CN109284671A - It is a kind of based on ASMP threshold value is optimal and the seawater temperature field restructing algorithm of low-pass filtering - Google Patents
It is a kind of based on ASMP threshold value is optimal and the seawater temperature field restructing algorithm of low-pass filtering Download PDFInfo
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Abstract
The present invention is a kind of based on the optimal seawater temperature field restructing algorithm with low-pass filtering of ASMP threshold value, stochastical sampling is carried out in observation area, after obtaining sampled value, convert temperature data to the form of one-dimensional column signal, and temperature field is reconstructed, process is as follows: carrying out the initialization of ASMP algorithm first and runs ASMP algorithm, determine the initiation threshold in refinement threshold search step, in refinement threshold search step, operation ASMP algorithm determines optimal input threshold value, using obtained optimal threshold as the input quantity of ASMP algorithm, operation ASMP algorithm obtains sparse estimation again, low-pass filtering treatment is carried out to sparse estimation, and by one-dimension temperature signals revivification be Two dimensional Distribution form, the Two dimensional Distribution in temperature field can be obtained.Present invention improves over ASMP restructing algorithms to keep the estimation of temperature field signal degree of rarefication more accurate by searching for optimal input threshold value；According to the characteristic of temperature field signal, low-pass filtering treatment is carried out to sparse estimation, further improves the reconstruction accuracy of ocean temperature field.
Description
Technical field
The invention belongs to compressed sensing reconfiguration technique fields, and in particular to one kind is based on ASMP threshold value is optimal and low-pass filtering
Seawater temperature field restructing algorithm.
Background technique
The acquisition of ocean temperature data generally uses actual measurement mode, but environment locating for ocean is very special, so that real
Higher cost is surveyed, meanwhile, ocean temperature fluctuation is big, and periodical and aperiodicity is simultaneously deposited, and the getable sampled data of actual measurement institute is not
With continuity and limited amount.Therefore, under normal circumstances, oceanographic observation can only obtain a small amount of discrete ocean temperature data,
In order to realize the continuous expression of seawater temperature field, it is necessary to which observation data are carried out with the reconstruct of seawater temperature field.Previous ocean temperature
The reconstruct of degree field is typically chosen interpolation algorithm, and this method is computationally intensive and complicated, the not costly and time consuming effort of accuracy, it usually needs
A large amount of observation can be reconstructed accurately.And compressed sensing its advantage lies in being able to utilize as a kind of emerging theory
Less sampled point, more accurately reconstructs original signal, while saving resource, also improves reconstruction accuracy.Tradition
Intelligence sample be based on Shannon's sampling theorem, it points out that the sample rate of signal is not less than twice of highest frequency, signal ability
Accurately reconstructed.The theory dominates the acquisition of nearly all signal, handles, stores and transmits.On the one hand, in many reality
In, such as ultra-wideband communications, nuclear magnetic resonance, space exploration, speed A/D converter etc., information in storage and processing, for up to
A large amount of sampled data is needed to sample rate, it is expensive so as to cause sampling hardware, inefficiency is obtained even certain
Situation is difficult to realize.On the other hand, at the aspect that stores and transmits of data, traditional way is first to obtain according to Nyquist mode
Access evidence, then compresses the data of acquisition, and compressed data are finally carried out storage or transmission.In recent years,
D.Donoho, E.Candes and scientist T.Tao of Chinese origin et al. propose a kind of new acquisition of information theory-compressed sensing.It should
Theory is pointed out: for compressible signal, can be lower than or far below Nyquist criterion by way of data are carried out to it
Sample simultaneously Accurate Reconstruction signal.Unlike Shannon's theorems, compressed sensing is not direct measuring signal itself, it is used
Non-adaptive linear projection obtains the overall construction of signal to directly obtain important information, ignores those in lossy compression
The middle information that can be dropped.
