CN104683649B - A kind of compression of compressed sensing vector geometrical model and restoration methods - Google Patents

A kind of compression of compressed sensing vector geometrical model and restoration methods Download PDF

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CN104683649B
CN104683649B CN201510072633.8A CN201510072633A CN104683649B CN 104683649 B CN104683649 B CN 104683649B CN 201510072633 A CN201510072633 A CN 201510072633A CN 104683649 B CN104683649 B CN 104683649B
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geometrical model
geometry signals
geometry
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CN104683649A (en
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周明全
杜卓明
耿国华
李康
王小凤
张雨禾
张海波
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Northwest University
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Abstract

The invention discloses a kind of compression of compressed sensing vector geometrical model and restoration methods.The present invention is for vector geometrical model in the presence of its Laplace operator, and geological information can be expressed as sparse signal；Employ random matrix to be sampled its geological information, complete compression, recycle the 0 norm fitting function for minimizing sparse signal

Description

A kind of compression of compressed sensing vector geometrical model and restoration methods
Technical field
The invention belongs to computer graphics digital processing field, more particularly to a kind of Fast Compression principle is carried out The compression method of vector geometrical model.The compression purpose of model is reached by efficient sampling techniques, in long-distance transmissions, model Holding, model index dimensionality reduction, etc. computer graphics application field there is important application value.
Background technology
As computer graphics techniques are in the deep application in the fields such as computer animation, video display game, vector geometry The application of model is more and more extensive, dependent on the progress of the technologies for information acquisition such as laser scanning and digital vedio recording, from real world Quick obtaining vector geometric data has become very easy, and user can be reconstructed the geometry of complexity by the high accuracy data obtained Model, by further handling to reuse existing geometrical model, improves geometry designs efficiency.And vector geometrical model remote transmission Core be model compression technology, and also there is very high application valency in the field such as compress technique is stored in model, retrieval dimensionality reduction Value.
Two more classifications of Compression Study are at present：Geometric compression technology (also referred to as spatial compression techniques) and based on signal The technology of compression.Common Geometric compression technology is the model compression technology that summit simplifies, and the technology is according to model vertices coordinate Position, a part of summit is merged, reduction summit quantity is reached, completes the purpose of compression, is meter the characteristics of the technology Calculate speed fast, summit quantity there are much relations with compression effectiveness, but Geometric compression technology changes the topological structure of model, and has Compression is damaged；One group of suitable coordinate base of searching is only required based on compression method, frequency domain decomposition is carried out to model.Itself and geometry Compress technique is compared, and great convenience is brought for a user, most classical is the pressure of LPF based on compression method Model is carried out multi-resolution representation by compression method, this method, and the HFS of model is filtered out using low pass filter, retains it Low frequency part, but its process is relative complex, and lossy compression method.
The content of the invention
For the defect or deficiency of prior art, it is an object of the invention to provide one kind have good compression speed with it is extensive The vector geometrical model compression method of multiple effect, to improve the transfers on network speed of vector geometrical model, and it is empty to reduce its storage Between.
To realize above-mentioned technical assignment, the present invention takes following technical solution：
The geological information of two-dimensional vector geometrical model is by geometry signals x in the method for the present invention2With geometry signals y2Constitute, The geological information of trivector geometrical model is by geometry signals x3, geometry signals y3With geometry signals z3Constitute, method especially by The following steps are realized：
(1) for two-dimensional vector geometrical model：Its Laplace operator n1For the summit sum of two-dimensional vector geometrical model, n1Take positive integer；
For trivector geometrical model：Its Laplace operatorWherein：A is trivector The adjacency matrix of geometrical model, D is the Vertex Degree matrix of trivector geometrical model, and
