CN107895063A - One kind compression EO-1 hyperion mask optimization method - Google Patents
One kind compression EO-1 hyperion mask optimization method Download PDFInfo
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- 238000009795 derivation Methods 0.000 claims description 8
- 238000011478 gradient descent method Methods 0.000 claims description 5
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- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
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- G01J3/0205—Optical elements not provided otherwise, e.g. optical manifolds, diffusers, windows
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- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
- G01J3/28—Investigating the spectrum
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- G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
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Abstract
The invention discloses one kind to compress EO-1 hyperion mask optimization method.Step of the present invention is as follows：Step (1) utilizes geometric optics by the position of mask in systems, obtains initial projections matrix P0, P0It is the matrix of a p × n in real number field, i.e.,Initial cycle iteration count variable q=0 is set；Step (2) is by matrix PqD enters ranks standardization, obtains effectively dictionaryStep (3) constructs Gram matrixesStep (4) shrinks Gram matrixes Gq, that is, update Gram matrixes：Step (5) is decomposed the Gram matrixes after contraction using SVDOrder be reduced to p；Step (6) solves Gram matrixesSquare root SqSo thatStep (7) finds Pq+1So that errorMinimum, q=q+1.The property consistent with each other of mask after present invention optimization is significantly lower than the property consistent with each other of random mask, and the signal to noise ratio of reconstruction image is also significantly improved.
Description
Technical field
The present invention relates to high light spectrum image-forming technology and the optimization of compression EO-1 hyperion mask, more particularly to applied compression height
During light spectrum image-forming, there is provided one kind compression EO-1 hyperion mask optimization method.
Background technology
High light spectrum image-forming is the big study hotspot of current one.How to realize quick hyper-spectral data gathering be all the time one urgently
Solve the problems, such as.Herein, mainly in the method that mask realization compression high light spectrum image-forming is placed before sensor, carry out
Further optimization and expansion.Learned on relevant knowledge and matrix class with reference to optimization projection matrix including matrix differential, projection
The related contents such as analysis realize the optimization of mask for the practical problem.
High light spectrum image-forming technology is to be combined traditional two-dimensional imaging technique with spectral technique, from ultraviolet to near-infrared
In spectral region, using imaging spectrometer, the tens of or hundreds of spectral bands in spectral coverage connect to target object
Continuous imaging, while object space characteristic imaging is obtained, also obtain the spectral information of testee, remote sensing, monitor with
And there is important application in the extensive field such as spectroscopy.The most important task of high light spectrum image-forming is exactly effectively to collect one
The three-dimensional data cube changed by two-dimensional space and one-dimensional spectral space.The most frequently used method be using mechanical scanning or when
The method of sequence scanning once records one or several data points.The method of snapshot imaging is by once independent imaging acquisition to completely
Three-dimensional data, this has obvious advantage gathering dynamic scene or method when taking photo by plane than scanning.Snapshot imaging is logical
Cross and realize higher-dimension signal multiplexing to two-dimensional CCD sensor, therefore sacrifice image resolution ratio.The sample of snapshot imaging method
Including four-dimensional imaging spectrometer (4DIS) and computed tomography imaging spectrometer (CTIS) etc..A kind of coding aperture is fast recently
Irradiation spectrometer (CASSI) is rebuild come coded light signal by computation compression.This calculating imaging method can overcome acquisition
Aerial image and light spectrum image-forming resolution ratio compromise.What CASSI systems can constantly be overturn by collection in piezoelectric working platform
Repeatedly imaging is improved corresponding to encoding mask.A kind of more flexible selection is to utilize DMD (DMD) continuous shooting
Spectrum imaging system (DMD-SSI).The trend for rebuilding data has been calculated very by compressing by optical encoding record data
Substantially, but during the method encoded colors of all compressed spectrums imaging be all based on space uniform it is assumed that this is substantially limited
The quality of compression algorithm for reconstructing with compression compression sparsity constraints.Passed so we propose in work before
Mask coding is placed before sensor, realizes the inconsistent modulation in space, and obtaining needs to do after the inconsistent modulation in space
Be exactly to carry out sparse reconstruction.How so that the information collected is how to optimize projection matrix most beneficial for sparse reconstruction
The problem of.And for compressing high light spectrum image-forming, this problem was not studied in detail all the time.So we are high in compression
On the basis of light spectrum image-forming, the relevant knowledge of matrix analysis, including matrix differential, Projection Analysis, matrix decomposition are further utilized
Knowledge, propose a kind of optimized algorithm of mask, the optimization of mask realized with this so that reconstructed results reach best.For
Checking proposes the feasibility of optimized algorithm, and We conducted some l-G simulation tests to prove and show the optimization of algorithm effect
Fruit.
