CN105451024A - Digital hologram coding transmission method employing compressed sensing - Google Patents

Abstract

The invention discloses a digital hologram coding transmission method employing compressed sensing. The method carries out the compression, transmission and decoding of a digital hologram based on the compressed sensing, carries out targeted reconstruction of the digital hologram in a wavelet domain through a total variation method, and improves the quality of image reproduction. The method specifically comprises the steps: carrying out the downsampling of the digital hologram at a sampling rate lower than the sampling rate of the Nyquist law through employing a variable density sampling matrix, so as to reduce the data amount for subsequent coding and transmission; further carrying out the compression and coding of the sample data through a Hoffman lossless coding method, wherein the iteration and reconstruction is multi-level partitioned iteration and reconstruction. Compared with a common method for reducing a measurement value for a measurement matrix, the method further improves the compression rate, reduces the calculation amount of a transmission end and the system complexity, improves the quality of image reproduction, reconstructs the digital hologram after decompression, and can be used for three-dimensional display in a space light modulator and other optical systems.

Description

A kind of digital hologram coding and transmission method adopting compressed sensing

Technical field

The invention belongs to digital image processing field, relate to a kind of digital hologram coding and transmission method adopting compressed sensing, be specifically related to the making of colorful digital holographic figure and reproduction, compressed sensing technique variation density are sampled and the correlation technique such as total variational reconstruct.

Background technology

2006, the people such as Candes are at document one " EmmanuelJ.Candes, JustinRombergandTerenceTao, " Robustuncertaintyprinciples:Exactsignalreconstructionfro mhighlyincompletefrequencyinformation, " IEEETransactionsonInformationTheory, Vol.52, No.2, pp.489-509, 2006. " middle first time proposition compressed sensing technology, propose the blank of compressive sensing theory and possible application, and propose the method for being carried out High precision reconstruction for height lack sampling data by non-linear estimations.

The amplitude of hologram record three-dimensional body and phase information, data volume is very huge, must to carry out compression process to carry out coding transmission.Compressed sensing technology is applied in the compression transmission of digital hologram, needs the subject matter of research to be how to improve the compression ratio of compression process and the quality improving reproduced image.Document two " Y.Rivenson; A.Stem; andB.Javidi; " CompressiveFresnelHolography; " J.DisplayTechnol.Vol.6, No.10, pp.506-509,2010 " describe a kind of solution: carry out down-sampled with low sampling rate logm word hologram, use less sampled data directly to obtain the reproduced image of hologram by the Methods Based on Total Variation under the sparse base of small echo.But this method Problems existing is the reconstruct not carrying out digital hologram, optical stereo display system can not be used for and carries out object dimensional stereo display.Document three " Li Ke, Li Jun. the Hologram compression based on compressed sensing is studied [J]. South China Normal University's journal: natural science edition, 2013, 44 (4): 61-65. " and document four " Wang Yuping, Chen Baoshen, Lan Jianhui, Deng. based on the digital hologram imaging technique [J] of compressed sensing. CYBERSPACE, 2013, 7th phase (7): 37-38. " all describe the compression method of reconstructed number hologram under compressed sensing technical pattern, the method uses calculation matrix fetching portion measured value to reach compression object, but its Problems existing is: calculation matrix carries out measurement to hologram needs a large amount of matrix operation, system operations complexity is high, simultaneously, measured value is floating number, bring extra storage and transmitted data amount, reduce data compression rate.

Summary of the invention

In order to overcome above-mentioned the deficiencies in the prior art, the invention provides a kind of digital hologram coding and transmission method adopting compressed sensing, carrying out compression transmission, to reach the object of high compression rate and the low loss of information based on compressed sensing for digital hologram.

In the present invention, agree as follows term:

Compressed sensing: Compressivesensing; Digital hologram: Digitalhologram.

Principle of the present invention is: compressed sensing technology is used for the compression transmission of digital hologram by the present invention, because digital hologram is interference fringe image, each pixel all carries the partial information of other pixel, the Global Information of digital hologram can be inferred by part Pixel Information, therefore, can carry out down-sampled to digital hologram by the sample rate far below Nyquist law, greatly reduce the data volume of compression transmission system process, and improve the compression ratio of image.Meanwhile, because Sampling Compression process does not introduce complex calculation, system complexity and the power consumption of compression transmitting terminal effectively can be reduced.Because object information is stored in upper frequency part by the interventional procedures of object light during digital hologram record and reference light, and the hologram of piecemeal has similar spectrum distribution at frequency domain, adopt total variational and the L1 mould Method for minimization specific aim reconstructed number hologram of Multilevel Block iteration in frequency domain, improve the quality of reproduced image.Be reconstructed digital hologram after decompression, the optical system such as application space optical modulator can carry out 3 D stereo display.The invention provides method and all can reach more excellent level for digital hologram compress technique qualitatively in compression ratio and Postprocessing technique.

