CN105976408A - Digital holographic compression transmission method of quantum backward propagation nerve network - Google Patents
Digital holographic compression transmission method of quantum backward propagation nerve network Download PDFInfo
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Abstract
The invention discloses a digital holographic compression transmission method of a quantum backward propagation nerve network. An original image is recorded to be a digital hologram through a Fresnel off-axis holographic calculation method. The quantum backward propagation (QBP) nerve network is constructed. The digital hologram is used to train the QBP nerve network. The trained QBP nerve network is used to compress, transmit and decompress the digital hologram so as to obtain a reconstructed hologram. Reproduction is performed on the reconstructed hologram so as to obtain a reproductive image. The method provided in the invention possesses a fast parallel processing speed and a high storage data capability and is suitable for calculating and processing of a large data volume of digital holograms. Less training frequencies can be used to complete the training of compressing and transmitting a network structure and a compression and transmission speed of the digit holograms can be increased. An image compression ratio is adjustable and reproductive image quality is good.
Description
Technical field
The invention belongs to digital image processing field, relate to a kind of employing quantum and inversely propagate (Quantum Back-
Propagation, QBP) the digital hologram compression transmitting method of neutral net, be specifically related to the making of digital hologram with again
The methods such as existing, QBP neural network image compression.
Background technology
How nineteen forty-seven English physicist Denis gal rich (Dennis Gabor) improves ultramicroscope in research
Resolution during invented holography.Holography is a kind of three-dimensional (Three-being able to record that and reproduce real world
Dimensional, 3D) technology of object.The light wave of object reflection produces interference fringe with reference light wave coherent superposition, is recorded
These interference fringes be referred to as hologram.Hologram reproduces under certain conditions, the three-dimensional image that the most reproducible original is true to nature.
1967 American scientist Gu Demen (J.W.Goodman) propose digital hologram first.Digital hologram is a kind of brand-new obtaining
The method taking optical information, the product that it is traditional holography and digital technology combines.Along with computer technology and high score
Developing rapidly of resolution imageing sensor, the advantage of Digital Holography is it is increasingly evident that show, it applies model
Enclose and have been directed to measuring three-dimensional morphology, distortion measurement, Particle measurement, many fields such as micro-and false proof.
Digital hologram have recorded amplitude and the phase information of object, and data volume is the hugest, necessary in order to be transmitted
It is compressed processing.The information of digital hologram is a kind of interference fringe pattern with nonlinearity intensity distributions, this
Intensity distributions comprises the information of object.Artificial neural network has been widely used in non-linear field, and it can be adaptive
Different image information distributions should be processed with adjusting intelligently in ground, therefore be especially suitable for processing holographic information distribution problem.According to
This, a superfine people is at document one " Chao Zhang, Guanglin Yang and Haiyan Xie, " Information
Compression of Computer-Generated Hologram Using BP Neural Network,"in
Biomedical Optics and 3-D Imaging,OSA Technical Digest(CD)(Optical Society of
America), paper JMA2,2010. " the middle feasibility demonstrating use artificial neural network transmission holographic information for the first time,
Propose and use reverse (Back-Propagation, the BP) neutral net of propagating of tradition to carry out the skill of digital hologram compression transmission
Art, and use Computer Simulation to obtain experimental result.But, owing to traditional BP neutral net has in the feelings contained much information
The defects such as under condition, processing speed is the slowest, memory capacity is limited, this technology of these drawbacks limit is applied to digital hologram
The effect of compression transmission and using value.
Summary of the invention
In order to overcome above-mentioned the deficiencies in the prior art, the present invention provides the numeral of the reverse Propagation Neural Network of a kind of quantum entirely
Breath compression transmitting method, is compressed transmitting to digital hologram based on QBP neutral net, it is possible to use less training time
Count up to into the training of compression transport network architecture, improve the compression transmission speed of digital hologram, ensure that the extensive of image simultaneously
Compound body amount.
The principle of the present invention is: QBP nerual network technique is used for the compression transmission of digital hologram by the present invention, due to number
Word hologram is interference fringe image, and each pixel all carries the partial information of other pixel, and data volume is the biggest；And quantum reason
The principle of superposition of states of opinion makes QBP neutral net have parallel processing speeds more faster than traditional BP neutral net and higher storage
The ability of data, thus the calculating being highly suitable to be applied for the digital hologram of big data quantity processes.According to quantum calculation principle,
One n position quantum register can preserve 2 simultaneouslynIndividual n bit (0 to 2n-l), they respectively exist with certain probability.
Quantum computing systems increases storage capacity all the 2 of energy one n position quantum register of parallel processing the most exponentiallyn
Number, its once-through operation can produce 2nIndividual operation result, is equivalent to conventionally calculation 2nSecondary operation.Therefore, by QBP is neural
Network application, in digital hologram information processing, can obtain ratio and use the more preferable effect of traditional BP neutral net.
