CN104615877A - Method for conducting signal denoising based on wavelet packet - Google Patents
Method for conducting signal denoising based on wavelet packet Download PDFInfo
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Abstract
The invention relates to a method for conducting signal denoising based on a wavelet packet. The method is mainly applied to signal processing in engineering surveying. Low-frequency parts and high-frequency parts of signals are respectively processed through wavelet packet denoising, and the resolution ratios of high frequencies and low frequencies are improved. When a signal processing method used at present is used for conducting denoising processing on the signals, negative phenomena of low speed and low efficiency will be caused by limitation of data; meanwhile, as hard threshold functions and soft threshold functions are numerously adopted in data analysis so as to conduct quantization processing on decomposition coefficients, the denoising signals are lack of fidelity, and the relatively-ideal denoising signals cannot be obtained.
Description
Technical field
This method relates to a kind of method of carrying out signal denoising based on wavelet packet, is mainly used in the signal transacting in engineering survey.
Background technology
Wavelet packet denoising theory is amplified by Wavelet Denoising Method, and it processes respectively to the low frequency of signal and HFS, improves the resolution of low-and high-frequency.When the signal processing method of current use carries out denoising to signal, due to the limitation of data, slow, the inefficient negative phenomena of speed can be brought, simultaneously because majority in data analysis all adopts hard threshold function or soft-threshold function to carry out quantification treatment to coefficient of dissociation, it can be denoised signal distortion, can not obtain the denoised signal of relative ideal.
Summary of the invention
The object of the invention is to the defect overcoming prior art, a kind of method of carrying out signal denoising based on wavelet packet is provided.
To achieve these goals, present invention employs following technical scheme:
Wavelet packet analysis has carried out meticulousr analysis on the basis of wavelet analysis, frequency band is carried out multilayer division by it, the high frequency series part that multi-frequency analysis is not segmented is decomposed further, and frequency band can be chosen according to the feature of analyzed signal is adaptive, make it to match with signal spectrum, thus when improving-frequency resolution, there is the prospect more wide than wavelet analysis.Effective wavelet packet analysis directly perceived is exactly carry out a threshold value quantizing to each node coefficient that WAVELET PACKET DECOMPOSITION obtains, and then to the coefficient reconstruct after quantification, thus reaches the object of denoising.
Signal antinoise method based on wavelet packet analysis will experience four basic steps: 1. the WAVELET PACKET DECOMPOSITION of signal, selects a small echo, then carries out WAVELET PACKET DECOMPOSITION to signals and associated noises; 2. choose cost function, conventional cost function is information entropy and logarithmic entropy; 3. the choosing of best wavelet packet basis, for a given entropy standard, adopts top-down searching algorithm to calculate optimal tree, chooses best wavelet packet basis; 4. selected threshold, adopts different choosing methods to obtain different threshold values according to different decomposition frequency domains; 5. the threshold value quantizing of WAVELET PACKET DECOMPOSITION coefficient, for the coefficient of each WAVELET PACKET DECOMPOSITION, adopts the soft-threshold function of the improvement threshold value corresponding with this coefficient to carry out quantification treatment; 6. the wavelet package reconstruction of signal, according to the WAVELET PACKET DECOMPOSITION coefficient of lowermost layer and the coefficient through quantification treatment, carries out wavelet package reconstruction.
In above-mentioned each step, it is crucial that how selected threshold and how to carry out threshold value quantizing, to a certain extent, he is directly connected to the quality of signal being carried out to noise reduction process, and accompanying drawing 1 carries out the concrete steps of signal denoising for the method.
Wavelet packet basis storehouse is made up of many wavelet packet basiss, and different wavelet packet basiss has different character, reacts different signal characteristics, and we wish to choose optimum wavelet packet basis to specific signal, is used for expressing the feature of this signal.From the viewpoint of signal transacting, the search procedure of optimal base is in fact with as far as possible few coefficient, reacts information as much as possible, to reach the object of characteristics extraction.Gap between coefficient is the bigger the better, if only have a few coefficients very large, so these coefficients just can the feature of representation signal, and contrary coefficients comparison is average, and gap not quite, is so just difficult to the feature finding out signal.