Wherein：diFor i-th of summit of trivector geometrical model Degree, n2For the summit sum of trivector geometrical model, n2Positive integer is taken with i；
(2) for two-dimensional vector geometrical model：
By the Laplace operator of two-dimensional vector geometrical modelIt is applied to the geometry signals of two-dimensional vector geometrical model x2, obtain vectorial λ '1：
According to the threshold epsilon of setting1, by vectorial λ '1In absolute value be less than ε1Element be entered as 0, obtain geometry signals x2 Sparse geometry signals λ1；
By the Laplace operator of two-dimensional vector geometrical modelIt is applied to the geometry letter of two-dimensional vector geometrical model Number y2, obtain vectorial λ '2：
According to the threshold epsilon of setting2, by vectorial λ '2In absolute value be less than ε2Element be entered as 0, obtain geometry signals y2 Sparse geometry signals λ2；
Wherein：λ1And λ2Dimension be n1, ε1And ε2Meet：λ1And λ2In non-zero element number it is equal；
For trivector geometrical model：
By the Laplace operator of trivector geometrical modelIt is applied to the geometry letter of trivector geometrical model Number x3, obtain vectorial λ '3：
According to the threshold epsilon of setting3, by vectorial λ '3In absolute value be less than ε3Element be entered as 0, obtain geometry signals x3 Sparse geometry signals λ3；
By the Laplace operator of trivector geometrical modelIt is applied to the geometry letter of trivector geometrical model Number y3, obtain vectorial λ '4：
According to the threshold epsilon of setting4, by vectorial λ '4In absolute value be less than ε4Element be entered as 0, obtain geometry signals y3 Sparse geometry signals λ4；
By the Laplace operator of trivector geometrical modelIt is applied to the geometry letter of trivector geometrical model Number z3, obtain vectorial λ '5：
According to the threshold epsilon of setting5, by vectorial λ '5In absolute value be less than ε5Element be entered as 0, obtain geometry signals z3 Sparse geometry signals λ5；
Wherein：λ3、λ4And λ5Dimension be n2, ε3、ε4And ε5Meet：λ3、λ4And λ5In non-zero element number it is equal；
(3) for two-dimensional vector geometrical model：Record sparse geometry signals λ1Or sparse geometry signals λ2In non-zero element Number r1, r1＜ ＜ n1；
For trivector geometrical model：Record sparse geometry signals λ3, sparse geometry signals λ4Or sparse geometry signals λ5 In non-zero element number r2, r2＜ ＜ n2；
Step 2, generation random matrix is sampled to the geological information of vector geometrical model：
For two-dimensional vector geometrical model：
Generate random sampling matrix
UtilizeTo the geometry signals x of two-dimensional vector geometrical model2It is sampled, the signal θ after being sampled1：
UtilizeTo the geometry signals y of two-dimensional vector geometrical model2It is sampled, the signal θ after being sampled2：
Wherein：θ1And θ2Length is 4r1, 4r1＜ ＜ n1, thus complete compression；
For trivector geometrical model：
Generate random sampling matrix
UtilizeTo the geometry signals x of trivector geometrical model3It is sampled, the signal θ after being sampled3,
UtilizeTo the geometry signals y of trivector geometrical model3It is sampled, the signal θ after being sampled4,
UtilizeTo the geometry signals z of trivector geometrical model3It is sampled, the signal θ after being sampled5,Wherein：θ3、θ4And θ5Length is 4r2, 4r2＜ ＜ n2；
And then complete compression；
Step 3, carries out the recovery of model：
For two-dimensional vector geometrical model：
Utilize the fitting function for minimizing sparse signalPass through the signal θ after sampling1 Recover geometry signals x2Sparse geometry signals λ1, hjRepresent λ1J-th of component, j=1,2,3 ..., n1：
Utilize the fitting function for minimizing sparse signalPass through the signal θ after sampling2It is extensive Geometry signals of appearing again y2Sparse geometry signals λ2, hiRepresent λ2I-th of component, i=1,2,3 ..., n1：
Then, the inverse Laplace operator of two-dimensional vector geometrical model is utilizedAnd λ1Recover original geometry signals x2：
Utilize the inverse Laplace operator of two-dimensional vector geometrical modelAnd λ2Recover original geometry signals y2：
For trivector geometrical model：
Utilize the fitting function for minimizing sparse signalPass through the signal θ after sampling3 Recover geometry signals x3Sparse geometry signals λ3, hmRepresent λ3M-th of component, m=1,2,3 ..., n2：
Utilize the fitting function for minimizing sparse signalPass through the signal θ after sampling4 Recover geometry signals y3Sparse geometry signals λ4, hpRepresent λ4P-th of component, p=1,2,3 ..., n2：
Utilize the fitting function for minimizing sparse signalPass through the signal θ after sampling5 Recover geometry signals z3Sparse geometry signals λ5, hqRepresent λ5Q-th of component, q=1,2,3 ..., n2：
Then, the inverse Laplace operator of trivector geometrical model is utilizedWith sparse geometry signals λ3Recover Original geometry signals x3：
