CN103995973B - Signal sparse decomposition method based on set partitioning of over-complete dictionary - Google Patents
Signal sparse decomposition method based on set partitioning of over-complete dictionary Download PDFInfo
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Abstract
The invention discloses a signal sparse decomposition method based on set partitioning of an over-complete dictionary and relates to a signal sparse decomposition method. The method is provided in order to solve the problem that when a classic MP method and an existing improvement method are used for decomposing signals, the operation time is too long. According to the method, the over-complete dictionary is subjected to set partitioning by selecting different factors, a huge redundant dictionary is divided into a plurality of sub-dictionaries, appropriate time frequency is selected from the sub-dictionaries through a matching pursuit algorithm to accurately and rapidly decompose signals, signal residuals are decomposed again according to the standard of actual requirements till reconstructed signals conforming to the standard are obtained, and the reconstructed signals can be shown in the form of the sum of the products of all stages of iteration residuals and corresponding matched atoms. The signal sparse decomposition method is applicable to the field of signal sparse decomposition.
Description
Technical field
The present invention relates to a kind of signal Its Sparse Decomposition method being divided based on complete dictionary set excessively is and in particular to signal
Decomposition method.
Background technology
Signal decomposition and expression are particularly significant in signal transacting research field.Especially in the process to signal and analysis
In, signal decomposition plays vital role.In the method that signal is decomposed, traditional classical method is to be thrown
It is mapped on one group of complete orthogonal basement, such as Fourier transformation or wavelet transformation.
The linear decomposition on similar Fourier's base or wavelet basis, or the single substrate of other substrate, signal being carried out
Flexible not enough.Some sparse characteristic of signal itself are not fully showed.Fourier's base is only capable of fixed to time domain
The good signal in position carries out a certain degree of expression, and its frequency domain polarization is poor.And wavelet basis is then not suitable for for Fourier
The signal having a close limit high-frequency band in frequency domain after conversion carries out exploded representation.Information due to carrying on signal is divided in signal
It is scattered in during solution on whole substrate, the expression coefficient of signal is difficult with this two traditional orthogonal basis
Detection and differentiate the unique forms that have of signal and characteristic.Same problem also can be run on other orthogonal basement.
For a signal that orientation range changes greatly in time domain and frequency domain, flexible isolation is for table
State this signal to play an important role.Signal demand is launched into the stacking pattern of some waveforms, the time-frequency characteristic of these waveforms
Match with the partial structurtes of this signal, these ripples are referred to as time-frequency atom.For example, a class signal of similar impact signal
Should be broken down on the base of time domain concentration, frequency domain part is had the ripple of narrower-band to represent simultaneously.When signal has simultaneously
When having two above constituent, time-frequency atom has to make corresponding adjustment.Classical MP method is sought in huge dictionary
Look for consuming overlong time in matched atoms, thus leading to operation time long.Though the existing improved method based on shift factor
So more classical MP method shortens the time to a certain extent, but precision is relatively low, and the time is still long.Existing based on frequency
The improved method of the rate factor improves precision on this basis, also further reduces the time of decomposition and reconstruction signal, but
Still to consume a longer time, when especially signal length is longer, the consuming time still long it is therefore necessary to find a kind of energy
On the premise of enough ensureing enough accuracy, matched atoms can be gone out by quick-pick from the dictionary being made up of a large amount of time-frequency atom
Method.
Content of the invention
The present invention is in order to solve to exist when signal is decomposed using classical MP method and existing improved method
Operation time long problem, especially for solving in actual applications when signal is long, when dictionary is excessively huge, during computing
Between the problem that can lengthen further.And then propose a kind of signal Its Sparse Decomposition method dividing based on excessively complete dictionary set.