B.Chen, P.Pandey, and D.Pompili propose a kind of distributed sample mode, utilize compressed sensing technology
Ocean temperature field is reconstructed, to realize the preliminary understanding to regional temperature field, Hummel R, Poduri S, Hover F
Stochastical sampling scheme is devised, ocean temperature field is reconfigured quickly in applied compression sensing reconstructing technology.The above research does not all account for
To the characteristic of ocean temperature field, to compressive sensing theory using compared with based on, reconstruction accuracy is not high.It there is no at present for ocean
The data characteristic in temperature field improves the research of the restructing algorithm of compressed sensing.The invention proposes one kind to be based on ASMP threshold value most
Excellent and low-pass filtering seawater temperature field restructing algorithm keeps the estimation of degree of rarefication more accurate, improves by searching for optimal threshold
The reconstruction accuracy in temperature field, simultaneously, it is contemplated that temperature field energy is concentrated mainly on lower frequency region.
Summary of the invention
The present invention is implemented as follows:
It is a kind of based on ASMP threshold value is optimal and the seawater temperature field restructing algorithm of low-pass filtering, include the following steps:
(1) sparse transformation is carried out to the temperature data of acquisition；
(2) carry out the initialization of ASMP algorithm, and run ASMP algorithm: threshold value search range is tmin~tmax, will
Input parameter of the threshold value t as ASMP algorithm reconstructs echo signal using ASMP algorithm；
(3) initiation threshold in refinement threshold search step is determined.
Each iteration ASMP algorithm exports sparse estimation x, remembers that the nonzero element number of rear 1/2 element of x is p, iteration
The minimum value of p is searched in the process and is denoted as pmin；Record reaches p for the first timeminCorresponding ASMP algorithm inputs threshold value tminp, as
Refine the initiation threshold in optimal threshold search step；(3) are repeated until reaching iteration number nfirst_loop, wherein nfirst_loop
It is the number of iterations of (2) setting；
(4) operation ASMP algorithm carries out the search of refinement threshold value, and determines optimal threshold；
(5) it using optimal threshold as input quantity, runs ASMP algorithm and obtains sparse estimation:
By optimal threshold t obtained in (4)bestAs the input parameter of ASMP algorithm, the sparse estimation of output is denoted as xbest
=[x1,x2..., xn]；
(6) moving average filtering processing is carried out to sparse estimation:
Moving average filter is introduced, low-pass filtering is carried out to the sparse estimation of output, high-frequency signal is filtered out, defaults window width
It is 5, the signal after being denoised is denoted as x'best=[x'1,x'2..., x'n]；
(8) remodeling temperature field distribution.
The step (1) specifically includes:
F is the one-dimensional signal that can be sparse that the temperature data obtained is arranged in, wherein f=Ψ x, x ∈ Rn, Ψ=[ψ1,ψ2,
K,ψn]∈Rn×nIt is orthonormal basis, x is projection of the signal f on sparse basis Ψ；The Ψ of the sparse transformation uses DCT
Base, DCT base form are as follows:
Wherein, CnIt is DCT base, n is the dimension of signal f；
Φ=[φ1,φ2,K,φn] it is in RnAnother orthonormal basis on domain is n × n rank unit square；y1,y2,
KymIt is signal f in observation battle array Φ ∈ RnUnder observation yi=< f, φi>；Sampling location point is encoded into the matrix R into m × n rank
In, it is multiplied with unit matrix Φ, obtains the vector y=R Φ f being made of observation.