Utilize the inverse Laplace operator of trivector geometrical modelWith sparse geometry signals λ4Recover original Geometry signals y3：
Utilize the inverse Laplace operator of trivector geometrical modelWith sparse geometry signals λ5Recover original Geometry signals z3：
Optionally, formula (1) solution procedure is to convert thereof into unconstrained optimization：
In formula (6)：
It is Ψ 0 orthogonal space Base,It is n1-4r1The free vector of dimension；
A is n1Dimensional vector, a1a2…It is real number；
For n1×(n1-4r1) size matrix, v1v2…It is n1-4r1The row of dimension to Amount；
Formula (6) solution procedure is as follows：
Initial value
Step1, is calculatedK is 0 and natural number, δ=10-3；
Step2, as r ＞ 0, withAs the direction of search, I is identity matrix,
When r≤0, withAs the direction of search,
Step3, ifWhen,Otherwise it is transferred to Step1。
The present invention is for vector geometrical model in the presence of its Laplace operator, and geological information can be expressed as dilute Dredge signal；Employ random matrix to be sampled its geological information, complete compression, recycle the 0- models for minimizing sparse signal Number fitting functionThe sparse signal of original signal is recovered, and then recovers primary signal, is completed The compression and recovery of model.In recovery process, constrained optimization is converted into unconstrained optimization, and devise new searcher To being solved.The method of the present invention is the compression speed for accelerating model, and theoretic Lossless Compression is realized again.Actual behaviour Recovery effects can be controlled according to the accuracy requirement of user in work.
Brief description of the drawings
Fig. 1 (a) is the archetype figure of the two-dimensional vector geometrical model of embodiment 1；Fig. 1 (b) is that the two-dimensional vector of embodiment 1 is several Recovery effects figure after what model compression；
Fig. 2 (a) is the archetype figure of the two-dimensional vector geometrical model of embodiment 2；Fig. 2 (b) is that the two-dimensional vector of embodiment 2 is several Recovery effects figure after what model compression.
The invention will be further described with accompanying drawing with reference to embodiments.
Embodiment
The basic conception of the present invention is only to improve compression speed using the compression of sparse matrix one step of sampling, and using most The method for optimizing 1 norm recovers the sparse expression of original geometry signal, finally completes geometry signals using inverse Laplace operator Recovery.Compression speed, and Lossless Compression in theory can so be accelerated.
The specific embodiment provided the following is inventor is, it is necessary to which explanation, the embodiment provided is to the present invention Further explain, protection scope of the present invention is not limited to given embodiment.
Embodiment 1：
The embodiment is that two-dimensional vector geometrical model (shown in such as Fig. 1 (a)) is compressed, the two-dimensional vector geometrical model Geological information by geometry signals x2With geometry signals y2Constitute, specific method is as follows：
(1) for the two-dimensional vector geometrical model：Its Laplace operatorn1For the summit sum of two-dimensional vector geometrical model, n1=896；
(2) by the Laplace operator of two-dimensional vector geometrical modelIt is applied to the geometry of two-dimensional vector geometrical model Signal x2Obtain vectorial λ '1：
According to the threshold epsilon of setting1, by vectorial λ1' in absolute value be less than ε1Element be entered as 0, obtain geometry signals x2 Sparse geometry signals λ1；
By the Laplace operator of two-dimensional vector geometrical modelIt is applied to the geometry letter of two-dimensional vector geometrical model Number y2Obtain vectorial λ '2：
According to the threshold epsilon of setting2, by vectorial λ '2In absolute value be less than ε2Element be entered as 0, obtain geometry signals y2 Sparse geometry signals λ2；
Wherein：λ1And λ2Dimension be n1, ε1And ε2Meet：λ1And λ2In non-zero element number it is equal, ε1=0.17, ε2=0.15；
(3) sparse geometry signals λ is recorded1Or sparse geometry signals λ2In non-zero element number r1, r1＜ ＜ n1；
Step 2, generation random matrix is sampled to the geological information of vector geometrical model：
Generate random sampling matrix
UtilizeTo the geometry signals x of two-dimensional vector geometrical model2It is sampled, the signal θ after being sampled1,
UtilizeTo the geometry signals y of two-dimensional vector geometrical model2It is sampled, the signal θ after being sampled2,Wherein：θ1And θ2Length is 4r1, 4r1＜ ＜ n1；And then complete compression；
Step 3, carries out the recovery of model：
Utilize the fitting function for minimizing sparse signalPass through the signal θ after sampling1 Recover geometry signals x2Sparse geometry signals λ1, hjRepresent λ1J-th of component, j=1,2,3 ..., n1：
Utilize the fitting function for minimizing sparse signalPass through the signal θ after sampling2It is extensive Geometry signals of appearing again y2Sparse geometry signals λ2, hiRepresent λ2I-th of component, i=1,2,3 ..., n1：