A kind of process of the signal Its Sparse Decomposition method being divided based on complete dictionary set excessively is：
Step one：Set up different excessively complete dictionary D for the different signal f of characteristic, when entering to Gaussian modulation window signal
During row analysis, set up the excessively complete dictionary D based on Gaussian modulation signal；
Step 2：Excessively complete dictionary is divided into some mutually disjoint sub- dictionaries by the modulation correlation according to atom, makes
Every sub- dictionary is all to be collectively formed by the atom meeting equivalence relation, is collectively formed by the atom of identical modulating characteristic；
Step 3：Using matching pursuit algorithm decomposed signal, some sub- dictionary being divided into according to excessively complete dictionary, from every
Choose an atom in the sub- dictionary of the individual atomic building meeting equivalence relation as representative, substitute into matching judgment formula one by one and carry out
Relatively, until find with the atom of current input signal best match till, the sub- dictionary that this atom is located is as optimal
The sub- dictionary joined；
Step 4：In the sub- dictionary of the best match selected, start to last atom from first atom,
Atom is substituted into one by one matching judgment formula to be compared, select the atom with current input signal best match, using selecting
Atom signal is reconstructed；
Step 5：Contrast input signal f and reconstruction signal, obtain signal residual error, default with according to available accuracy requirement
Standard is compared, if signal residual error size reaches preset standard, terminates whole calculating process, with reconstruct letter described in step 4
Number represent input signal, if signal residual error size is not reaching to preset standard, return to step three to signal remnants Rf enter again
Row decomposes.
Linearly is deployed on one group of Non-orthogonal basis set the present invention, is entered by the excessively complete dictionary of factor pair choosing different
Row set divides, and huge redundant dictionary is divided into some sub- dictionaries, chooses conjunction using matching pursuit algorithm from sub- dictionary
Suitable time-frequency atom carrys out decomposed signal.Meaning of the present invention is that it can be under ensureing enough precision, can be quickly from superfluous
Choose suitable time-frequency atom in remaining dictionary and carry out decomposed signal, thus significantly cutting down operation time.Signal is longer, this method excellent
Gesture is more obvious, and when signal length N=1024, the operation time of this method is classical match tracing method operation time
1.29%, it is the 12.73% of shift factor improved method operation time, be frequency factor improved method operation time
23.37%.
Brief description
Fig. 1 is the flow chart of the signal Its Sparse Decomposition method being divided based on excessively complete dictionary set；
Fig. 2 is primary signal figure；
Fig. 3 is matched atoms signal graph；
Fig. 4 is the remaining figure of signal；
Fig. 5 is reconstruct signal graph.
Specific embodiment
Specific embodiment one：In conjunction with Fig. 1, present embodiment, a kind of signal being divided based on excessively complete dictionary set are described
Its Sparse Decomposition method, it comprises the steps：
Step one：Set up different excessively complete dictionary D for the different signal f of characteristic, when entering to Gaussian modulation window signal
During row analysis, set up the excessively complete dictionary D based on Gaussian modulation signal.
Step 2：Excessively complete dictionary is divided into some mutually disjoint sub- dictionaries by the modulation correlation according to atom, makes
Every sub- dictionary is all to be collectively formed by the atom meeting equivalence relation, is collectively formed by the atom of identical modulating characteristic.
Step 3：Using matching pursuit algorithm decomposed signal, some sub- dictionary being divided into according to excessively complete dictionary, from every
Choose an atom in the sub- dictionary of the individual atomic building meeting equivalence relation as representative, substitute into matching judgment formula one by one and carry out
Relatively, until find with the sub- dictionary of current input signal best match till, sub- dictionary that this atom is located is as optimal
The sub- dictionary of coupling.
Step 4：In the sub- dictionary of the best match selected, start to last atom from first atom,
Atom is substituted into one by one matching judgment formula to be compared, select the atom with current input signal best match, using selecting
Atom signal is reconstructed.
Step 5：Contrast input signal f and reconstruction signal, obtain signal residual error, default with according to available accuracy requirement
Standard is compared, if signal residual error size reaches preset standard, terminates whole calculating process, with reconstruct letter described in step 4
Number represent input signal, if signal residual error size is not reaching to preset standard, return to step three to signal remnants Rf enter again
Row decomposes.
Specific embodiment two：The concrete operation step of the step one described in present embodiment is：
In the Hilbert space H=L being made up of complex function2(R), in, have
Wherein f represents input signal, and t represents the time.