The content of the invention
The technical problems to be solved by the invention are：In order that the information that must be collected most beneficial for it is sparse rebuild, it is necessary to
A kind of evaluation criterion for judging that projection matrix is good and bad in compression high light spectrum image-forming is determined, and based on this, passes through proposition
Mask optimized algorithm improves the purpose of sparse reconstruction quality to realize.
Mask is the vector of one 100 × 1 in the present invention, and the projection matrix P of one 3100 × 100 is constructed by it.
For the above-mentioned purpose, the object applied first is spectrum camera, and compared with general camera, spectrum camera is in image planes position
Put and placed one block of grating to produce multispectral camera, be equivalent to the spectral information of scene being mapped to the different angles of image planes
At the emergent ray of degree, i.e. the angle dimension of light field.We are it needs to be determined that one of irrelevance of a measurement matrix first
Standard, that we select here is the most commonly used μtTo be weighed.
The present invention solves the target for the technical scheme present invention that its technical problem uses:Minimize μt(PD)
The parameter of input is as follows:
t:Degree of correlation threshold value
n:Cross complete dictionary
p:Pendulous frequency
γ:Degree of correlation threshold value
Iter:Iterations
The target of the present invention:Minimize μt(PD)
The parameter of input is as follows:
t:Degree of correlation threshold value
n:Cross complete dictionary
p:Pendulous frequency
γ:Degree of correlation threshold value
P：Projection matrix, by the array between 100 × 10 to 1 into.
D：The excessively complete dictionary obtained by dictionary learning, size are 3100 × 387.
Iter:Iterations
It is as follows to implement step：
Step (1) utilizes geometric optics by the position of mask in systems, obtains initial projections matrix P0, P0It is real number
P × n matrix on domain, i.e.,Initial cycle iteration count variable q=0 is set；
Described initial projections matrix P0Derivation it is as follows：
The null matrix of one 100 × 100 is constructed first；
Then the diagonal entry using 100 numbers of mask as the null matrix, and surface element stores shape on diagonal
Formula is symbolic variable form.By this 100 × 100 reproduction matrix 31 times, 3100 × 100 matrix, i.e. projection matrix are formed
P0.Element is identical on diagonal wherein in this 31 100 × 100 matrix, but element sequence is different, has on position
Translation.This 3100 × 100 matrix is exactly the projection matrix P that we construct0。
Step (2) is by matrix PqD enters ranks standardization, obtains effectively dictionary
Described standardization is exactly by matrix PqD each row normalization is unit vector so that its each column vector
Modulus value is one, wherein PqRepresent to circulate obtained projection matrix P the q times；
Step (3) constructs Gram matrixes
That is effectively dictionaryTransposition and itself be multiplied construction Gram matrixes.
Step (4) shrinks Gram matrixes Gq, i.e., update Gram matrixes using formula (1)：
Wherein：gijRepresent the element that the i-th row jth arranges in Gram matrixes；Represent new after formula (1) conversion
Value；
Step (5) is decomposed the Gram matrixes after contraction using SVDOrder be reduced to p, specifically：
ByUnderstand, due to unusual value-based algorithm obtain Σ matrix diagonals members be it is non-negative, therefore V and
U matrix columns vector may differ sign, and because U, V vector are that unit is orthogonal, matrix also only has in actual calculating
The negative semidefinite member of only a few, therefore directly calculated using absolute value, that is, utilize V Σ UTTo ask for the flat of Gram matrixes
Root.
Step (6) solves Gram matrixesSquare root SqSo thatWherein
Step (7) finds the q+1 times and circulates obtained projection matrix Pq+1So that errorMinimum, q=q+1.