Then, the inverse Laplace operator of two-dimensional vector geometrical model is utilizedAnd λ1Recover original geometry signals x2：
Utilize the inverse Laplace operator of two-dimensional vector geometrical modelAnd λ2Recover original geometry signals y2：
Formula (1) solution procedure is to convert thereof into unconstrained optimization：
In formula (6)：
Using SVD,It is Ψ 0 sky Between orthogonal basis,It is n1-4r1The free vector of dimension；
A is n1Dimensional vector, a1a2…It is real number；
For n1×(n1-4r1) size matrix, v1v2…It is n1-4r1The row of dimension to Amount；
(formula 6) solution procedure is as follows：
Initial value
Step1, is calculatedK is 0 and natural number, δ=10-3；
Step2, as r ＞ 0, withAs the direction of search, I is identity matrix,
When r≤0, withAs the direction of search,
Step3, ifWhen,Otherwise it is transferred to Step1。
The solution procedure of (formula 2) is with (formula 1)；Shown in the model recovered such as Fig. 1 (b).
Used in above-mentioned stepsOrProcess is sampled to vector geometrical model geometry signals In, random sampling matrix is adjusted according to the degree of rarefactionOr matrixLine number.
Embodiment 2：
The embodiment is that trivector geometrical model (shown in such as Fig. 2 (a)) is compressed, the trivector geometrical model Geological information by geometry signals x3, geometry signals y3With geometry signals z3Constitute, method is realized especially by the following steps：
(1) for the trivector geometrical model：Its Laplace operatorWherein：A is three-dimensional The adjacency matrix of vector geometrical model, D is the Vertex Degree matrix of trivector geometrical model, and
Wherein：diFor i-th of summit of trivector geometrical model Degree, n2For the summit sum of trivector geometrical model, n2Positive integer, n are taken with i2=7609, can be according to read model Topological structure, A and D are can determine that according to figure connection theory,
(2) by the Laplace operator of trivector geometrical modelIt is applied to the geometry of trivector geometrical model Signal x3, obtain vectorial λ '3：
According to the threshold epsilon of setting3, by vectorial λ '3In absolute value be less than ε3Element be entered as 0, obtain geometry signals x3 Sparse geometry signals λ3；
By the Laplace operator of trivector geometrical modelIt is applied to the geometry letter of trivector geometrical model Number y3Obtain vectorial λ '4：
According to the threshold epsilon of setting4, by vectorial λ '4In absolute value be less than ε4Element be entered as 0, obtain geometry signals y3 Sparse geometry signals λ4；
By the Laplace operator of trivector geometrical modelIt is applied to the geometry letter of trivector geometrical model Number z3Obtain vectorial λ '5：
According to the threshold epsilon of setting5, by vectorial λ5' in absolute value be less than ε5Element be entered as 0 and obtain geometry signals z3 Sparse geometry signals λ5；
Wherein：λ3、λ4And λ5Dimension be n2, to meet λ3、λ4And λ5In non-zero element number it is equal, ε3= 0.0073465,ε4=0.04653, ε5=0.0045784；
(3) for trivector geometrical model：Record sparse geometry signals λ3, sparse geometry signals λ4Or sparse geometry letter Number λ5In non-zero element number r2, r2＜ ＜ n2；
Step 2, generation random matrix is sampled to the geological information of vector geometrical model：
Generate random sampling matrix
UtilizeTo the geometry signals x of trivector geometrical model3It is sampled, the signal θ after being sampled3,
UtilizeTo the geometry signals y of trivector geometrical model3It is sampled, the signal θ after being sampled4,
UtilizeTo the geometry signals z of trivector geometrical model3It is sampled, the signal θ after being sampled5,Wherein：θ3、θ4And θ5Length is 4r2, 4r2＜ ＜ n2, and then complete compression；
Step 3, carries out the recovery of model：
Utilize the fitting function for minimizing sparse signalPass through the signal θ after sampling3 Recover geometry signals x3Sparse geometry signals λ3, hmRepresent λ3M-th of component, m=1,2,3 ..., n2：
Utilize the fitting function for minimizing sparse signalPass through the signal θ after sampling4 Recover geometry signals y3Sparse geometry signals λ4, hpRepresent λ4P-th of component, p=1,2,3 ..., n2：
Utilize the fitting function for minimizing sparse signalPass through the signal θ after sampling5 Recover geometry signals z3Sparse geometry signals λ5, hqRepresent λ5Q-th of component, q=1,2,3 ..., n2：
Then, the inverse Laplace operator of trivector geometrical model is utilizedWith sparse geometry signals λ3Recover Original geometry signals x3：
Utilize the inverse Laplace operator of trivector geometrical modelWith sparse geometry signals λ4Recover original Geometry signals y3：
Utilize the inverse Laplace operator of trivector geometrical modelWith sparse geometry signals λ5Recover original Geometry signals z3：
The solution procedure of the same formula of solution procedure (1) of formula (3), formula (4) and formula (5)；The model recovered such as Fig. 2 (b) institutes Show.

