proposed that compressive sensing theory, this theory for
Signal sparse in sparse signal or certain transform domain, uses linear transformation that signal is projected to lower dimensional space, then passes through non-thread
Property decoding high probability recovery primary signal；Compressive sensing theory makes full use of the sparse characteristic of signal, reduces sampling rate；
In actual applications, the compression collection of signal must carry out quantification treatment, and limited quantified precision can introduce quantization error；1-
Bit compressed sensing is that compression observation is carried out limit equalization process, by retaining the symbolic information of observation, alleviates hardware pressure
Power, improves storage efficiency；At present, the signal reconfiguring method of 1-Bit compressed sensing mainly has iteration signal reconstructing method, greed letter
Number reconstructing method and trusted zones signal reconfiguring method etc.；Wherein, the letter of the binary system iteration hard-threshold in iteration signal reconstructing method
The reconfiguration principle of number reconstructing method (BinaryIterative HardThresholding, BIHT) is simple, it is simple to understand, calculates
Complexity is low and quality reconstruction is preferable；Although BIHT signal reconfiguring method has an outstanding quality reconstruction, but this signal reconstruction
Method requires that the degree of rarefication of signal is it is known that and this is difficulty with in reality is measured；In addition, existing signal reconstruction
Method restorability is low, and computational complexity is high.
Summary of the invention
The deficiency existed for prior art, the present invention provides a kind of signal reconfiguring method based on splits' positions perception.
Technical scheme is as follows:
A kind of signal reconfiguring method based on splits' positions perception, specifically includes following steps:
Step 1: primary signal is uniformly divided into L block subsignal xi, wherein, i={1,2 ..., L}, L ＞ 1；
Step 2: calculate each subsignal sparse signal x' in complete base ΨiI.e. expansion coefficient, every piece of subsignal is equal
Can launch in complete base Ψ, and every piece of corresponding different expansion coefficient of subsignal；Described complete base Ψ is by feature bases
The orthogonal square formation constituted；
Step 3: to L sparse signal x'iIt is filtered processing, obtains rebuilding subsignal；
Step 4: structure calculation matrix Φ, and use calculation matrix Φ that each reconstruction subsignal is carried out at splits' positions perception
Reason, obtains each piece of observation vector y corresponding to subsignali；
Step 5: utilize expansion coefficient, observation vector yiAnd calculation matrix, calculate each subsignal x respectivelyiReconstruct letter
Number；
Step 6: reconstruct subsignal is carried out linear combination and obtains reconstruction signal.
Beneficial effect: the signal reconfiguring method based on splits' positions perception of the present invention compared with prior art, have as
Lower advantage:
(1) make full use of the method that the characteristic proposition of feature base carries out signal reconstruction based on splits' positions perception, improve
Signal recovery performance；
(2) the matrix inversion process of complexity is avoided, particularly, when the length of signal is long, and order of matrix number is the biggest
Time, it is possible to efficiently reduce signal and recover computational complexity.
Accompanying drawing explanation
Fig. 1 is a kind of based on splits' positions perception the signal reconfiguring method flow chart of one embodiment of the present invention.
Detailed description of the invention
Below in conjunction with the accompanying drawings one embodiment of the present invention is elaborated.
As it is shown in figure 1, a kind of signal reconfiguring method based on splits' positions perception, comprise the steps:
Step 1: primary signal is uniformly divided into L block subsignal xi, wherein, i={1,2 ..., L}, L ＞ 1；
Step 2: calculate each subsignal sparse signal x' in complete base ΨiI.e. expansion coefficient, every piece of subsignal is equal
Can launch in complete base Ψ, and every piece of corresponding different expansion coefficient of subsignal；Described complete base Ψ is by feature bases
The orthogonal square formation constituted；Complete base Ψ is a kind of special matrix, is linear independence between this matrix column vector, any one
Individual subsignal can linearly add with the column vector in this matrix and corresponding expansion coefficient and represent, feature bases refers to
The characteristic vector obtained after this matrix is carried out Eigenvalues Decomposition, these characteristic vectors are linear independences；Described expansion coefficient
Scope is the real number in [0.1,0], and wherein, described expansion coefficient scope is determined by the expansion on Ψ S, take Ne of Ψ arrange to
Amount, constitutes the subspace of Ψ, is denoted as Ψ ', thus constructs the matrix of Ψ, wherein, D'＞ Ne >=1, and Ne is natural number；Ψ S is
The orthogonal square formation being made up of feature bases S；S is characterized base vector；D' is the subsignal length after launching.
Step 3: be filtered L sparse signal processing, obtains rebuilding subsignal；
Step 4: structure calculation matrix Φ, and use calculation matrix Φ that each reconstruction signal is compressed perception process,
To the observation vector y that each piece of subsignal is correspondingi；Described calculation matrix Φ is the matrix on K × N rank, and each element in Φ is independent
And obedience average is the normal distribution of 0；The measurement sample number needed when N is not use compressed sensing, when K is for using compressed sensing
The measurement sample number needed, K is natural number, N=Ne × L, 0 < K ＜ ＜ N.
Step 5: utilize expansion coefficient, observation vector yiAnd calculation matrix, calculate each subsignal x respectivelyiReconstruct letter
Number；
Step 5-1: initialize iterations t=0, the vector reciprocal of N number of variance corresponding to element in calculation matrix Φ
β &RightArrow=[β1, β2..., βN], wherein, βNFor n-th variance；
Step 5-2: calculate Σ=(α0ΦTΦ+A)-1；Wherein, α0Posterior probability for the expansion coefficient of every piece of subsignal is close
The average of degree function；Σ is the covariance of the posterior probability density function of the expansion coefficient of signal, A be N × N rank to angular moment
Battle array, the element on leading diagonal position is that in β, element arranges in order, and the element on remaining position is all 0；
Step 5-3: iteration updates t=t+1 time, if meeting iterations t less than maximum iteration time iterNum or residual error
rtIt is zero, then performs step 6-2；Otherwise, Σ is normalized, obtains reconstructing subsignal.
Step 6: to reconstruct subsignal x'iCarry out linear combination and obtain reconstruction signal.
Claims (2)
1. a signal reconfiguring method based on splits' positions perception, it is characterised in that comprise the steps:
Step 1: primary signal is uniformly divided into L block subsignal xi, wherein, i={1,2 ..., L}, L ＞ 1；
Step 2: calculate each subsignal sparse signal x' in complete base ΨiI.e. expansion coefficient, every piece of subsignal all can be complete
Standby base Ψ launches, and every piece of corresponding different expansion coefficient of subsignal；Described complete base Ψ is be made up of feature bases
Orthogonal square formation；
Step 3: to L sparse signal x'iIt is filtered processing, obtains rebuilding subsignal；
Step 4: structure calculation matrix Φ, and use calculation matrix Φ that each reconstruction subsignal is carried out splits' positions perception process,
Obtain each piece of observation vector y corresponding to subsignali；
Step 5: utilize expansion coefficient, observation vector yiAnd calculation matrix, calculate each subsignal x respectivelyiReconstruct subsignal；
Step 6: reconstruct subsignal is carried out linear combination and obtains reconstruction signal.
Signal reconfiguring method based on splits' positions perception the most according to claim 1, it is characterised in that described measurement square
Battle array Φ is the matrix on K × N rank, and each element in Φ is independent and obedience average is the normal distribution of 0；N is not for using compression sense
The measurement sample number needed when knowing, the measurement sample number that K needs when being to use compressed sensing, K is natural number, and 0 < K ＜ ＜ N.
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