When searching for optimal base, first will provide the cost function of a burst, cost function can be defined as any function about burst, and find the base making cost function minimum in all wavelet packet basiss then in wavelet library, this base is just optimal base.In order to reduce calculated amount, improve program operation speed, reduce unknown parameter simultaneously, this method adopts the top-down Binomial Trees based on " beta pruning " to be that cost function carries out choosing of optimal base with logarithmic entropy, that is logarithmic entropy that is that only have the logarithm entropy of lower one deck and that be less than this layer is just decomposed, otherwise with regard to beta pruning, detailed algorithm flow is as follows:
to signal node U
n jcarry out WAVELET PACKET DECOMPOSITION, calculate each node logarithmic entropy;
comparison node U
n jentropy and its two child node U decomposed
2n j+1, U
2n+1 j+1entropy and, and mark the less node of entropy;
decision node U
n jwhether be labeled, if be labeled, then deletion of node U
2n j+1, U
2n+1 j+1decompose downwards no longer further, if be not labeled, then by node U
2n j+1, U
2n+1 j+1as node U
n jrepeat above step.
Threshold denoising is that a kind of realization is simple, the good Wavelet Package Denoising Method of effect.Its basic thought be to wavelet decomposition after each layer coefficients in the mould coefficient that is greater than or less than certain threshold value process respectively, then carry out inverse transformation reconstruct denoising after signal.
The selection of threshold value is the key point of denoising, and threshold value is selected large, and the feature of useful signal will be filtered, if contrary Threshold selection is too small, and still noisy existence in the signal after denoising.Because the selection of threshold value directly affects de-noising effect, people propose an a lot of empirical model: soft-threshold, hard-threshold, minimax threshold value, fixed threshold etc., but all models are not general, have its scope of application.
In Practical Project signal, useful information mainly concentrates on low frequency part, and HFS majority is noise, only containing a small amount of useful information.If choose unified threshold value to process coefficient of dissociation, be difficult to reflect the different characteristic of signal at different frequency bands.Therefore need to choose multiple threshold value to carry out quantification treatment for different frequency bands.Natural order and the frequency band order of WAVELET PACKET DECOMPOSITION tree node there are differences, and want to choose different threshold value for different frequency bands, first will understand fully the frequency band order of WAVELET PACKET DECOMPOSITION tree node.When wavelet packet often decomposes one deck, low frequency decomposition part arranges from small to large by frequency, and HFS is by arranging from big to small.Accompanying drawing 2 is the frequency domain distribution rule of three layers of WAVELET PACKET DECOMPOSITION, visible, in WAVELET PACKET DECOMPOSITION, each layer frequency domain arranges and naturally arranges and there is inconsistent phenomenon, to rearrange frequency domain sequence when selected threshold, then adopt different Research on threshold selection selected threshold for different high, normal, basic frequency domains.For low frequency sequence this method thr=σ * [log (n)] with the formula
0.5/ (2n)
0.5for threshold model carries out choosing of threshold value, wherein n is signal length, and σ is the standard deviation of original signal WAVELET PACKET DECOMPOSITION coefficient.The WAVELET PACKET DECOMPOSITION coefficient of medium-high frequency sequence then adopts Stein without partial likelihood estimation principle self-adaptation selected threshold.
After trying to achieve threshold value, wavelet packet analysis majority all adopt hard threshold function (as | ω | during >T, η (ω)=ω, when | ω | during≤T, η (ω)=0) or soft-threshold function (when | ω | during >T, η (ω)=ω-sign (ω) * T, when | ω | during≤T, η (ω)=0) each decomposition node coefficient is processed.Hard thresholding method can be good at retaining the local features such as image border, but image there will be the vision distortion such as ring, pseudo-Gibbs' effect, and relative smooth is wanted in soft-threshold process, but may cause the distortion phenomenons such as edge fog.It shows in one-dimensional signal it is then that hard-threshold can make signal become coarse, and some point there will be interruption, and discontinuous point shrinks by soft-threshold, also can cause the contraction of signal simultaneously.And the soft threshold method of the improvement that this method proposes (when | ω | during >T, η (ω)=ω-sign (ω) * T+ sign (ω) * T/ (2*k+1), when | ω | during≤T, η (ω)=ω
2k+1/ [(2*k+1) * T
2k]) be compromise process to first two method, the large threshold function method of change along with Decomposition order is gradually near soft-threshold disposal route, then closer to hard-threshold disposal route when calculating the little node of Decomposition order, desirable denoising effect can be gathered in the crops like this while stick signal is complete.Accompanying drawing 3 is the function curve of three kinds of methods, and from figure, also can find out that hard thresholding method occurs being interrupted at threshold value T, soft threshold method makes curve produce contraction on η (ω) direction.