Present invention provide the technical scheme that
The digital hologram compression transmitting method of the reverse Propagation Neural Network of a kind of quantum, including the making of digital hologram
With reproduce, quantum inversely propagates the processes such as (QBP) neural network image compression, has faster parallel processing speeds and higher
The ability of storage data, iterations is few, and compression transmission speed is fast, it is adaptable at the calculating of the digital hologram of big data quantity
Reason；Less frequency of training can be used to complete to compress the training of transport network architecture, improve the compression transmission of digital hologram
Speed；Image compression ratio is adjustable, reproduces picture quality preferable；Comprise the steps:
1) original image is recorded as digital hologram by Fresnel off-axis gaussian beam computational methods；
2) build the reverse Propagation Neural Network of quantum, the reverse Propagation Neural Network of described quantum comprise an input layer, one
Individual hidden layer and an output layer, each layer of the reverse Propagation Neural Network of described quantum comprises multiple quantum neuron；Use step
Rapid 1) digital hologram obtained Propagation Neural Network reverse to described quantum is trained, and obtains training complete quantum reverse
Propagation Neural Network；
3) step 2 is used) the complete reverse Propagation Neural Network of quantum of training that obtains is to step 1) numeral that obtains is complete
Breath figure is compressed, transmits and decompresses, the hologram after being reconstructed；
4) to step 3) hologram after the reconstruct that obtains reproduces, and obtains reproduction image.
For the digital hologram compression transmitting method of the reverse Propagation Neural Network of above-mentioned quantum, further, step 1) institute
State record and include that fresnel diffraction computational methods and off-axis reference light interfere computational methods；
Described fresnel diffraction computational methods are calculated by means of Fresnel diffraction, and described means of Fresnel diffraction is formula 2:
In formula 2, d is diffraction distance；K is wave number；J is imaginary unit；(x0,y0) it is starting material popin face；(x, y) for spreading out
Penetrate plane；O(x0,y0) it is starting material popin surface information, (x y) is complex amplitude function before diffraction distance is for the Object light wave of d to U；
Before described off-axis reference light interferes computational methods to utilize interference record object light diffracted wave, complex amplitude function forms holography
Figure IH(x, y), such as formula 1:
In formula 1, IH(x y) is the light intensity of hologram record；(x y) is function before reference light wave to R；(x y) is original thing to U
Function before bulk wave；R*(x, y) and U*(x, (x, y) with U (x, conjugation item y) y) to be respectively R.
For the digital hologram compression transmitting method of the reverse Propagation Neural Network of above-mentioned quantum, further, by formula 3
Carry out fast Fourier transform, fresnel diffraction calculated:
In formula 3, F represents Fourier transform；D is diffraction distance；K is wave number；J is imaginary unit；L0For starting material popin
Surface sample scope；The number of pixels that sampling number is N × N, i.e. initial pictures in starting material popin face；Starting material popin surface sample
That puts is spaced apart Δ x0=Δ y0=L0/N；Δ x=Δ y is discrete Fourier transform (DFT) post-sampling interval, starting material popin face, at sky
Between in territory, the corresponding sampling interval for diffraction plane.
For the digital hologram compression transmitting method of the reverse Propagation Neural Network of above-mentioned quantum, further, step 2) tool
Body comprises the steps:
21) set up new quantum neural network based on quantum door, be used for realizing quantum calculation；Described new quantum neural
In meta-model, neuron state phase shift is realized by the result that weights are multiplied with input by phase sliding door:
If Ii(i=1,2 ..., M) it is the i-th quantum state x that is input to neuroni=f (Ii) (i=1,2 ..., M) phase
Position, then this quantum neuron exports and is expressed as quantum neural network:
O=f (y) (formula 9)
Wherein, θi(i=1,2 ..., M) it is the phase shift coefficient of weights；λ is threshold coefficient；δ is phase control factor；
O is output state；Arg (u) is that plural number u is extracted phase place, i.e. arg (u)=actag (Im (u)/Re (u)), wherein, Im (u) is for asking
The imaginary part of plural number u；Re (u) is for seeking the real part of plural number u；G (δ) is sigmoid function；The definition of function f () is as shown in Equation 5；
F (θ)=eiθ=cos θ+isin θ (formula 5)
Wherein,Represent imaginary number unit；θ represents the phase place of quantum state；
22) building the reverse Propagation Neural Network of quantum for image compressing transmission, described quantum inversely propagates nerve net
The input of the quantum neuron that network is each layer and output are the superpositions of multiple quantum state；
23) definition neutral net inversely propagate training method, training step 22) quantum that builds inversely propagates nerve net
Network；The reverse training method of propagating of described neutral net uses the steepest descent algorithm of approximation mean square error, adjusts described quantum
Phase rotated coefficient θ, threshold coefficient λ and phase control factor δ in reverse Propagation Neural Network, make the average of training error be less than
Terminate training during expectation target, obtain training the reverse Propagation Neural Network of complete quantum.
For the digital hologram compression transmitting method of the reverse Propagation Neural Network of above-mentioned quantum, further, step 21)
Described quantum Men Youyi position phase sliding door and two controlled not-gate compositions, as the activation primitive of neutral net, use plural form table
Show quantum state and Universal Quantum gate group.