The step (2) specifically includes:
According to the empirical value of ASMP restructing algorithm threshold value, t is setmin=0.5, tmax=2.5, initial threshold value t=tmin；Repeatedly
For frequency nfirst_loopIt is set as 100 times, each iteration threshold t is with (tmax-tmin)/nfirst_loopAmplitude is incremented by；
(2.1) outer circulation initialization is carried out, sparse estimation and residual error surplus is set: setting sparse estimation x=0, more than residual error
Measure r=y；
(2.2) inner product is calculated, update outer circulation indexed set: inner product is expressed as v=ΦTR, by absolute value ratio in inner product vThe position of big atom is added in outer circulation supported collection, is denoted as Ω, wherein degree of rarefication is estimated as s；
(2.3) loop initialization in carrying out, setting residual error surplus, sparse estimation and interior cycle counter k: setting residual error
Surplus and sparse estimation r(0)=r, x(0)=x, wherein loop iteration counter is k=1, and the value of every carry out an iteration, k increases
Add 1；
(2.4) inner product is calculated, interior loop index collection: inner product u=Φ is updatedTr(k-1), wherein Φ is calculation matrix, r(k-1)
For the residual error surplus of loop iteration in kth -1 time, the position of the preceding s maximum absolute value element of u is added to indexed set, is denoted as
Λ；
(2.5) recycle supported collection in updating, and using least square method update the sparse estimation recycled in kth time iteration and
Residual error surplus: Γ=Λ ∪ q (x(k-1)), wherein q (x(k-1)) be -1 iteration of kth interior circulation supported collection, utilize least square
Method updates the sparse estimation x recycled in kth time iteration(k)With residual error surplus r(k)；
(2.6) judge whether residual error meets the requirements: if the residual error of kth time iteration is more than or equal to the residual of -1 iteration of kth
Difference, i.e., | | r(k)||2≥||r(k-1)||2, then return to (2.2) and rerun, if not satisfied, returning to (2.5)；
(2.7) check whether outer circulation number is up to standard: checking whether and reached largest loop the number of iterations N, if
Reach, then by echo signalAs output quantity, otherwise returns to (2.2) and rerun.
The step (4) specifically includes:
(4.1) search of optimal threshold, the initiation threshold t obtained from (3) are refinedminpStart, threshold value t is with (tmax-tmin)/
(nfirst_loop× 2) amplitude is incremented by；
(4.2) ASMP algorithm is run, sparse estimation x: the iteration j ASMP algorithm input threshold value for exporting reconstruct is tj=
tminp+(tmax-tmin)/(nfirst_loop× 2) j, j < nsecond_loop, wherein tminIt is threshold search model lower limit value, tmaxIt is
Threshold search range higher limit, nfirst_loopIt is the number of iterations of (2) setting, nsecond_loopFor the number of iterations of (4.1) setting；
(4.3) the preceding 1/2 nonzero element number q of nonzero element the number p and x of rear 1/2 element of sparse estimation x,
In p < pminThreshold value t in the range of+3 checks that it corresponds to the q value of the sparse estimation x of reconstruct, and search meets condition p < pmin+ 3 q
Maximum value q in valuemax, qmaxCorresponding threshold value t is exactly the optimal threshold value found, and is denoted as tbest；
(4.4) it checks whether to reach maximum number of iterations nsecond_loop, if so, output optimal threshold tbest, otherwise return
(4.2)；
The step (8) specifically includes:
Each element calculation method is as follows:
x'1=x1；
x'2=(x1+x2+x3)/3；
x'3=(x1+x2+x3+x4+x5)/5；
x'4=(x2+x3+x4+x5+x6)/5；
x'5=(x3+x4+x5+x6+x7)/5；
……
x'n=(xn-2+xn-1+xn+xn+1+xn+2)/5；
Wherein xi' indicate signal x' after denoisingbest=[x'1,x'2..., x'n] in i-th of element, 1≤i≤n.
The step (8) specifically includes:
It reconstructs thermal field distribution and utilizes following calculating formula:
F=Ψ xbest'；
In formula, xbest' it is the sparse estimation of temperature signal after the denoising obtained by (7), it is DCT base that Ψ, which is sparse matrix,
F is the one-dimensional signal of Temperature Distribution.
The present invention has the advantages that
Present invention improves over the inputs of the threshold value of ASMP algorithm to be made subject to the estimation more of degree of rarefication by searching for optimal threshold
Really, the reconstruction accuracy in temperature field is improved, simultaneously, it is contemplated that temperature field energy is concentrated mainly on lower frequency region, therefore using movement
Average filter carries out low-pass filtering, further improves the reconstruction accuracy in temperature field.