Technical scheme provided by the invention is:

A kind of digital hologram coding and transmission method adopting compressed sensing, described method is compressed digital hologram based on compressed sensing, transmits and is decoded, total variational and the L1 mould Method for minimization reconstructed number hologram pointedly of Multilevel Block iteration is adopted in frequency domain, to reach high compression rate and the low loss of information, to improve the object of the quality of reproduced image, reproduced image can be applicable to 3 D stereo display; Described digital hologram coding and transmission method specifically comprises the steps:

1) original color three-dimensional body is transformed into rgb space, by Fresnel off-axis gaussian beam computational methods, original color three-dimensional body is recorded as digital hologram; Or adopt optical table to build Fresnel off-axis hologram recording beam path, use ccd video camera record to obtain digital hologram;

2) to step 1) digital hologram that obtains compresses, comprising: carry out down-sampled to described digital hologram, then carry out compressed encoding to sampled data, obtains packed data;

3) by step 2) packed data that obtains transmits between transmitting terminal and receiving terminal;

4) packed data that receiving terminal receives is decompressed, be included in receiving terminal and decode, then by the total variational of Multilevel Block iteration and L1 mould Method for minimization, decoded data is reconstructed, obtain the hologram after reconstructing;

5) to step 4) hologram after the reconstruct that obtains reproduces, and obtains reproduction image.

For the digital hologram coding and transmission method of above-mentioned employing compressed sensing, further, step 2) specifically use change density sampling matrix to carry out down-sampled with the sample rate lower than Nyquist law to digital hologram, to reach the object of the data volume reducing next code transmission; Further sampled data compressed by Huffman lossless coding method again and encode.

For the digital hologram coding and transmission method of above-mentioned employing compressed sensing, further, step 2) describedly carry out down-sampled to digital hologram, specifically comprise the steps:

211) by a length be the signal f of N, be expressed as the linear combination of one group of orthonormal basis, as shown in Equation 4:

F=Ψ θ (formula 4)

In formula 4, Ψ=[ψ ₁ψ ₂ψ _n], θ is ψ _iweight coefficient; If θ only has K (K < < N) individual nonzero element, signal f is claimed to have K degree of rarefication at territory Ψ;

212) signal f is transformed to after certain transform domain obtains its rarefaction representation, M × N (K < M < < N) is tieed up calculation matrix and projects to conversion coefficient θ by through type 5, obtain M measured value y, to reach the object of the quantity reducing measured value:

$y=\mathrm{\&Phi;}\mathrm{\&theta;}={\mathrm{\&Phi;\&Psi;}}^{-1}f=\widehat{\mathrm{\&Phi;}}f$ (formula 5)

In formula 5, for M × N ties up observing matrix, be chosen as gaussian random matrix, two-value random matrix or structuring random matrix; Ψ ^-1for the inverse matrix of Ψ; Measured value y is that the Signal Compression of required acquisition represents; Describedly be transformed to Fourier transform, dct transform or wavelet transformation.

For the digital hologram coding and transmission method of above-mentioned employing compressed sensing, further, step 212) in, observing matrix for random binary matrix, the data format of measured value and image pixel data form are consistent, thus the loss of additional compression rate can not be introduced.

For the digital hologram coding and transmission method of above-mentioned employing compressed sensing, further, step 212) in, observing matrix for the change density sampling matrix improved random binary matrix, through type 6 ~ formula 7 produces a random binary matrix pockety, and wherein distribution density becomes negative correlation with range image centre distance:

$mask(x,y)=\left\{\begin{array}{cc}1,& r(x,y)\&GreaterEqual;g(x,y)\\ 0,& r(x,y)<g(x,y)\end{array}\right.$ (formula 6)

$r(x,y)=1-\frac{\sqrt{{(x-m/2)}^2+{(y-n/2)}^2}}{\sqrt{{(m/2)}^2+{(n/2)}^2}}$ (formula 7)

In formula 6 ~ formula 7, g (x, y) be by meeting [0,1] random matrix of the element value composition of even random distribution between, the matrix that r (x, y) is made up of apart from picture centre normalized cumulant its pixel coordinate, (x, y) be matrix pixel coordinate, m, n are the size of image and sampling matrix; Act on hologram with observing matrix g (x, y) for mask, extract wherein fractional-sample value, thus reduce sample rate further.