Step 22) in, the input of described quantum neuron and output specifically:
Set { INl(l=1,2 ..., L), { HIDEk(k=1,2 ..., K) and { OUTn(n=1,2 ..., N) difference table
Show the quantum neuron set of the input layer of the reverse Propagation Neural Network of described quantum, hidden layer and output layer；L, K and N are respectively
The neuron number of corresponding each layer；When normalized input value inputl(l=1,2 ..., L) it is imported into input layer { INl, defeated
Entering each neuron of layer will make the input value between [0,1] be converted to quantum state x between [0, pi/2]l(l=1,2 ...,
L) phase value Il(l=1,2 ..., L), then its quantum state is exported to hidden layer；Expression formula is:
xl=f (Il) (formula 11)
Wherein, the definition of function f () is as shown in Equation 5；
Described hidden layer { HIDEkAnd described output layer { OUTnProcessing procedure according to formula 7～formula 9；
Defining the superposition state that quantum state is activated state and aepression of any one quantum neuron, described neuron is
Whole output valve putputn(n=1,2 ..., N) be activated state | 1 > time probability；The reverse Propagation Neural Network of described quantum exports
The final output value table of layer the n-th neuron is shown as formula 12:
outputn=| Im (On)|2(formula 12)
In formula 12, O is output state.
For the digital hologram compression transmitting method of the reverse Propagation Neural Network of above-mentioned quantum, further, step 23)
In, the reverse training method of propagating of described neutral net uses step 1) described quantum inversely propagated by the digital hologram that obtains
Neutral net is trained, and specifically includes following steps:
231) the reverse Propagation Neural Network of described quantum is initialized, by step 1) digital hologram that size is X × Y that obtains
Figure normalized, is then divided into xp×ypImage block, each image block becomes M × 1 (M=xp×yp) vector tieed up, make
Training sample for the reverse Propagation Neural Network of described quantum；
232) it is input to a training sample in the reverse Propagation Neural Network of described quantum calculate network output；
233) the actual output of record network and the error of target output, according to steepest descent method, the most successively adjust each layer
Parameter；
234) step 232 is repeated)～233), until all training samples input the most；
235) set frequency of training, sets accumulative total error as the numeral exported after input digital hologram and network processes
Error between hologram；Calculating the actual output of all training samples and the accumulative total error of target output, frequency of training adds
1；When described accumulative total error is more than, less than the accumulative total error set or described frequency of training, the frequency of training set, training
Terminate；Otherwise reenter step 232).
For the digital hologram compression transmitting method of the reverse Propagation Neural Network of above-mentioned quantum, further, step 3) tool
Body includes: by step 1) it is input to the complete quantum of described training after the digital hologram normalized that obtains and inversely propagates god
Through the input layer of network, realized the coding/compression of image by input layer to hidden layer, realize figure by hidden layer to output layer
Decoding/the decompression of picture, the normalization hologram after being reconstructed；Normalization hologram after described reconstruct is returned through counter again
One change processes, the hologram after being reconstructed.
For the digital hologram compression transmitting method of the reverse Propagation Neural Network of above-mentioned quantum, further, described amount
The input layer of the reverse Propagation Neural Network of son and the quantum neuron quantity of output layer are equal, are denoted as L=N；Each neuron pair
Answer a pixel；The quantum neuron quantity of described hidden layer is designated as K, K less than N；By adjusting the neuron of described hidden layer
The size of quantity K, reaches to regulate the purpose of image compression ratio.
For the digital hologram compression transmitting method of the reverse Propagation Neural Network of above-mentioned quantum, further, step 4) institute
State reproduction and realize the reproduction of Fresnel off-axis hologram especially by off-axis reference light irradiation process and fresnel diffraction process.
Compared with prior art, the invention has the beneficial effects as follows:
The present invention provides the digital hologram compression transmitting method of the reverse Propagation Neural Network of a kind of quantum, uses QBP neural
Network is compressed transmission for digital hologram.
Advantages of the present invention is mainly reflected in following several respects:
(1) QBP neutral net used in the present invention principle of superposition of states based on its quantum theory, has and compares traditional BP
The faster parallel processing speeds of neutral net and the ability of higher storage data, be highly suitable to be applied for the numeral of big data quantity
The calculating of hologram processes.
(2) for an identical digital hologram, the frequency of training needed for training QBP neutral net is much smaller than tradition
BP neutral net, shortens the calculating time, improves the speed of transmission holographic information；
(3) during QBP neural network algorithm is incorporated into the compression transmission of digital hologram information by the present invention, image compression ratio
Adjustable, and can ensure that and preferably reproduce picture quality.
Accompanying drawing explanation
Fig. 1 is the flow chart element of the digital hologram compression transmitting method of the reverse Propagation Neural Network of quantum that the present invention provides
Figure.
Fig. 2 is the schematic diagram of quantum neural network.
Fig. 3 is the schematic diagram of three layers of QBP neutral net.
Fig. 4 is QBP e-learning and the flow chart of training calculating.
Fig. 5 is digital hologram and the reproduction image thereof of original lena image；
Wherein, (a) is original lena image (128 × 128 pixel)；(b) be lena image digital hologram (256 ×
256 pixels)；C () is the reproduction image of lena image.