Asked for using gradient descent methodProblem, detailed calculating process are as follows：
7-1.Definition be calculate：
Minimize
tr(Sq TSq-Sq TPD-DTPTSq+DTPTPD) (3)
Using Matrix Calculating trace property, former formula can be changed to
F (x)=tr (Sq TSq-2DTPTSq+DTPTPD) (4)
Further gradient is asked to obtain
Using substep differential formulas, according to the property of the generation projection matrix of mask before, it becomes possible to obtained from formula (5)
It is directed to the Grad of each unknown mask variable.
F (x) is a function on projection matrix P, but projection matrix P is formed by 100 × 1 mask configuration
3100 × 100 size two-dimensional matrixs, the inside variable only have 100, and other elements are 0, it is also necessary to ensure the element holding for 0
It is constant.Therefore, directly cannot to projection matrix P derivations.For this in MATLAB, 100 variables therein are distinguished
Symbolic variable is defined as, function f (x) is allowed in MATLAB to this 100 sign function derivations, it is direct to bypass in this way
The problem of being brought to projection matrix P derivations.
Step (8) repeat step (2) arrives step (7) Iter times, the projection matrix P after output optimizationiter.Due to operation side
Formula is fixed, therefore threshold value t is the definite value of setting.
Beneficial effects of the present invention：
Method of the present invention only need to be by optimizing to mask so that and the property consistent with each other of projection matrix reduces,
To realize the more rarefaction of projection matrix, beneficial to reconstruction.The simulation experiment result shows, is covered at random compared to usually used
Film, the property consistent with each other of the mask after optimization are significantly lower than the property consistent with each other of random mask, and the signal to noise ratio of reconstruction image is also bright
It is aobvious to be improved.
Brief description of the drawings
Fig. 1 is flow chart of the present invention；
Fig. 2 is projection matrix P of the present invention property convergence curves consistent with each other.
Embodiment
Below in conjunction with drawings and Examples, the present invention is described in further detail.
As shown in Figure 1-2, a kind of compression EO-1 hyperion mask optimized algorithm proposed by the present invention, projection is reduced by algorithm
The property size consistent with each other of matrix, to obtain more sparse projection matrix.The method of the invention comprises the following steps：
Step (1) utilizes geometric optics by the position of mask in systems, is derived by projection matrix
Loop iteration counting variable q=0 is set, it is common Iter times to step 7 to repeat step 2.Due to mode of operation be it is fixed, because
This threshold value t is the definite value of setting.
Step (2) is by matrix PqD enters ranks standardization, obtains effectively dictionaryHere the method standardized is exactly will
Matrix PqD each row normalization is unit vector so that the modulus value of its each column vector is one.
Step (3) calculates Gram matrixesHere we use matrix correlation knowledge, allow effectively dictionaryTransposition and itself be multiplied construction Gram matrixes.
Step (4) shrinks matrix, updates Gram matrixes using formula once：
Here the purpose done so is to shrink Gram matrixes to allow matrix to be easier to restrain.
Step (5) is decomposed the Gram matrixes after contraction using SVDOrder be reduced to p.ByUnderstand,
Because the Σ matrix diagonals members that unusual value-based algorithm obtains are non-negative, therefore V and U matrix columns vector may differ positive and negative
Number, because U, V vector are that unit is orthogonal, it is actual calculate in matrix also only have the negative semidefinite member of only a few, therefore here I
Directly calculated using absolute value, that is, utilize V Σ UTTo ask for the square root of Gram matrixes, results of calculation shows
Show, for the error under this problem two norm meanings caused by such 1 or so.
Step (6) solves Gram matrixesSquare root SqSo thatWhereinHere we
IfSo doing can be by sacrificing limited more solving precisions, to ensure the solving speed of algorithm.
Step (7) finds Pq+1So that errorMinimum, q=q+1.Asking forDuring problem
We have attempted gradient descent method respectively.Detailed calculating process is as follows：
1, it is understood thatDefinition be calculate：
Minimize
tr(Sq TSq-Sq TPD-DTPTSq+DTPTPD)
Using Matrix Calculating trace property, former formula can be changed to
F (x)=tr (Sq TSq-2DTPTSq+DTPTPD)
Further gradient is asked to obtain
Here with substep differential formulas, according to the property of the generation projection matrix of mask before, it is possible to from above-mentioned matrix
The Grad for being directed to each unknown mask variable is obtained in gradient.