The invention has the beneficial effects as follows, it, for traditional denoising method, decreases calculated amount, improves the efficiency of program; The limitation of the obvious distortion of signal brought when overcoming hard-threshold or soft-threshold quantization parameter, while stick signal integrality, can obtain desirable denoised signal.
Accompanying drawing explanation
Fig. 1 is the signal denoising process flow diagram based on wavelet packet analysis.
Fig. 2 is the frequency domain distribution schematic diagram of three layers of WAVELET PACKET DECOMPOSITION.
Fig. 3 is the curve map of three kinds of threshold function functions, and wherein 3-1 is hard threshold function, and 3-2 is soft-threshold function, and 3-3 is the soft-threshold function of the improvement that this granting proposes.
Embodiment
Wavelet packet analysis has carried out meticulousr analysis on the basis of wavelet analysis, frequency band is carried out multilayer division by it, the high frequency series part that multi-frequency analysis is not segmented is decomposed further, and frequency band can be chosen according to the feature of analyzed signal is adaptive, make it to match with signal spectrum, thus when improving-frequency resolution, there is the prospect more wide than wavelet analysis.Effective wavelet packet analysis directly perceived is exactly carry out a threshold value quantizing to each node coefficient that WAVELET PACKET DECOMPOSITION obtains, and then to the coefficient reconstruct after quantification, thus reaches the object of denoising.
Signal antinoise method based on wavelet packet analysis will experience four basic steps: 1. the WAVELET PACKET DECOMPOSITION of signal, selects a small echo, then carries out WAVELET PACKET DECOMPOSITION to signals and associated noises; 2. choose cost function, conventional cost function is information entropy and logarithmic entropy; 3. the choosing of best wavelet packet basis, for a given entropy standard, adopts top-down searching algorithm to calculate optimal tree, chooses best wavelet packet basis; 4. selected threshold, adopts different choosing methods to obtain different threshold values according to different decomposition frequency domains; 5. the threshold value quantizing of WAVELET PACKET DECOMPOSITION coefficient, for the coefficient of each WAVELET PACKET DECOMPOSITION, adopts the soft-threshold function of the improvement threshold value corresponding with this coefficient to carry out quantification treatment; 6. the wavelet package reconstruction of signal, according to the WAVELET PACKET DECOMPOSITION coefficient of lowermost layer and the coefficient through quantification treatment, carries out wavelet package reconstruction.
In above-mentioned each step, it is crucial that how selected threshold and how to carry out threshold value quantizing, to a certain extent, he is directly connected to the quality of signal being carried out to noise reduction process, and accompanying drawing 1 carries out the concrete steps of signal denoising for the method.
Wavelet packet basis storehouse is made up of many wavelet packet basiss, and different wavelet packet basiss has different character, reacts different signal characteristics, and we wish to choose optimum wavelet packet basis to specific signal, is used for expressing the feature of this signal.From the viewpoint of signal transacting, the search procedure of optimal base is in fact with as far as possible few coefficient, reacts information as much as possible, to reach the object of characteristics extraction.Gap between coefficient is the bigger the better, if only have a few coefficients very large, so these coefficients just can the feature of representation signal, and contrary coefficients comparison is average, and gap not quite, is so just difficult to the feature finding out signal.