In Hilbert space H=L2(R) the set D=(g of one group of vector defined inγ)γ∈ΓFor dictionary, and have | | gγ||
=1, make g (t) be continuously differentiable real function, its higher-order shear deformation is O (1/ (t2+ 1)), | | g (t) | | the integration of=1, g (t)
It is not zero, and g (0) ≠ 0.Define shown in Gabor cluster expression formula such as formula (2)
Γ=R+×R2Represent two-dimentional arithmetic number domain, wherein R+Represent arithmetic number domain, R2Represent element in this real number field
Many dimensions are two dimension, and the two representative set Γ that is multiplied is provided simultaneously with above-mentioned 2 points of requirements.γ=(s, u, v, w) refers to for time and frequency parameter
Mark collection, is Γ=R+×R2One of element.In formula, s is scale factor, and u is shift factor, and v is frequency factor, and w is phase place
The factor, the factor in formulaEffect be to gγT () is normalized.Gabor cluster gγT () is based on function g
T () builds.
By time and frequency parameter index set γ=(s, u, v, w) discretization, obtain γ=(aj,paj△u,ka-j△v,i△w).
Wherein a=2, △ u=1/2, △ v=π, △ w=π/6,0<j<log2N, 0≤p≤N2-j+1, 0≤k≤2j+1, 0≤i≤12.From
After dispersion, discrete parameter j in index set, p, k, i only allow value in the range of definition, each group of discrete indicator collection parameter
Value all correspond to an atom, all atoms is arranged and obtains an excessively complete dictionary D together.
Other steps are identical with specific embodiment one.
Specific embodiment three：The concrete operation step of present embodiment step 2 is：
S in time and frequency parameter index set γ=(s, u, v, w), u factor is identical, v, w factor is different atom are divided into one
Individual set, makes β=(s, u) represent the index set of the sub- dictionary of equivalence, then Γβ={ βi| i=1,2 ... }.Sub- dictionary such as formula
(3) shown in
Sub- dictionary is by atom gγConstitute, these atomic properties are close, i.e. (s, u)i=βi, each group of discrete indicator collection γ=
(s, u, v, w) parameter value all correspond to an atom gγ, discrete indicator integrates form as γ=(aj,paj△u,ka-j△v,i△
w).
Cross complete dictionary D by some sub- dictionariesConstitute, meet following condition,
Whole excessively complete dictionary is equivalent to and is divided on the sub- dictionary form of two dimension, arbitrary atom and its week in form
The adjacent atom enclosing has akin property.Each sub- dictionary carrys out generation by an atom with the specific modulation factor
Table.
Other steps are identical with specific embodiment two.
Specific embodiment four：The concrete operation step of step 3 described in present embodiment is：
By inner product<f,g>∈L2(R)2Definition be
WhereinComplex conjugate version for g (t).
Choose one in every sub- dictionary and represent Atomic Decomposition signal, signal f can be broken down into
F=<f,gγ0>gγ0+Rf (6)
Wherein gγ0∈ D, gγ0It is certain atom participating in first time interative computation, be all of atom gγIn one
Point, Rf is using atom gγ0Remaining vector after signal f is approached.gγ0Mutually orthogonal with Rf, have
||f||2|<F, gγ0>|2+||Rf||2(7)
Select suitable gγ0∈ D makes f, gγ0As far as possible big, remnants | | Rf | | is as far as possible little for signal.Representative in the institute choosing
Finding one in atom makes |<f,gγ0>| g that is maximum and meeting formula (8)γ0As optimum atom, and with this optimum atom institute
Sub- dictionary as best match sub- dictionary.
In formula, α is range factor, takes 1, sup | | represent and seek supremum.
Other steps are identical with specific embodiment three.
Specific embodiment five：The concrete operation step of step 4 described in present embodiment is：
In the sub- dictionary of the best match selected, start to last atom from first atom, by atom
Substitute into matching judgment formula one by one to be compared, finding one in the sub- dictionary of best match makes |<f,g'γ0>| maximum and satisfaction public affairs
The g' of formula (9)γ0As optimum atom,
Wherein g'γ0∈ D, g'γ0It is certain atom in the sub- dictionary of best match, be also all of atom gγIn one
Point, select the atom with current input signal best match, using the atom selected, signal is reconstructed.