Claims (2)

1. the geometry of two-dimensional vector geometrical model in compression and the restoration methods of a kind of compressed sensing vector geometrical model, this method Information is by geometry signals x2With geometry signals y2Constitute, the geological information of trivector geometrical model is by geometry signals x3, geometry letter Number y3With geometry signals z3Constitute, method is realized especially by the following steps：
(1) for two-dimensional vector geometrical model：Its Laplace operatorn1For two The summit sum of n dimensional vector n geometrical model, n1Take positive integer；
For trivector geometrical model：Its Laplace operatorWherein：A is trivector geometry The adjacency matrix of model, D is the Vertex Degree matrix of trivector geometrical model, and
Wherein：diFor i-th summit of trivector geometrical model Degree, n2For the summit sum of trivector geometrical model, n2Positive integer is taken with i；
(2) for two-dimensional vector geometrical model：
By the Laplace operator of two-dimensional vector geometrical modelIt is applied to the geometry signals x of two-dimensional vector geometrical model2, obtain To vectorial λ '1：
<mrow> <msubsup> <mi>&amp;lambda;</mi> <mn>1</mn> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>L</mi> <mrow> <msub> <mi>n</mi> <mn>1</mn> </msub> <mo>&amp;times;</mo> <msub> <mi>n</mi> <mn>1</mn> </msub> </mrow> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>;</mo> </mrow>
According to the threshold epsilon of setting1, by vectorial λ '1In absolute value be less than ε1Element be entered as 0, obtain geometry signals x2It is dilute Dredge geometry signals λ1；
By the Laplace operator of two-dimensional vector geometrical modelIt is applied to the geometry signals y of two-dimensional vector geometrical model2, Obtain vectorial λ '2：
<mrow> <msubsup> <mi>&amp;lambda;</mi> <mn>2</mn> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>L</mi> <mrow> <msub> <mi>n</mi> <mn>1</mn> </msub> <mo>&amp;times;</mo> <msub> <mi>n</mi> <mn>1</mn> </msub> </mrow> </msub> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>;</mo> </mrow>
According to the threshold epsilon of setting2, by vectorial λ '2In absolute value be less than ε2Element be entered as 0, obtain geometry signals y2It is dilute Dredge geometry signals λ2；
Wherein：λ1And λ2Dimension be n1, ε1And ε2Meet：λ1And λ2In non-zero element number it is equal；
For trivector geometrical model：
By the Laplace operator of trivector geometrical modelIt is applied to the geometry signals x of trivector geometrical model3, Obtain vectorial λ '3：
<mrow> <msubsup> <mi>&amp;lambda;</mi> <mn>3</mn> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>L</mi> <mrow> <msub> <mi>n</mi> <mn>2</mn> </msub> <mo>&amp;times;</mo> <msub> <mi>n</mi> <mn>2</mn> </msub> </mrow> </msub> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>;</mo> </mrow>
According to the threshold epsilon of setting3, by vectorial λ '3In absolute value be less than ε3Element be entered as 0, obtain geometry signals x3It is dilute Dredge geometry signals λ3；
By the Laplace operator of trivector geometrical modelIt is applied to the geometry signals y of trivector geometrical model3, Obtain vectorial λ '4：
<mrow> <msubsup> <mi>&amp;lambda;</mi> <mn>4</mn> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>L</mi> <mrow> <msub> <mi>n</mi> <mn>2</mn> </msub> <mo>&amp;times;</mo> <msub> <mi>n</mi> <mn>2</mn> </msub> </mrow> </msub> <msub> <mi>y</mi> <mn>3</mn> </msub> <mo>;</mo> </mrow>
According to the threshold epsilon of setting4, by vectorial λ '4In absolute value be less than ε4Element be entered as 0, obtain geometry signals y3It is dilute Dredge geometry signals λ4；