Fig. 6 is QBP with BP neutral net frequency of training figure under four different compression ratios；
Wherein, (a) (b) corresponding R=0.5000, ErrmaxThe situation of=0.0005；(c) (d) corresponding R=0.2500,
ErrmaxThe situation of=0.0015；(e) (f) corresponding R=0.1250, ErrmaxThe situation of=0.0023；(g) (h) corresponding R=
0.0625,ErrmaxThe situation of=0.0030.
Fig. 7 is at optimal learning rate ηQBP=0.40 and ηBPNumeral when=0.20, after the process of QBP and BP obtained
Hologram and the comparison diagram of reproduction image；
Wherein, the digital hologram after Fig. 7 (a) (b) is based on BP Processing with Neural Network and reproduction image；Fig. 7 (c) (d)
For based on the digital hologram after QBP Processing with Neural Network and reproduction image.
Detailed description of the invention
Below in conjunction with the accompanying drawings, further describe the present invention by embodiment, but limit the model of the present invention never in any form
Enclose.
FB(flow block) such as Fig. 1 of the digital hologram compression transmitting method of the reverse Propagation Neural Network of quantum that the present invention provides
Shown in, the method is suitable for processing Fresnel off-axis hologram, including that produced by Computer Simulation or by optical system record,
It is not limited to digital hologram.In embodiments of the present invention, the present invention provides method to specifically include following steps:
1) original image is recorded as digital hologram by Fresnel off-axis gaussian beam computational methods；
According to Fresnel off-axis gaussian beam algorithm, original image (object) is recorded as digital hologram.Fresnel is the most complete
Breath figure record is interfered two parts to form by fresnel diffraction and off-axis reference light.
Wherein, fresnel diffraction (Fresnel diffraction) refers to the light wave diffraction at near-field region.Fresnel
Diffraction integral formula can be used to the propagation calculating light wave at near-field region.Calculate by object every bit institute outgoing light wave to holographic note
The fresnel diffraction of record plane superposition, can calculate object before the Object light wave of holographic recording plane.
It is bright with twin image and Zero-order diffractive that off-axis reference light interference there are reproduction image when referring to hologram reconstruction simultaneously
Speckle, overlapped impact reproduces picture quality.Introduce and exist before Object light wave the reference light of certain angle when hologram record,
Different order diffraction pictures can be separated, obtain individually reproducing image clearly.
According to off-axis gaussian beam formula, complex amplitude function before interfering record object light diffracted wave is utilized to form hologram IH(x, y):
In formula 1, IH(x, y) is the light intensity of hologram record, and (x, y) is function before reference light wave to R, and (x y) is original thing to U
Function before bulk wave.R*(x, y) and U*(x, (x, y) with U (x, conjugation item y) y) to be respectively R.
The diffraction process of object light wave is calculated by means of Fresnel diffraction (formula 2):
In formula 2, d is diffraction distance, and k is wave number, and j is imaginary unit；(x0,y0) it is starting material popin face, (x, y) for spreading out
Penetrate plane；O(x0,y0) it is starting material popin surface information, (x y) is complex amplitude function before diffraction distance is for the Object light wave of d to U.
Use computer that this diffraction integral is calculated, fast Fourier transform can be carried out by formula 3:
In formula 3, F represents Fourier transform, and d is diffraction distance, and k is wave number, and j is imaginary unit；L0For starting material popin
Surface sample scope；The number of pixels that sampling number is N × N, i.e. initial pictures in starting material popin face；Starting material popin surface sample
That puts is spaced apart Δ x0=Δ y0=L0/N；Δ x=Δ y is discrete Fourier transform (DFT) post-sampling interval, starting material popin face, at sky
Between in territory, the corresponding sampling interval for diffraction plane.
2) building QBP neutral net, use step 1) it is trained by the digital hologram that obtains；
This process mainly includes setting up quantum neural network, builds and train QBP neutral net.
2.1 set up quantum neural network
Setting up quantum neural network is the basis building QBP neutral net, and quantum neuron is the base of QBP neutral net
This component units.New quantum neuron mould is set up based on quantum door (being specifically related to a phase sliding door and two controlled not-gates)
Type, it is achieved quantum calculation.
Quantum door is the basis of physics realization quantum calculation, can be made up of arbitrary quantum door group network quantum door, this
What invention used is exactly to be formed basic computing unit, as the activation of neutral net by a phase sliding door and two controlled not-gates
Function constitutes new quantum neural network.For the ease of application, represent quantum state and Universal Quantum logic with plural form
Door group.