Other steps are identical with specific embodiment four.
Specific embodiment six：The concrete operation step of step 5 described in present embodiment is：
According to the best match atom selected, signal f has been broken down into f=<f,g'γ0>g'γ0+ Rf, by signal residual error
Require default standard to be compared with according to available accuracy, if signal residual error size reaches preset standard, terminate whole counting
Calculation process, represents input signal with this reconstruction signal, if signal residual error size is not reaching to preset standard, return to step three will
Signal remnants Rf is decomposed again；R during computing first0F=f is iterated, the season R of computing afterwardsjF=f is iterated, 0≤
J≤n, obtains the remaining R of n-th order eventually through iterative calculationnF, n represent iterations, n >=0.N-th order remnants RnThe size of f
The Rule of judgment that can terminate as algorithm.
Using formula (10) from setMiddle selection is to remaining RnThe atom of f coupling.
Primary signal f is decomposed on the base that some matched atoms are constituted, and its reconstruction signal can be expressed as every one-level and change
For residual error and the product of corresponding matched atoms and form.
Other steps are identical with specific embodiment five.
Specific embodiment
According to specific embodiment two：The expression formula of g (t) continuously differentiable function described in test is, it is
One Gauss function.According to specific embodiment three：Determine frequency constant factor v and a phase constant factor first
w.According to stimulus modulating characteristic, make v=π and w=π/6 be the initial value of sub- dictionary index set, initial value is added and subtracted
Parameter increase △ v and △ w operation, to obtain different sub- dictionaries.After initial parameter value sets, need in computer simulation program
It is converted into discrete form computing.According to specific embodiment four, specific embodiment five and specific embodiment six by signal
Decomposed and reconstructed.Fig. 2 is primary signal figure, Fig. 3 is matched atoms signal graph, Fig. 4 is the remaining figure of signal, Fig. 5 is reconstruct
Signal graph, from the point of view of reconstruction signal result, this method carries out quality ten sub-argument reconstructing again after Its Sparse Decomposition to primary signal
Think.Table 1 is the run time comparative effectiveness of this method and additive method.
Table 1
It can be seen that the present invention, under ensureing enough precision, quickly can choose suitable time-frequency former from redundant dictionary
Son carrys out decomposed signal, thus significantly cutting down operation time, when signal length N=1024, the operation time of this method is classics
The 1.29% of match tracing method operation time, is the 12.73% of shift factor improved method operation time, is that frequency factor changes
Enter the 23.37% of method operation time.In a practical situation, the length of signal can be quite big, and the advantage of this method can be brighter
Aobvious.
Claims (1)
1. a kind of signal Its Sparse Decomposition method being divided based on excessively complete dictionary set is it is characterised in that it comprises the steps：
Step one：Set up different excessively complete dictionary D for the different signal f of characteristic, when carrying out to Gaussian modulation window signal point
During analysis, set up the excessively complete dictionary D based on Gaussian modulation signal；The process of realizing of step one is：
In the Hilbert space H=L being made up of complex function2(R), in, have
Wherein f represents input signal, and t represents the time；
In Hilbert space H=L2(R) the set D=(g of one group of vector defined inγ)γ∈ΓFor dictionary, and have | | gγ| |=1,
G (t) is made to be continuously differentiable real function, its higher-order shear deformation is O (1/ (t2+ 1)), | | g (t) | | the integration of=1, g (t) is not
Zero, and g (0) ≠ 0；Define shown in Gabor cluster expression formula such as formula (2)
Γ=R+×R2Represent two-dimentional arithmetic number domain, wherein R+Represent arithmetic number domain, R2Represent the element multidimensional in this real number field