By the Laplace operator of trivector geometrical modelIt is applied to the geometry signals z of trivector geometrical model3, Obtain vectorial λ '5：
<mrow> <msubsup> <mi>&amp;lambda;</mi> <mn>5</mn> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>L</mi> <mrow> <msub> <mi>n</mi> <mn>2</mn> </msub> <mo>&amp;times;</mo> <msub> <mi>n</mi> <mn>2</mn> </msub> </mrow> </msub> <msub> <mi>z</mi> <mn>3</mn> </msub> <mo>;</mo> </mrow>
According to the threshold epsilon of setting5, by vectorial λ '5In absolute value be less than ε5Element be entered as 0, obtain geometry signals z3It is dilute Dredge geometry signals λ5；
Wherein：λ3、λ4And λ5Dimension be n2, ε3、ε4And ε5Meet：λ3、λ4And λ5In non-zero element number it is equal；
(3) for two-dimensional vector geometrical model：Record sparse geometry signals λ1Or sparse geometry signals λ2In non-zero element Number r1, r1＜ ＜ n1；
For trivector geometrical model：Record sparse geometry signals λ3, sparse geometry signals λ4Or sparse geometry signals λ5In The number r of non-zero element2, r2＜ ＜ n2；
(4) generation random matrix is sampled to the geological information of vector geometrical model：
For two-dimensional vector geometrical model：
Generate random sampling matrix
UtilizeTo the geometry signals x of two-dimensional vector geometrical model2It is sampled, the signal θ after being sampled1：
UtilizeTo the geometry signals y of two-dimensional vector geometrical model2It is sampled, the signal θ after being sampled2：
Wherein：θ1And θ2Length is 4r1, 4r1＜ ＜ n1, thus complete compression；
For trivector geometrical model：
Generate random sampling matrix
UtilizeTo the geometry signals x of trivector geometrical model3It is sampled, the signal θ after being sampled3,
UtilizeTo the geometry signals y of trivector geometrical model3It is sampled, the signal θ after being sampled4,
UtilizeTo the geometry signals z of trivector geometrical model3It is sampled, the signal θ after being sampled5,Wherein：θ3、θ4And θ5Length is 4r2, 4r2＜ ＜ n2；
And then complete compression；
(5) recovery of model is carried out：
For two-dimensional vector geometrical model：
Utilize the fitting function for minimizing sparse signalPass through the signal θ after sampling1Recover Go out geometry signals x2Sparse geometry signals λ1, hjRepresent λ1J-th of component, j=1,2,3 ..., n1：
Utilize the fitting function for minimizing sparse signalPass through the signal θ after sampling2Recover Geometry signals y2Sparse geometry signals λ2, hiRepresent λ2I-th of component, i=1,2,3 ..., n1：
Then, the inverse Laplace operator of two-dimensional vector geometrical model is utilizedAnd λ1Recover original geometry signals x2：
<mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>=</mo> <msup> <msub> <mi>L</mi> <mrow> <msub> <mi>n</mi> <mn>1</mn> </msub> <mo>&amp;times;</mo> <msub> <mi>n</mi> <mn>1</mn> </msub> </mrow> </msub> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>&amp;lambda;</mi> <mn>1</mn> </msub> <mo>;</mo> </mrow>
Utilize the inverse Laplace operator of two-dimensional vector geometrical modelAnd λ2Recover original geometry signals y2：
<mrow> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>=</mo> <msup> <msub> <mi>L</mi> <mrow> <msub> <mi>n</mi> <mn>1</mn> </msub> <mo>&amp;times;</mo> <msub> <mi>n</mi> <mn>1</mn> </msub> </mrow> </msub> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>&amp;lambda;</mi> <mn>2</mn> </msub> <mo>;</mo> </mrow>
For trivector geometrical model：
Utilize the fitting function for minimizing sparse signalPass through the signal θ after sampling3Recover Geometry signals x3Sparse geometry signals λ3, hmRepresent λ3M-th of component, m=1,2,3 ..., n2：