Quantum bit is from classical the different of bit: a quantum bit state | φ > be in state | 0 > and | 1 > phase
On dry superposition state, represent by formula 4:
| φ >=α | 0 >+β | 1 > (formula 4)
Wherein, α and β is complex representation probability amplitude, meets normalization requirement | α |2+|β|2=1.Come by a complex function
Describing the state of quantum state, the representation of complex function is formula 5:
F (θ)=eiθ=cos θ+isin θ (formula 5)
Wherein,Represent imaginary number unit；θ represents the phase place of quantum state.| 0 > this complex function of probability amplitude
Real part represent, | 1 > probability amplitude represent by its imaginary part, then a quantum state can be described as formula 6:
| ψ >=cos θ | 0 >+sin θ | 1 > (formula 6)
According to the definition of formula 5, the quantum neural networks such as Fig. 2 institute constituted based on 1 phase sliding door and 2 controlled not-gates
Showing, its input uses the form of multiple quant um teleportation, is divided amplitude and the phase place of input quantum state by these three quantum doors
Do not process, obtain the output of multiple quant um teleportation.
In fig. 2, xi(i=1,2 ..., M) represent that i-th is input to the quantum state of neuron；θi(i=1,2 ..., M) be
The phase shift coefficient of weights；λ is threshold coefficient；δ is phase control factor；O is output state；Arg (u) is to extract plural number u
Phase place, i.e. arg (u)=actag (Im (u)/Re (u)), wherein, Im (u) is the imaginary part seeking plural number u；Re (u) is for asking plural number u's
Real part；The definition of function f () is as shown in (formula 5)；G () is sigmoid function.
Set I hereini(i=1,2 ..., M) it is the i-th quantum state x that is input to neuroni=f (Ii) (i=1,2 ..., M)
Phase place, then the output of this quantum neuron is expressed as quantum neural network:
O=f (y) (formula 9)
In this quantum neural network, there is two kinds of parametric form, a kind of phase sliding door that corresponds to
The weighting parameter θ and threshold parameter λ of phase place；Another kind of upset controls parameter δ corresponding to controlled-not gate.Unit is different from traditional neural
, weights f (θ in quantum neuroni) and input xi=f (Ii) result that is multiplied, it is by the phase sliding door phase to neuron state
In-migration realizes.
2.2 build QBP neutral net
According to quantum neural network presented above, it is used for the principle of image compressing transmission by traditional BP neutral net
And network structure, set up the QBP neutral net for image compressing transmission.In order to reduce the operation time of system and improve network
Efficiency, the QBP network hidden layer for compression of images set up only has one layer, and its network structure is as shown in Figure 3.Can see
Go out its network structure identical with traditional three layers of BP network, comprise an input layer, a hidden layer and an output layer, same to layer
Without connecting between neuron, each neuron then realizes entirely connecting between layers.Different being in QBP neutral net is each
The neuron (the black node of network in Fig. 3) of layer is quantum neuron, and its input and output are the folded of multiple quantum state
Add.
In three shown in Fig. 3 layer QBP network, { INl(l=1,2 ..., L), { HIDEk(k=1,2 ..., K) and
{OUTn(n=1,2 ..., N) represent the quantum neuron set of input layer, hidden layer and output layer respectively；L, K and N are the most right
Should the neuron number of each layer.
When normalized input value inputl(l=1,2 ..., L) it is imported into input layer { INl, each neuron of input layer
Quantum state x between [0, pi/2] is converted to by making the input value between [0,1]l(l=1,2 ..., L) phase value Il
(l=1,2 ..., L), then its quantum state is exported to hidden layer.Expression formula is:
xl=f (Il) (formula 11) hidden layer { HIDEkAnd output layer { OUTnProcessing procedure carry out according to formula 7-9.
In quantum neuron, quantum state | 1 > be equivalent to the activated state for neuron, quantum state | 0 > be equivalent to neuron
Aepression, then the quantum state of any one neuron is defined as the superposition state of activated state and aepression, its neuron
Final output valve outputn(n=1,2 ..., N) be activated state | 1 > time probability.So, three layers of QBP neutral net output layer
The final output valve of the n-th neuron is:
outputn=| Im (On)|2(formula 12)
2.3 training QBP neutral net
For training QBP neutral net, by plural number BP algorithm, the reverse propagation in definition network inversely propagates calculation for quantum
Method (QBP algorithm), uses the steepest descent algorithm of approximation mean square error, adjusts phase rotated coefficient θ, threshold coefficient in network
λ and phase control factor δ, make the average of training error less than till expectation target, be embodied as:
In formula 12-14, η is learning rate.EtotalFor mean square error function, its expression formula is:
Wherein, B represents total number of training sample, and the b training sample is produced by the b image block.targetn,bWith
outputn,bWhen representing b training sample of input respectively, the target output of output layer the n-th neuron and actual output.
Reverse training process such as Fig. 4 that propagates of QBP neutral net:
(1) QBP neutral net is initialized, by step 1) the digital hologram normalized that size is X × Y that obtains,
Then x it is divided intop×ypImage block, each image block becomes M × 1 (M=xp×yp) vector tieed up, as this QBP nerve net
Training (study) sample of network.
(2) it is input to a training sample in QBP neutral net calculate network output.
(3) the actual output of record network and the error of target output, according to steepest descent method, the most successively adjust each layer ginseng
Number.
(4) repetition (2nd), (3) step, until all training samples input the most.