Number is two dimension, and the two representative set Γ that is multiplied is provided simultaneously with above-mentioned 2 points of requirements；γ=(s, u, v, w) is time and frequency parameter index
Collection, is Γ=R+×R2One of element；In formula s be scale factor, u be shift factor, v be frequency factor, w be phase place because
Son, the factor in formulaEffect be to gγT () is normalized；Gabor cluster gγT () is based on function g (t)
Build；
By time and frequency parameter index set γ=(s, u, v, w) discretization, obtain γ=(aj,paj△u,ka-j△v,i△w)；Wherein a
=2, △ u=1/2, △ v=π, △ w=π/6,0 ＜ j ＜ log2N, 0≤p≤N2-j+1, 0≤k≤2j+1, 0≤i≤12；Discretization
Afterwards, discrete parameter j in index set, p, k, i only allow value in the range of definition, and each group of discrete indicator collection parameter value is equal
Correspond to an atom, all atoms are arranged and obtains an excessively complete dictionary D together；
Step 2：Excessively complete dictionary is divided into some mutually disjoint sub- dictionaries by the modulation correlation according to atom, makes each
Sub- dictionary is all to be collectively formed by the atom meeting equivalence relation, is collectively formed by the atom of identical modulating characteristic；Step
Two process of realizing is：
Will be identical to s, u factor in time and frequency parameter index set γ=(s, u, v, w), the different atom of v, w factor is divided into a collection
Close, make β=(s, u) represent the index set of the sub- dictionary of equivalence, then Γβ={ βi| i=1,2 ... }；Sub- dictionary such as formula (3) institute
Show
Sub- dictionary is by atom gγConstitute, these atomic properties are close, i.e. (s, u)i=βi, each group of discrete indicator collection γ=(s, u,
V, w) parameter value all correspond to an atom gγ, discrete indicator integrates form as γ=(aj,paj△u,ka-j△v,i△w)；
Cross complete dictionary D by some sub- dictionariesConstitute, meet following condition,
Whole excessively complete dictionary is equivalent to and is divided on the sub- dictionary form of two dimension, in form arbitrary atom with about
Adjacent atom has akin property；Each sub- dictionary to be represented by an atom with the specific modulation factor；
Step 3：Using matching pursuit algorithm decomposed signal, some sub- dictionary being divided into according to excessively complete dictionary, expire from each
Choose an atom in the sub- dictionary of the atomic building of sufficient equivalence relation as representative, substitute into matching judgment formula one by one and compared
Relatively, until find with the atom of current input signal best match till, using this atom be located sub- dictionary as best match
Sub- dictionary；The process of realizing of step 3 is：
By inner product<f,g>∈L2(R)2Definition be
WhereinComplex conjugate version for g (t)；
Signal f can be broken down into
F=<f,gγ0>gγ0+Rf (6)
Wherein gγ0∈ D, gγ0It is certain atom participating in first time interative computation, be all of atom gγIn a part, Rf
It is using atom gγ0Remaining vector after signal f is approached；gγ0Mutually orthogonal with Rf, have
||f||2=|<f,gγ0>|2+||Rf||2(7)
Select suitable gγ0∈ D makes |<f,gγ0>| as far as possible big, remnants | | Rf | | is as far as possible little for signal；One is found in sub- dictionary
Make |<f,gγ0>| g that is maximum and meeting formula (8)γ0As optimum atom, and the sub- dictionary being located using this optimum atom as
The sub- dictionary of best match；
In formula, α is range factor, takes 1, sup | | represent and seek supremum；
Step 4：In the sub- dictionary of the best match selected, start to last atom from first atom, will
Atom substitutes into matching judgment formula one by one and is compared, and selects the atom with current input signal best match, using select
Atom signal is reconstructed, and obtains reconstruction signal；The process of realizing of step 4 is：
In the sub- dictionary of the best match selected, start to last atom from first atom, by atom one by one
Substitute into matching judgment formula to be compared, finding one in the sub- dictionary of best match makes |<f,g'γ0>| maximum and meet formula
(9) g'γ0As optimum atom,
Wherein g'γ0∈ D, g'γ0It is certain atom in the sub- dictionary of best match, be also all of atom gγIn a part, choosing
Select out the atom with current input signal best match, using the atom selected, signal is reconstructed；