Detailed description of the invention
Fig. 1 be the present invention use based on ASMP threshold value is optimal and the process of the seawater temperature field restructing algorithm of low-pass filtering
Figure；
Fig. 2 is the flow chart for the ASMP restructing algorithm that the present invention uses；
Fig. 3 is the flow chart for the optimal restructing algorithm of ASMP threshold value that the present invention uses.
Specific embodiment
Invention is further explained with reference to the accompanying drawing:
It is a kind of based on ASMP threshold value is optimal and the seawater temperature field restructing algorithm of low-pass filtering, as shown in Figure 1, including following
Several steps:
The temperature data that step 1. pair obtains carries out sparse transformation
Being distributed for ocean temperature field has certain Spatial Variability, between the temperature data of spatial distribution mutually solely
It is vertical, and variation is more stable process in temperature data space, and the data value of mutation is less.Therefore, temperature signal energy
It is concentrated mainly on low frequency part, so needing to carry out temperature data approximate sparse processing, is concentrated mainly on nonzero coefficient
On low frequency base.
Consider Ψ=[ψ1,ψ2,K,ψn]∈Rn×nOrthonormal basis, f be the temperature data obtained be arranged in can be sparse
One-dimensional signal, wherein f=Ψ x, x ∈ Rn, x is projection of the signal f on sparse basis Ψ, i.e., sparse estimation.Ψ in the present invention
Using DCT base.DCT base form is as follows:
Wherein, CnIt is DCT base, n is the dimension of signal f.
Φ=[φ1,φ2,K,φn] it is in RnAnother orthonormal basis on domain, y1,y2,KymIt is that signal f is being observed
Battle array Φ ∈ RnUnder observation yi=< f, φi>.It is n × n rank unit matrix that Φ, which is arranged, in the present invention.
Sampling location point is encoded into the matrix R of m × n rank, is multiplied with unit matrix Φ, obtain from observation form to
Measure y=R Φ f.
Step 2. carries out the initialization of ASMP algorithm, and runs ASMP algorithm
Threshold value search range is tmin~tmax, the present invention is according to the empirical value of ASMP restructing algorithm threshold value setting tmin
=0.5, tmax=2.5, initial threshold value t=tmin.Based on experience value, the number of iterations nfirst_loopIt is set as 100 times, every time repeatedly
For threshold value t with (tmax-tmin)/nfirst_loopAmplitude is incremented by.
Using threshold value t as the input parameter of ASMP algorithm, echo signal is reconstructed using ASMP algorithm, if signal is sparse
It is estimated as x, residual error surplus is r, and measurement amount is y, and sensing matrix A=R Φ Ψ, R, Φ, Ψ are the coding square in step 1 respectively
Battle array, calculation matrix and sparse matrix, t are the input threshold values of algorithm, and M is the dimension size of measured value, the i.e. number of sampled point, outside
Circulation maximum number of iterations is N.Specific step is as follows:
Step 2.1. carries out outer circulation initialization, sets sparse estimation x=0, residual error surplus r=y.
Step 2.2. inner product is expressed as v=ΦTR, by absolute value ratio in inner product vThe position of big atom is added to
In outer circulation supported collection, it is denoted as Ω, wherein degree of rarefication is estimated as s.
Step 2.3. carries out interior loop initialization, sets residual error surplus and sparse estimation r(0)=r, x(0)=x, wherein follow
Ring iterative counter is k=1, and the value of every carry out an iteration, k increases by 1.
Step 2.4 calculates inner product u=ΦTr(k-1), wherein Φ is calculation matrix, r(k-1)For loop iteration in kth -1 time
The position of the preceding s maximum absolute value element of u is added to indexed set, is denoted as Λ by residual error surplus.
Step 2.5. recycles supported collection, Γ=Λ ∪ q (x in updating(k-1)), wherein q (x(k-1)) it is -1 iteration of kth
Interior circulation supported collection updates the sparse estimation x recycled in kth time iteration using least square method(k)With residual error surplus r(k)。
Step 2.6. judges whether residual error meets the requirements.If the residual error of kth time iteration is more than or equal to -1 iteration of kth
Residual error, i.e., | | r(k)||2≥||r(k-1)||2, then return to 2.2 and rerun, if not satisfied, returning to 2.5.