Utilize the fitting function for minimizing sparse signalPass through the signal θ after sampling4Recover Go out geometry signals y3Sparse geometry signals λ4, hpRepresent λ4P-th of component, p=1,2,3 ..., n2：
Utilize the fitting function for minimizing sparse signalPass through the signal θ after sampling5Recover Go out geometry signals z3Sparse geometry signals λ5, hqRepresent λ5Q-th of component, q=1,2,3 ..., n2：
Then, the inverse Laplace operator of trivector geometrical model is utilizedWith sparse geometry signals λ3Recover original Geometry signals x3：
<mrow> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>=</mo> <msup> <msub> <mi>L</mi> <mrow> <msub> <mi>n</mi> <mn>2</mn> </msub> <mo>&amp;times;</mo> <msub> <mi>n</mi> <mn>2</mn> </msub> </mrow> </msub> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>&amp;lambda;</mi> <mn>3</mn> </msub> <mo>;</mo> </mrow>
Utilize the inverse Laplace operator of trivector geometrical modelWith sparse geometry signals λ4Recover original geometry Signal y3：
<mrow> <msub> <mi>y</mi> <mn>3</mn> </msub> <mo>=</mo> <msup> <msub> <mi>L</mi> <mrow> <msub> <mi>n</mi> <mn>2</mn> </msub> <mo>&amp;times;</mo> <msub> <mi>n</mi> <mn>2</mn> </msub> </mrow> </msub> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>&amp;lambda;</mi> <mn>4</mn> </msub> <mo>;</mo> </mrow>
Utilize the inverse Laplace operator of trivector geometrical modelWith sparse geometry signals λ5Recover original geometry Signal z3：
<mrow> <msub> <mi>z</mi> <mn>3</mn> </msub> <mo>=</mo> <msup> <msub> <mi>L</mi> <mrow> <msub> <mi>n</mi> <mn>2</mn> </msub> <mo>&amp;times;</mo> <msub> <mi>n</mi> <mn>2</mn> </msub> </mrow> </msub> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>&amp;lambda;</mi> <mn>5</mn> </msub> <mo>.</mo> </mrow>
2. compression and the restoration methods of compressed sensing vector geometrical model as claimed in claim 1, it is characterised in that
(formula 1) solution procedure is to convert thereof into unconstrained optimization：
In formula (6)：
It is Ψ 0 orthogonal space base,It is n1-4r1The free vector of dimension；
A is n1Dimensional vector,It is real number；
For n1×(n1-4r1) size matrix,It is n1-4r1The row of dimension Vector；
Formula (6) solution procedure is as follows：
Initial value
Step1, is calculatedK is 0 and natural number, δ=10-3；
Step2, as r ＞ 0, withAs the direction of search, I is identity matrix,
When r≤0, withAs the direction of search,
Step3, ifWhen,Otherwise it is transferred to Step1。
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101232625A (en) * 2008-02-26 2008-07-30 吉林大学 High efficient multidimensional video stream encoding and decoding method
EP2157791A2 (en) * 2008-08-19 2010-02-24 Broadcom Corporation Method and system for motion-compensated frame-rate up-conversion for both compressed and decompressed video bitstreams
CN102665027A (en) * 2012-04-20 2012-09-12 西北大学 Geometrical vector model compressing method

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101232625A (en) * 2008-02-26 2008-07-30 吉林大学 High efficient multidimensional video stream encoding and decoding method
EP2157791A2 (en) * 2008-08-19 2010-02-24 Broadcom Corporation Method and system for motion-compensated frame-rate up-conversion for both compressed and decompressed video bitstreams
CN102665027A (en) * 2012-04-20 2012-09-12 西北大学 Geometrical vector model compressing method

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
基于图形矢量模式的图像几何信息压缩方法;李翠芳 等;《计算机系统应用 》;20091215(第12期);全文 *
文再文.压缩感知和稀疏优化简介.《运筹学学报》.2012,第16卷(第3期), *
杜卓明 等.一种压缩感知信号的快速恢复方法.《计算机辅助设计与图形学学报》.2014,第26卷(第12期), *

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