2nd, f (x) is a function on projection matrix P here, but projection matrix P is by 100 × 1 mask configuration
3100 × 100 size two-dimensional matrixs formed, the inside variable only have 100, and other elements are 0, it is also necessary to ensure the member for 0
Element keeps constant.Therefore, directly cannot to projection matrix P derivations.For this in MATLAB, we are by therein 100
Individual variable is respectively defined as symbolic variable, function f (x) is allowed in MATLAB to this 100 sign function derivations, in this way
To bypass the problem of directly being brought to projection matrix P derivations.
3rd, to ask for process using gradient descent method as follows：
Step1：Given initial point；
Step2：
Step3：Linear search, step-length t is determined by recalling linear search method；
Step4：X=x+ Δs x；
Repeat step2-step4, until meeting stopping criterion.
Projection matrix P after step (8) output optimizationiter。
Projection matrix P is constructed with 100 × 1 new mask after gradient descent method convergence, as new throwing
Shadow matrix Piter, output, examine whether its property consistent with each other obtains convergence.
Claims (2)
1. one kind compression EO-1 hyperion mask optimization method, it is characterised in that be implemented as follows：
Target:Minimize μt(PD)
The parameter of input is as follows:
t:Degree of correlation threshold value
n:Cross complete dictionary
p:Pendulous frequency
γ:Degree of correlation threshold value
P：Projection matrix, by the array between 100 × 10 to 1 into；
D：The excessively complete dictionary obtained by dictionary learning, size are 3100 × 387
Iter:Iterations
Wherein mask is the vector of one 100 × 1, and the projection matrix P of one 3100 × 100 is constructed by it；
It is as follows to implement step：
Step (1) utilizes geometric optics by the position of mask in systems, obtains initial projections matrix P0, P0It is in real number field
One p × n matrix, i.e.,Initial cycle iteration count variable q=0 is set；
Step (2) is by matrix PqD enters ranks standardization, obtains effectively dictionary
Described standardization is exactly by matrix PqD each row normalization is unit vector so that the modulus value of its each column vector is
One, wherein PqRepresent to circulate obtained projection matrix P the q times；
Step (3) constructs Gram matrixes
That is effectively dictionaryTransposition and itself be multiplied construction Gram matrixes；
Step (4) shrinks Gram matrixes Gq, i.e., update Gram matrixes using formula (1)：
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Step (5) is decomposed the Gram matrixes after contraction using SVDOrder be reduced to p, specifically：
ByUnderstand, because the Σ matrix diagonals members that unusual value-based algorithm obtains are non-negative, therefore V and U matrixes
Column vector may differ sign, because U, V vector are that unit is orthogonal, it is actual calculate in matrix also only have only a few
Negative semidefinite member, therefore directly calculated using absolute value, that is, utilize V Σ UTTo ask for the square root of Gram matrixes；
Step (6) solves Gram matrixesSquare root SqSo thatWherein
Step (7) finds the q+1 times and circulates obtained projection matrix Pq+1So that errorMinimum, q=q+1；
Asked for using gradient descent methodProblem, detailed calculating process are as follows：
Definition be calculate：
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<mi>DS</mi>
<mi>q</mi>
<mi>T</mi>
</msubsup>
<mo>+</mo>
<mn>2</mn>
<msup>
<mi>DD</mi>
<mi>T</mi>
</msup>
<msup>
<mi>P</mi>
<mi>T</mi>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
Using substep differential formulas, according to the property of the generation projection matrix of mask before, it becomes possible to be directed to from formula (5)
In the Grad of each unknown mask variable；
Step (8) repeat step (2) arrives step (7) Iter times, the projection matrix P after output optimizationiter；Because mode of operation is
Fixed, therefore threshold value t is the definite value of setting.
A kind of 2. compression EO-1 hyperion mask optimization method according to claim 1, it is characterised in that described initial projections
Matrix P0Derivation it is as follows：
The null matrix of one 100 × 100 is constructed first；
Then the diagonal entry using 100 numbers of mask as the null matrix, and surface element storage form is on diagonal
Symbolic variable form；By this 100 × 100 reproduction matrix 31 times, 3100 × 100 matrix, i.e. projection matrix P are formed0；Its
In element is identical on diagonal in this 31 100 × 100 matrix, but element sequence is different, has the translation on position；
This 3100 × 100 matrix is exactly the projection matrix P that we construct0。
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