Step 2.7. checks whether outer circulation number is up to standard.It checks whether and has reached largest loop the number of iterations N, if
Through reaching, then by echo signalAs output quantity, otherwise returns to 2.2 and rerun.
Step 3. determines the initiation threshold in refinement threshold search step.
In step 2, i-th iteration ASMP algorithm inputs threshold value ti=tmin+(tmax-tmin)/(nfirst_loop) i, (i
< nfirst_loop), wherein tminIt is threshold search lower range limit, tmaxThreshold search range higher limit, the present invention according to
T is arranged in the empirical value of ASMP restructing algorithm threshold valuemin=0.5, tmax=2.5, nfirst_loopIt is the number of iterations that step 2 is arranged.
Each iteration ASMP algorithm exports sparse estimation x, remembers that the nonzero element number of rear 1/2 element of x is p, searches in iterative process
The minimum value of rope p is simultaneously denoted as pmin.Record reaches p for the first timeminCorresponding ASMP algorithm inputs threshold value tminp, optimal as refining
Initiation threshold in threshold search step.Step 3 is repeated until reaching iteration number nfirst_loop。
Step 4. operation ASMP algorithm carries out the search of refinement threshold value, and determines optimal threshold
Step 4.1. refines the search of optimal threshold, based on experience value, the number of iterations nsecond_loopIt is set as 100 times, from
The initiation threshold t that step 3 obtainsminpStart, threshold value t is with (tmax-tmin)/(nfirst_loop× 2) amplitude is incremented by, nfirst_loop
For the number of iterations in step 2, tminFor lower threshold limit value, tmaxUpper threshold limit value.
Step 4.2. runs ASMP algorithm, and it is t that iteration j ASMP algorithm, which inputs threshold value,j=tminp+(tmax-tmin)/
(nfirst_loop× 2) j, (j < nsecond_loop), wherein tminIt is threshold search model lower limit value, tmaxIt is in threshold search range
Limit value, nfirst_loopIt is the number of iterations that step 2 is arranged, nsecond_loopThe number of iterations being arranged for step 4.1.Output reconstruct
Sparse estimation x.ASMP algorithm specific steps are shown in step 2 of the present invention.
Step 4.3. two parameters of consideration, preceding the 1/2 of nonzero element the number p and x of rear 1/2 element of sparse estimation x
Nonzero element number q, in p < pminThreshold value t in the range of+3 checks that it corresponds to the q value of the sparse estimation x of reconstruct, and search is full
Sufficient condition p < pminMaximum value q in+3 q valuemax, qmaxCorresponding threshold value t is exactly the optimal threshold value found, and is denoted as tbest。
Wherein, pminIt is the minimum value that the nonzero element number of rear 1/2 element of sparse estimation x is obtained in step 3.
Step 4.4. checks whether to reach maximum number of iterations nsecond_loop, if so, output optimal threshold tbest, otherwise return
Return step 4.2.
Step 5. runs ASMP algorithm and obtains sparse estimation using optimal threshold as input quantity.
By optimal threshold t obtained in step 4bestAs the input parameter of ASMP algorithm, the sparse estimation of output is denoted as
xbest=[x1,x2..., xn].ASMP algorithm specific steps are shown in step 2 of the present invention.
Step 6. carries out moving average filtering processing to sparse estimation
Moving average filter is introduced, low-pass filtering is carried out to the sparse estimation of output, high-frequency signal is filtered out, defaults window width
It is 5, the signal after being denoised is denoted as x'best=[x'1,x'2..., x'n], wherein each element calculation method is as follows:
x'1=x1
x'2=(x1+x2+x3)/3
x'3=(x1+x2+x3+x4+x5)/5
x'4=(x2+x3+x4+x5+x6)/5
x'5=(x3+x4+x5+x6+x7)/5
……
x'n=(xn-2+xn-1+xn+xn+1+xn+2)/5
Wherein x'iIndicate signal x' after denoisingbest=[x1',x'2..., x'n] in i-th of element, wherein 1≤i≤n.