Step 5：Contrast input signal f and reconstruction signal, obtain signal residual error, require default standard with according to available accuracy
It is compared, if signal residual error size reaches preset standard, terminate whole calculating process, with reconstruction signal table described in step 4
Show input signal；If signal residual error size is not reaching to preset standard, return to step three is carried out point again to signal remnants Rf
Solution；The process of realizing of step 5 is：
According to the best match atom selected, signal f has been broken down into f=<f,g'γ0>g'γ0+ Rf, by signal residual error and root
Factually required precision default standard in border is compared, if signal residual error size reaches preset standard, terminates entirely calculating
Journey, represents input signal with this reconstruction signal, if signal residual error size is not reaching to preset standard, return to step three is by signal
Remaining Rf is decomposed again；R during computing first0F=f is iterated, the season R of computing afterwardsjF=f is iterated, and 0≤j≤
N, obtains the remaining R of n-th order eventually through iterative calculationnF, n represent iterations, n >=0；N-th order remnants RnThe big I of f is made
The Rule of judgment terminating for algorithm；
Using formula (10) from setMiddle selection is to remaining RnThe atom of f coupling；
Primary signal f is decomposed on the base that some matched atoms are constituted, and it is residual that its reconstruction signal can be expressed as every one-level iteration
Difference with the product of corresponding matched atoms and form.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108917917A (en) * | 2018-05-16 | 2018-11-30 | 国网山东省电力公司莱芜供电公司 | A kind of breaker mechanical vibration signal denoising method based on sparse decomposition |
Families Citing this family (12)
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| CN104506198B (en) * | 2014-12-30 | 2017-08-01 | 大连理工大学 | Cardiechema signals compression algorithm based on repeated feature |
| CN105279481B (en) * | 2015-09-17 | 2018-12-28 | 厦门大学 | Targets in ocean based on cascade atom recognizes detection method |
| CN109344847B (en) * | 2017-12-07 | 2022-03-15 | 太原理工大学 | Mining XLPE cable insulation electric branch growth stage identification method based on sparse decomposition |
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| CN109632973B (en) * | 2018-12-26 | 2021-07-13 | 西安科技大学 | Ultrasonic echo signal extraction method based on multi-scale matching pursuit |
| CN109507291B (en) * | 2018-12-26 | 2021-08-06 | 西安科技大学 | Signal preprocessing method |
| CN109682892B (en) * | 2018-12-26 | 2021-07-09 | 西安科技大学 | Signal denoising method based on time-frequency analysis |
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| CN110245321A (en) * | 2019-05-09 | 2019-09-17 | 东北石油大学 | Duration power quality disturbances method and device based on match tracing sparse decomposition |
| CN110572161B (en) * | 2019-09-10 | 2020-12-11 | 安徽寒武纪信息科技有限公司 | Data encoding method and device, computer equipment and readable storage medium |
| CN112075932B (en) * | 2020-10-15 | 2023-12-05 | 中国医学科学院生物医学工程研究所 | High-resolution time-frequency analysis method for evoked potential signals |
| CN112906632B (en) * | 2021-03-18 | 2022-11-11 | 中北大学 | Automatic extraction method of highly adaptive time delay target signal |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103413134A (en) * | 2013-07-11 | 2013-11-27 | 四川大学 | Ground moving target micro-tremor signal characteristic extraction based on sparse decomposition |
-
2014
- 2014-05-27 CN CN201410228157.XA patent/CN103995973B/en active Active
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103413134A (en) * | 2013-07-11 | 2013-11-27 | 四川大学 | Ground moving target micro-tremor signal characteristic extraction based on sparse decomposition |
Non-Patent Citations (4)
| Title |
|---|
| 信号稀疏分解及压缩感知理论应用研究;刘丹华;《万方学位论文》;20110328;第3-4章 * |
| 基于压缩感知的图像稀疏表示方法;管蓉;《万方学位论文》;20130627;全文 * |
| 基于稀疏分解的数据分类算法;乔奕等;《计算机工程》;20100331;第36卷(第5期);57-58 * |
| 基于自适应超完备稀疏表示的图像去噪方法;肖泉等;《仪器仪表学报》;20090930;第30卷(第9期);1886-1890 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108917917A (en) * | 2018-05-16 | 2018-11-30 | 国网山东省电力公司莱芜供电公司 | A kind of breaker mechanical vibration signal denoising method based on sparse decomposition |
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