When searching for optimal base, first will provide the cost function of a burst, cost function can be defined as any function about burst, and find the base making cost function minimum in all wavelet packet basiss then in wavelet library, this base is just optimal base.In order to reduce calculated amount, improve program operation speed, reduce unknown parameter simultaneously, this method adopts the top-down Binomial Trees based on " beta pruning " to be that cost function carries out choosing of optimal base with logarithmic entropy, that is logarithmic entropy that is that only have the logarithm entropy of lower one deck and that be less than this layer is just decomposed, otherwise with regard to beta pruning, detailed algorithm flow is as follows:
to signal node U
n jcarry out WAVELET PACKET DECOMPOSITION, calculate each node logarithmic entropy;
comparison node U
n jentropy and its two child node U decomposed
2n j+1, U
2n+1 j+1entropy and, and mark the less node of entropy;
decision node U
n jwhether be labeled, if be labeled, then deletion of node U
2n j+1, U
2n+1 j+1decompose downwards no longer further, if be not labeled, then by node U
2n j+1, U
2n+1 j+1as node U
n jrepeat above step.
Threshold denoising is that a kind of realization is simple, the good Wavelet Package Denoising Method of effect.Its basic thought be to wavelet decomposition after each layer coefficients in the mould coefficient that is greater than or less than certain threshold value process respectively, then carry out inverse transformation reconstruct denoising after signal.
The selection of threshold value is the key point of denoising, and threshold value is selected large, and the feature of useful signal will be filtered, if contrary Threshold selection is too small, and still noisy existence in the signal after denoising.Because the selection of threshold value directly affects de-noising effect, people propose an a lot of empirical model: soft-threshold, hard-threshold, minimax threshold value, fixed threshold etc., but all models are not general, have its scope of application.
In Practical Project signal, useful information mainly concentrates on low frequency part, and HFS majority is noise, only containing a small amount of useful information.If choose unified threshold value to process coefficient of dissociation, be difficult to reflect the different characteristic of signal at different frequency bands.Therefore need to choose multiple threshold value to carry out quantification treatment for different frequency bands.Natural order and the frequency band order of WAVELET PACKET DECOMPOSITION tree node there are differences, and want to choose different threshold value for different frequency bands, first will understand fully the frequency band order of WAVELET PACKET DECOMPOSITION tree node.When wavelet packet often decomposes one deck, low frequency decomposition part arranges from small to large by frequency, and HFS is by arranging from big to small.Accompanying drawing 2 is the frequency domain distribution rule of three layers of WAVELET PACKET DECOMPOSITION, visible, in WAVELET PACKET DECOMPOSITION, each layer frequency domain arranges and naturally arranges and there is inconsistent phenomenon, to rearrange frequency domain sequence when selected threshold, then adopt different Research on threshold selection selected threshold for different high, normal, basic frequency domains.For low frequency sequence this method thr=σ * [log (n)] with the formula
0.5/ (2n)
0.5for threshold model carries out choosing of threshold value, wherein n is signal length, and σ is the standard deviation of original signal WAVELET PACKET DECOMPOSITION coefficient.The WAVELET PACKET DECOMPOSITION coefficient of medium-high frequency sequence then adopts Stein without partial likelihood estimation principle self-adaptation selected threshold.
After trying to achieve threshold value, wavelet packet analysis majority all adopt hard threshold function (as | ω | during >T, η (ω)=ω, when | ω | during≤T, η (ω)=0) or soft-threshold function (when | ω | during >T, η (ω)=ω-sign (ω) * T, when | ω | during≤T, η (ω)=0) each decomposition node coefficient is processed.Hard thresholding method can be good at retaining the local features such as image border, but image there will be the vision distortion such as ring, pseudo-Gibbs' effect, and relative smooth is wanted in soft-threshold process, but may cause the distortion phenomenons such as edge fog.It shows in one-dimensional signal it is then that hard-threshold can make signal become coarse, and some point there will be interruption, and discontinuous point shrinks by soft-threshold, also can cause the contraction of signal simultaneously.And the soft threshold method of the improvement that this method proposes (when | ω | during >T, η (ω)=ω-sign (ω) * T+ sign (ω) * T/ (2*k+1), when | ω | during≤T, η (ω)=ω
2k+1/ [(2*k+1) * T
2k]) be compromise process to first two method, the large threshold function method of change along with Decomposition order is gradually near soft-threshold disposal route, then closer to hard-threshold disposal route when calculating the little node of Decomposition order, desirable denoising effect can be gathered in the crops like this while stick signal is complete.Accompanying drawing 3 is the function curve of three kinds of methods, and from figure, also can find out that hard thresholding method occurs being interrupted at threshold value T, soft threshold method makes curve produce contraction on η (ω) direction.