Step 8. remodeling temperature field distribution
Utilize calculating formula:
F=Ψ xbest'
In formula, xbest' it is the sparse estimation of temperature signal after the denoising obtained by step 7, Ψ is sparse matrix, is DCT
Base, f are the one-dimensional signals of Temperature Distribution.After carrying out two-dimensional transform to one-dimensional signal f, the Two dimensional Distribution of temperature can be obtained.
Claims (6)
1. it is a kind of based on the optimal seawater temperature field restructing algorithm with low-pass filtering of ASMP threshold value, include the following steps:
(1) sparse transformation is carried out to the temperature data of acquisition；
(2) carry out the initialization of ASMP algorithm, and run ASMP algorithm: threshold value search range is tmin~tmax, by threshold value t
As the input parameter of ASMP algorithm, echo signal is reconstructed using ASMP algorithm；
(3) initiation threshold in refinement threshold search step is determined:
Each iteration ASMP algorithm exports sparse estimation x, remembers that the nonzero element number of rear 1/2 element of x is p, iterative process
The minimum value of middle search p is simultaneously denoted as pmin；Record reaches p for the first timeminCorresponding ASMP algorithm inputs threshold value tminp, as refinement
Initiation threshold in optimal threshold search step；(3) are repeated until reaching iteration number nfirst_loop, wherein nfirst_loopIt is (2)
The number of iterations of setting；
(4) operation ASMP algorithm carries out the search of refinement threshold value, and determines optimal threshold；
(5) it using optimal threshold as input quantity, runs ASMP algorithm and obtains sparse estimation:
By optimal threshold t obtained in (4)bestAs the input parameter of ASMP algorithm, the sparse estimation of output is denoted as xbest=
[x1,x2..., xn]；
(6) moving average filtering processing is carried out to sparse estimation:
Moving average filter is introduced, low-pass filtering is carried out to the sparse estimation of output, filters out high-frequency signal, default window width is 5,
Signal after being denoised, is denoted as x'best=[x '1,x′2..., x 'n]；
(8) remodeling temperature field distribution.
2. it is according to claim 1 a kind of based on ASMP threshold value is optimal and the seawater temperature field restructing algorithm of low-pass filtering,
It is characterized in that, the step (1) specifically includes:
F is the one-dimensional signal that can be sparse that the temperature data obtained is arranged in, wherein f=Ψ x, x ∈ Rn, Ψ=[ψ1,ψ2,K,ψn]
∈Rn×nIt is orthonormal basis, x is projection of the signal f on sparse basis Ψ；The Ψ of the sparse transformation uses DCT base, DCT
Base form is as follows:
Wherein, CnIt is DCT base, n is the dimension of signal f；
Φ=[φ1,φ2,K,φn] it is in RnAnother orthonormal basis on domain is n × n rank unit square；y1,y2,KymIt is letter
Number f is in observation battle array Φ ∈ RnUnder observation yi=< f, φi>；Sampling location point is encoded into the matrix R of m × n rank, with list
Position battle array Φ is multiplied, and obtains the vector y=R Φ f being made of observation.