(5) calculate actual output and the accumulative total error of target output of all training samples, i.e. input digital hologram
And after network processes output digital hologram between error, frequency of training adds 1, if this total error less than set total error or
Frequency of training is more than setting frequency of training, and network training terminates, and otherwise reenters step (2).Network total error is defined as follows:
Wherein, g (b, m) is the digital hologram of input neural network after normalized,It is through QBP
Normalization digital hologram after the compressed and decompressed process of neutral net.
3) step 2 is used) the complete QBP neutral net of training that obtains is to step 1) digital hologram that obtains presses
Contract, transmit and decompress, the hologram after being reconstructed；
By step 1) it is input to train the input of complete QBP neutral net after the digital hologram normalized that obtains
Layer, compresses transmission digital hologram by the hidden layer of eel-like figure.Wherein, the volume of image is realized by input layer to hidden layer
Code/compression, realizes the decoding/decompression of image by hidden layer to output layer, and the normalization hologram after being reconstructed is (corresponding
The final output valve of formula 12)；Hologram after being reconstructed after renormalization processes again by this hologram, for step
4)。
After view data is input to input layer, the hidden layer forcing it through eel-like figure reaches the purpose of compression transmission, so
After realized the decoding and rebuilding of image by hidden layer to output layer.Therefore, in the QBP network of 3 shown in Fig. 3 layer, the input of network
Layer and output layer generally take equal neuron number, i.e. L=N, its size by original image compression during according to concrete feelings
Condition determines, the corresponding pixel of each neuron；Hidden layer neuron number is K, and K < N, by adjusting the size of K, it is achieved
The function of regulation image compression ratio.
4) to step 3) hologram after the reconstruct that obtains reproduces, and obtains reproduction image.
Reconstructed hologram is reproduced, with specific reference to Fresnel off-axis gaussian beam algorithm, digital hologram is reproduced as former
Beginning image, needs to be irradiated by off-axis reference light to realize the reproduction of Fresnel off-axis hologram with two processes of fresnel diffraction.
Reproducing formula according to off-axis gaussian beam, (x y) irradiates hologram I to utilize the reproduction light R consistent with reference lightH(x,y)
Reproduce:
IH(x, y) × R (x, y)=(| R (x, y) |2+|U(x,y)|2)R(x,y)+|R(x,y)|2U(x,y)+R2(x,y)U*
(x, y) (formula 16)
In formula 16, IH(x, y) is the light intensity of hologram record, R (x, is y) reference light and reproduce light wavefront function, U (x,
Y) it is that original objects reproduces wavefront function, U*(x y) is the conjugation item of reproduction image.
Count by fresnel diffraction formula (formula 2～formula 3) through reproducing the diffraction process of the digital hologram light wave that light irradiates
Calculate, the reproduction image of original image can be obtained at diffraction plane.
In order to test compression transmission speed (i.e. network training speed) and the reproduction picture quality of the present invention, use and BP god
Through the method measurement compression transmission speed of network comparative training number of times, compression ratio (R), mean square error (MSE) is used to believe with peak value
Make an uproar and weigh the quality of reproduction image than evaluation methodologys such as (PSNR).
R, MSE, PSNR are respectively defined as:
Wherein, ScRepresent the digital hologram size of data after compression, SoRepresent original figure hologram data size.f
(x, y) represents the reproduction image function of original hologram,Represent after neutral net compression and decompression
The presentation function of hologram.xpeakThe peak-to-peak value of data representing image.
Fig. 5 is digital hologram and the reproduction image thereof of original lena image.Fig. 5 (a) is original lena image (128 × 128
Pixel)；Fig. 5 (b) is the digital hologram (256 × 256 pixel) of lena image；Fig. 5 (c) is the reproduction image of lena image.?
In the present embodiment, we use the digital hologram in Fig. 5 (b) through normalization, then as the input of QBP neutral net.
Set the x of QBP and BP neutral netp=yp=8, therefore this digital hologram is divided into 1024 training samples.Neutral net
Input and output layer neuron number be L=N=p2=64, hidden layer neuron number K value 32,16,8,4} change,
The most corresponding different compression ratio { 0.5000,0.2500,0.1250,0.0625}.
Fig. 6 is QBP with BP neutral net frequency of training under the different compression ratio of aforementioned four.R=in Fig. 6 (a) (b)
0.5000,Errmax=0.0005；R=0.2500, Err in Fig. 6 (c) (d)max=0.0015；R=0.1250 in Fig. 6 (e) (f),
Errmax=0.0023；R=0.0625, Err in Fig. 6 (g) (h)max=0.0030.Wherein the frequency of training upper limit is set to 5000.Net
The maximum Err of network total errormaxSet according to different compression ratios.Learning rate η span is [0.05,0.70].
Experimental result data contrast under the different compression ratio of table 1QBP from BP
Table 1 is under different compression ratio, and the QBP compression method that the present invention provides contrasts with the experimental result data of BP method.
It can be seen that under optimal learning rate, the frequency of training of QBP neutral net is much smaller than the BP nerve net under identical compression ratio
Network, therefore the speed of the digital hologram compression transmitting method of the present invention is faster.