Claims (4)
1. one kind is carried out the method for signal denoising based on wavelet packet, wavelet packet analysis has carried out meticulousr analysis on the basis of wavelet analysis, frequency band is carried out multilayer division by it, the high frequency series part that multi-frequency analysis is not segmented is decomposed further, and frequency band can be chosen according to the feature of analyzed signal is adaptive, make it to match with signal spectrum, thus when improving-frequency resolution, it is characterized in that, concrete steps are:
1) WAVELET PACKET DECOMPOSITION of signal, selects a small echo, then carries out WAVELET PACKET DECOMPOSITION to signals and associated noises;
2) information entropy or logarithmic entropy is chosen as cost function;
3) the choosing of best wavelet packet basis, for a given entropy standard, adopts top-down searching algorithm to calculate optimal tree, chooses best wavelet packet basis;
4) selected threshold, adopts different choosing methods to obtain different threshold values according to different decomposition frequency domains;
5) threshold value quantizing of WAVELET PACKET DECOMPOSITION coefficient, for the coefficient of each WAVELET PACKET DECOMPOSITION, adopts the soft-threshold function of the improvement threshold value corresponding with this coefficient to carry out quantification treatment;
6) wavelet package reconstruction of signal, according to the WAVELET PACKET DECOMPOSITION coefficient of lowermost layer and the coefficient through quantification treatment, carries out wavelet package reconstruction.
2. method of carrying out signal denoising based on wavelet packet according to claim 1, it is characterized in that, the concrete steps chosen of best wavelet packet basis described in step 3) are: the cost function first providing a burst, then find the base making cost function minimum in all wavelet packet basiss in wavelet library, this base is just optimal base; The top-down Binomial Trees based on " beta pruning " is adopted to be that cost function carries out choosing of optimal base with logarithmic entropy, that is logarithmic entropy that is that only have the logarithm entropy of lower one deck and that be less than this layer is just decomposed, otherwise with regard to beta pruning, detailed algorithm flow is as follows:
to signal node U
n jcarry out WAVELET PACKET DECOMPOSITION, calculate each node logarithmic entropy;
comparison node U
n jentropy and its two child node U decomposed
2n j+1, U
2n+1 j+1entropy and, and mark the less node of entropy;
decision node U
n jwhether be labeled, if be labeled, then deletion of node U
2n j+1, U
2n+1 j+1decompose downwards no longer further, if be not labeled, then by node U
2n j+1, U
2n+1 j+1as node U
n jrepeat above step.
3. method of carrying out signal denoising based on wavelet packet according to claim 1, it is characterized in that, step 4) is specially: rearrange frequency domain sequence, different Research on threshold selection selected threshold is adopted, for low frequency sequence thr=σ * [log (n)] with the formula for different high, normal, basic frequency domains
0.5/ (2n)
0.5for threshold model carries out choosing of threshold value, wherein n is signal length, and σ is the standard deviation of original signal WAVELET PACKET DECOMPOSITION coefficient, and the WAVELET PACKET DECOMPOSITION coefficient of medium-high frequency sequence then adopts Stein without partial likelihood estimation principle self-adaptation selected threshold.
4. method of carrying out signal denoising based on wavelet packet according to claim 1, it is characterized in that, the soft-threshold function of the improvement described in step 5) is: when | ω | during >T, η (ω)=ω-sign (ω) * T+ sign (ω) * T/ (2*k+1), when | ω | during≤T, η (ω)=ω
2k+1/ [(2*k+1) * T
2k]; The large threshold function method of change along with Decomposition order, gradually near soft-threshold disposal route, then closer to hard-threshold disposal route when calculating the little node of Decomposition order, can gather in the crops desirable denoising effect like this while stick signal is complete.
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