3. it is according to claim 1 a kind of based on ASMP threshold value is optimal and the seawater temperature field restructing algorithm of low-pass filtering,
It is characterized in that, the step (2) specifically includes:
According to the empirical value of ASMP restructing algorithm threshold value, t is setmin=0.5, tmax=2.5, initial threshold value t=tmin；Iteration time
Number nfirst_loopIt is set as 100 times, each iteration threshold t is with (tmax-tmin)/nfirst_loopAmplitude is incremented by；
(2.1) outer circulation initialization is carried out, sparse estimation and residual error surplus is set: setting sparse estimation x=0, residual error surplus r=
y；
(2.2) inner product is calculated, update outer circulation indexed set: inner product is expressed as v=ΦTR, by absolute value ratio in inner product v
The position of big atom is added in outer circulation supported collection, is denoted as Ω, wherein degree of rarefication is estimated as s；
(2.3) loop initialization in carrying out, setting residual error surplus, sparse estimation and interior cycle counter k: setting residual error surplus
With sparse estimation r(0)=r, x(0)=x, wherein loop iteration counter is k=1, and the value of every carry out an iteration, k increases by 1；
(2.4) inner product is calculated, interior loop index collection: inner product u=Φ is updatedTr(k-1), wherein Φ is calculation matrix, r(k-1)It is
The residual error surplus of loop iteration, is added to indexed set for the position of the preceding s maximum absolute value element of u, is denoted as Λ in k-1 times；
(2.5) supported collection is recycled in updating, and the sparse estimation and residual error recycled in kth time iteration is updated using least square method
Surplus: Γ=Λ ∪ q (x(k-1)), wherein q (x(k-1)) be -1 iteration of kth interior circulation supported collection, more using least square method
The sparse estimation x recycled in new kth time iteration(k)With residual error surplus r(k)；
(2.6) judge whether residual error meets the requirements: if the residual error of kth time iteration is more than or equal to the residual error of -1 iteration of kth, i.e.,
||r(k)||2≥||r(k-1)||2, then return to (2.2) and rerun, if not satisfied, returning to (2.5)；
(2.7) check whether outer circulation number is up to standard: checking whether and reached largest loop the number of iterations N, if having reached,
Then by echo signalAs output quantity, otherwise returns to (2.2) and rerun.
4. it is according to claim 1 a kind of based on ASMP threshold value is optimal and the seawater temperature field restructing algorithm of low-pass filtering,
It is characterized in that, the step (4) specifically includes:
(4.1) search of optimal threshold, the initiation threshold t obtained from (3) are refinedminpStart, threshold value t is with (tmax-tmin)/
(nfirst_loop× 2) amplitude is incremented by；
(4.2) ASMP algorithm is run, sparse estimation x: the iteration j ASMP algorithm input threshold value for exporting reconstruct is tj=tminp+
(tmax-tmin)/(nfirst_loop× 2) j, j < nsecond_loop, wherein tminIt is threshold search model lower limit value, tmaxIt is that threshold value is searched
Rope range higher limit, nfirst_loopIt is the number of iterations of (2) setting, nsecond_loopFor the number of iterations of (4.1) setting；
(4.3) it is sparse estimation x rear 1/2 element nonzero element number p and x preceding 1/2 nonzero element number q, p <
pminThreshold value t in the range of+3 checks that it corresponds to the q value of the sparse estimation x of reconstruct, and search meets condition p < pminIn+3 q value
Maximum value qmax, qmaxCorresponding threshold value t is exactly the optimal threshold value found, and is denoted as tbest；
(4.4) it checks whether to reach maximum number of iterations nsecond_loop, if so, output optimal threshold tbest, otherwise return
(4.2)。
5. it is according to claim 1 a kind of based on ASMP threshold value is optimal and the seawater temperature field restructing algorithm of low-pass filtering,
It is characterized in that, the step (8) specifically includes:
Each element calculation method is as follows:
x′1=x1；
x′2=(x1+x2+x3)/3；
x′3=(x1+x2+x3+x4+x5)/5；
x′4=(x2+x3+x4+x5+x6)/5；
x′5=(x3+x4+x5+x6+x7)/5；
……
x′n=(xn-2+xn-1+xn+xn+1+xn+2)/5；
Wherein x 'iIndicate signal x ' after denoisingbest=[x '1,x′2..., x 'n] in i-th of element, 1≤i≤n.
6. it is according to claim 1 a kind of based on ASMP threshold value is optimal and the seawater temperature field restructing algorithm of low-pass filtering,
It is characterized in that, the step (8) specifically includes:
It reconstructs thermal field distribution and utilizes following calculating formula:
F=Ψ xbest'；
In formula, xbest' it is the sparse estimation of temperature signal after the denoising obtained by (7), it is DCT base that Ψ, which is sparse matrix, and f is temperature
Spend the one-dimensional signal of distribution.