In the present embodiment, in the case of we to compression ratio are 0.5000, QBP and BP neutral net compression processes image
Result carried out quality evaluation.Fig. 7 is at optimal learning rate ηQBP=0.40 and ηBPWhen=0.20, QBP's and BP obtained
Digital hologram after process and the contrast of reproduction image.Wherein, the numeral after Fig. 7 (a) (b) is based on BP Processing with Neural Network
Hologram and reproduction image；Fig. 7 (c) (d) be based on QBP Processing with Neural Network after digital hologram and reproduce image.Table 2 is
The reproduction image quality measure parameter of QBP Yu BP.It can be seen that under this compression ratio, the QBP method that the present invention uses is than BP side
Method can obtain better image Quality of recovery.
Table 2QBP Yu BP reproduces image quality measure parameter (R=0.5000)
In sum, this programme has a good application prospect in 3D hologram Information Compression is transmitted.This programme thinking
In compression transmission speed and image Quality of recovery, more excellent level all can be reached for digital hologram Compression Transmission Technology.
It should be noted that publicizing and implementing the purpose of example is that help is further appreciated by the present invention, but the skill of this area
Art personnel are understood that various substitutions and modifications are all without departing from the present invention and spirit and scope of the appended claims
Possible.Therefore, the present invention should not be limited to embodiment disclosure of that, and the scope of protection of present invention is with claim
Book defines in the range of standard.
Claims (10)
1. a digital hologram compression transmitting method for the reverse Propagation Neural Network of quantum, comprises the steps:
1) original image is recorded as digital hologram by Fresnel off-axis gaussian beam computational methods；
2) build the reverse Propagation Neural Network of quantum, the reverse Propagation Neural Network of described quantum comprise an input layer, one hidden
Containing layer and an output layer, each layer of the reverse Propagation Neural Network of described quantum comprises multiple quantum neuron；Use step 1)
The digital hologram obtained Propagation Neural Network reverse to described quantum is trained, and obtains training complete quantum inversely to propagate
Neutral net；
3) step 2 is used) the complete reverse Propagation Neural Network of quantum of training that obtains is to step 1) digital hologram that obtains
It is compressed, transmits and decompresses, the hologram after being reconstructed；
4) to step 3) hologram after the reconstruct that obtains reproduces, and obtains reproduction image.
2. the digital hologram compression transmitting method of the reverse Propagation Neural Network of quantum as claimed in claim 1, is characterized in that, step
1) described record includes that fresnel diffraction computational methods and off-axis reference light interfere computational methods；
Described fresnel diffraction computational methods are calculated by means of Fresnel diffraction, and described means of Fresnel diffraction is formula 2:
In formula 2, d is diffraction distance；K is wave number；J is imaginary unit；(x0,y0) it is starting material popin face；(x is y) that diffraction is put down
Face；O(x0,y0) it is starting material popin surface information, (x y) is complex amplitude function before diffraction distance is for the Object light wave of d to U；
Described off-axis reference light is interfered computational methods to utilize and is interfered complex amplitude function formation hologram I before record object light diffracted waveH
(x, y), such as formula 1:
IH(x, y)=| R (x, y)+U (x, y) |2
=| R (x, y) |2+|U(x,y)|2+R*(x,y)U(x,y)+R(x,y)U*(x, y) (formula 1)
In formula 1, IH(x y) is the light intensity of hologram record；(x y) is function before reference light wave to R；(x y) is original objects ripple to U
Front function；R*(x, y) and U*(x, (x, y) with U (x, conjugation item y) y) to be respectively R.
3. the digital hologram compression transmitting method of the reverse Propagation Neural Network of quantum as claimed in claim 2, is characterized in that, pass through
Formula 3 carries out fast Fourier transform, calculates fresnel diffraction:
In formula 3, F represents Fourier transform；D is diffraction distance；K is wave number；J is imaginary unit；L0For starting material popin surface sample
Scope；The number of pixels that sampling number is N × N, i.e. initial pictures in starting material popin face；Between starting material popin surface sample point
It is divided into Δ x0=Δ y0=L0/N；Δ x=Δ y is discrete Fourier transform (DFT) post-sampling interval, starting material popin face, in spatial domain
In, the corresponding sampling interval for diffraction plane.
4. the digital hologram compression transmitting method of the reverse Propagation Neural Network of quantum as claimed in claim 1, is characterized in that, step
2) following steps are specifically included:
21) set up new quantum neural network based on quantum door, be used for realizing quantum calculation；Described new quantum neuron mould
In type, neuron state phase shift is realized by the result that weights are multiplied with input by phase sliding door:
If Ii(i=1,2 ..., M) it is the i-th quantum state x that is input to neuroni=f (Ii) (i=1,2 ..., M) phase place,
This quantum neuron exports and is expressed as quantum neural network:
O=f (y) (formula 9)
Wherein, θi(i=1,2 ..., M) it is the phase shift coefficient of weights；λ is threshold coefficient；δ is phase control factor；O is defeated
Go out state；Arg (u) is that plural number u extracts phase place, i.e. arg (u)=actag (Im (u)/Re (u)), wherein, Im (u) is for seeking plural number u
Imaginary part；Re (u) is for seeking the real part of plural number u；G (δ) is sigmoid function；The definition of function f () is as shown in Equation 5；
F (θ)=eiθ=cos θ+isin θ (formula 5)
Wherein,Represent imaginary number unit；θ represents the phase place of quantum state；
22) building the reverse Propagation Neural Network of quantum for image compressing transmission, the reverse Propagation Neural Network of described quantum is every
The input of the quantum neuron of a layer and output are the superpositions of multiple quantum state；
23) definition neutral net inversely propagate training method, training step 22) the reverse Propagation Neural Network of quantum that builds；
The reverse training method of propagating of described neutral net uses the steepest descent algorithm of approximation mean square error, adjusts described quantum reverse
Phase rotated coefficient θ, threshold coefficient λ and phase control factor δ in Propagation Neural Network, make the average of training error less than expectation
Terminate training during target, obtain training the reverse Propagation Neural Network of complete quantum.
5. the digital hologram compression transmitting method of the reverse Propagation Neural Network of quantum as claimed in claim 4, is characterized in that, step
21) described quantum Men Youyi position phase sliding door and two controlled not-gate compositions, as the activation primitive of neutral net, use plural form
Represent quantum state and Universal Quantum gate group.
6. the digital hologram compression transmitting method of the reverse Propagation Neural Network of quantum as claimed in claim 4, is characterized in that, step
22) in, the input of described quantum neuron and output specifically:
Set { INl(l=1,2 ..., L), { HIDEk(k=1,2 ..., K) and { OUTn(n=1,2 ..., N) represent institute respectively
State the quantum neuron set of the input layer of the reverse Propagation Neural Network of quantum, hidden layer and output layer；L, K and N are the most corresponding
The neuron number of each layer；When normalized input value inputl(l=1,2 ..., L) it is imported into input layer { INl, input layer
Each neuron is converted to quantum state x between [0, pi/2] by making the input value between [0,1]l(l=1,2 ..., L)
Phase value Il(l=1,2 ..., L), then its quantum state is exported to hidden layer；Expression formula is formula 10 and formula 11:
xl=f (Il) (formula 11)
Wherein, the definition of function f () is as shown in Equation 5；
Described hidden layer { HIDEkAnd described output layer { OUTnProcessing procedure according to formula 7～formula 9；
Define the superposition state that quantum state is activated state and aepression of any one quantum neuron, described neuron the most defeated
Go out to be worth outputn(n=1,2 ..., N) be activated state | 1 > time probability；Described quantum reverse Propagation Neural Network output layer n-th
The final output value table of individual neuron is shown as formula 12:
outputn=| Im (On)|2(formula 12)
In formula 12, O is output state.
7. the digital hologram compression transmitting method of the reverse Propagation Neural Network of quantum as claimed in claim 4, is characterized in that, step
23), in, the reverse training method of propagating of described neutral net uses step 1) digital hologram that obtains is reverse to described quantum
Propagation Neural Network is trained, and specifically includes following steps:
231) the reverse Propagation Neural Network of described quantum is initialized, by step 1) digital hologram that size is X × Y that obtains returns
One change processes, and is then divided into xp×ypImage block, each image block becomes M × 1 (M=xp×yp) vector tieed up, as institute
State the training sample of the reverse Propagation Neural Network of quantum；
232) it is input to a training sample in the reverse Propagation Neural Network of described quantum calculate network output；
233) the actual output of record network and the error of target output, according to steepest descent method, the most successively adjust each layer parameter；
234) step 232 is repeated)～233), until all training samples input the most；
235) set frequency of training, sets accumulative total error as the digital hologram exported after input digital hologram and network processes
Error between figure；Calculating the actual output of all training samples and the accumulative total error of target output, frequency of training adds 1；When
When described accumulative total error is more than, less than the accumulative total error set or described frequency of training, the frequency of training set, training knot
Bundle；Otherwise reenter step 232).
8. the digital hologram compression transmitting method of the reverse Propagation Neural Network of quantum as claimed in claim 1, is characterized in that, step
3) specifically including: by step 1) quantum that is input to described training complete after the digital hologram normalized that obtains inversely passes
Broadcast the input layer of neutral net, realized the coding/compression of image by input layer to hidden layer, real by hidden layer to output layer
Decoding/the decompression of existing image, the normalization hologram after being reconstructed；Normalization hologram after described reconstruct is passed through again
Renormalization processes, the hologram after being reconstructed.
9. the digital hologram compression transmitting method of the reverse Propagation Neural Network of quantum as claimed in claim 8, is characterized in that, described
The input layer of the reverse Propagation Neural Network of quantum and the quantum neuron quantity of output layer are equal, are denoted as L=N；Each neuron
A corresponding pixel；The quantum neuron quantity of described hidden layer is designated as K, K less than N；By adjusting the nerve of described hidden layer
The size of unit's quantity K, reaches to regulate the purpose of image compression ratio.
10. the digital hologram compression transmitting method of the reverse Propagation Neural Network of quantum as claimed in claim 1, is characterized in that, step
Rapid 4) described reproduction realizes Fresnel off-axis hologram again especially by off-axis reference light irradiation process and fresnel diffraction process
Existing.
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