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Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102915735A (en) * | 2012-09-21 | 2013-02-06 | 南京邮电大学 | Noise-containing speech signal reconstruction method and noise-containing speech signal device based on compressed sensing |
| CN104333389A (en) * | 2014-10-23 | 2015-02-04 | 湘潭大学 | Adaptive threshold value iterative reconstruction method for distributed compressed sensing |
| CN104574450A (en) * | 2014-12-31 | 2015-04-29 | 南京邮电大学 | Image reconstruction method based on compressed sensing |
| CN106130563A (en) * | 2016-06-17 | 2016-11-16 | 西安电子科技大学 | A kind of threshold value based on compressed sensing signal shrinks iteration difference reconstructing method |
| US20170035301A1 (en) * | 2015-08-04 | 2017-02-09 | General Electric Company | Proton density and t1 weighted zero te mr thermometry |
| CN106485074A (en) * | 2016-10-11 | 2017-03-08 | 哈尔滨工程大学 | A kind of ocean thermohaline quarry sampling method based on adaptive sample rate |
| CN106780636A (en) * | 2016-11-14 | 2017-05-31 | 深圳大学 | The sparse reconstructing method and device of a kind of image |
| CN107492103A (en) * | 2017-07-05 | 2017-12-19 | 上海斐讯数据通信技术有限公司 | Gray threshold acquisition methods, image partition method based on APSO algorithm |
| CN108038149A (en) * | 2017-11-30 | 2018-05-15 | 华东交通大学 | A kind of temperature field data reconstruction method |
| CN108259916A (en) * | 2018-01-22 | 2018-07-06 | 南京邮电大学 | Best match interpolation reconstruction method in frame in a kind of distributed video compressed sensing |
-
2018
- 2018-08-02 CN CN201810869587.8A patent/CN109284671B/en active Active
Patent Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102915735A (en) * | 2012-09-21 | 2013-02-06 | 南京邮电大学 | Noise-containing speech signal reconstruction method and noise-containing speech signal device based on compressed sensing |
| CN104333389A (en) * | 2014-10-23 | 2015-02-04 | 湘潭大学 | Adaptive threshold value iterative reconstruction method for distributed compressed sensing |
| CN104574450A (en) * | 2014-12-31 | 2015-04-29 | 南京邮电大学 | Image reconstruction method based on compressed sensing |
| US20170035301A1 (en) * | 2015-08-04 | 2017-02-09 | General Electric Company | Proton density and t1 weighted zero te mr thermometry |
| CN106130563A (en) * | 2016-06-17 | 2016-11-16 | 西安电子科技大学 | A kind of threshold value based on compressed sensing signal shrinks iteration difference reconstructing method |
| CN106485074A (en) * | 2016-10-11 | 2017-03-08 | 哈尔滨工程大学 | A kind of ocean thermohaline quarry sampling method based on adaptive sample rate |
| CN106780636A (en) * | 2016-11-14 | 2017-05-31 | 深圳大学 | The sparse reconstructing method and device of a kind of image |
| CN107492103A (en) * | 2017-07-05 | 2017-12-19 | 上海斐讯数据通信技术有限公司 | Gray threshold acquisition methods, image partition method based on APSO algorithm |
| CN108038149A (en) * | 2017-11-30 | 2018-05-15 | 华东交通大学 | A kind of temperature field data reconstruction method |
| CN108259916A (en) * | 2018-01-22 | 2018-07-06 | 南京邮电大学 | Best match interpolation reconstruction method in frame in a kind of distributed video compressed sensing |
Non-Patent Citations (4)
| Title |
|---|
| CHANG LIU等: "Optimal Configuration Method of Sampling Points Based on Variability of Sea Surface Temperature", 《ADVANCES IN METEOROLOGY》 * |
| HONGLIN WU等: "Adaptive Sparsity Matching Pursuit Algorithm for Sparse Reconstruction", 《IEEE SIGNAL PROCESSING LETTERS》 * |
| 焦俊等: "基于压缩感知的农田温度信息处理", 《安徽农业科学》 * |
| 郭岩松等: "压缩感知可重构网格的温度分布", 《计算机工程与设计》 * |
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