For the digital hologram coding and transmission method of above-mentioned employing compressed sensing, further, step 3) specifically use TCP/IP host-host protocol to be transmitted between transmitting terminal and receiving terminal by packed data.

For the digital hologram coding and transmission method of above-mentioned employing compressed sensing, further, step 4) total variational of described use Multilevel Block iteration and L1 mould Method for minimization carry out iterative reconstruction to decoded data, obtain the hologram after reconstructing, the measuring-signal y being specifically M by length reconstructs and obtains the process that length is the measuring-signal f of N, comprises the steps:

421) minimum L is as shown in Equation 8 solved ₀norm:

$\begin{array}{c}\begin{array}{ccc}\widehat{\mathrm{\&theta;}}={\min }_{\mathrm{\&theta;}}\left|\right|\mathrm{\&theta;}|{|}_0& s.t.& y=\mathrm{\&Phi;}\mathrm{\&theta;}={\mathrm{\&Phi;\&Psi;}}^{-1}f,\end{array}\\ \left|\right|\mathrm{\&theta;}|{|}_p={\left({\mathrm{\&Sigma;}}_{i=1}^N{\left|{\mathrm{\&theta;}}_i\right|}^p\right)}^{1/p}\end{array}$ (formula 8)

In formula 8, Ψ=[ψ ₁ψ ₂ψ _n], represent one group of orthonormal basis, θ is ψ _iweight coefficient, represent that the signal of reconstruct is to ψ _iweight coefficient, Ψ ^-1for the inverse matrix of Ψ, Φ Ψ ^-1for observing matrix, y is measured value, and f is primary signal; || θ || _pfor L _pthe definition of norm.

422) the minimum L of formula 8 will be solved ₀norm, by with L ₁norm carrys out L of equal value ₀norm is converted into optimization L ₁minimum norm, solves L in conjunction with Methods Based on Total Variation ₁norm minimum problem;

423) total variational and L is solved ₁norm minimum problem, reconstruct compressed sensing signal, obtains the hologram after reconstructing:

$\begin{array}{c}\begin{array}{ccc}\widehat{\mathrm{\&theta;}}=\underset{\mathrm{\&theta;}}{min}\left(\right|\left|\mathrm{\&theta;}\right|{|}_1+\mathrm{\&alpha;}TV\left(f\right))& s.t.& y=\mathrm{\&Phi;}\mathrm{\&theta;}={\mathrm{\&Phi;\&Psi;}}^{-1}f\end{array},\\ whichTV\left(f\right)=\sqrt{{\left(f_{i+1,j}-f_{i,j}\right)}^2+{\left(f_{i,j+1}-f_{i,j}\right)}^2}\end{array}$ (formula 9)

In formula 9, Ψ=[ψ ₁ψ ₂ψ _n], represent one group of orthonormal basis, be Fourier transform substrate, θ is ψ _iweight coefficient, represent that the signal of reconstruct is to ψ _iweight coefficient, Ψ ^-1for the inverse matrix of Ψ, Φ Ψ ^-1for observing matrix, be change density random binary matrix, y is measured value, and f is primary signal; || θ || ₁represent L ₁norm, TV represents the definition of total variational, and α represents L ₁weight between norm and total variational.

Because each pixel of digital hologram all carries the partial information of other pixel, therefore, L ₁norm can ensure the consistency of reconstructed hologram and original hologram image, simultaneously, during digital hologram record, object information is stored in upper frequency part by the interventional procedures of object light and reference light, total variational is extracted the high-frequency information of image, can ensure the consistency of reconstructed hologram and original hologram image detail.

For the digital hologram coding and transmission method of above-mentioned employing compressed sensing, further, step 423) in, adopt block-iterative solutions piecemeal reconstructed number hologram.Hologram is carried out Multilevel Block, is initial with the minimum piecemeal in center, use step 423) described in total variational and L ₁mould Method for minimization, reconstructs the hologram of this piecemeal part; Secondly, by the frequency domain information of reconstruct piecemeal estimate, with the initial condition of iteration, to carry out iterative reconstruction to 8 partition neighborhood of this central partition as frequency-domain sparse; 9 piecemeals after this being reconstructed merge into the minimum piecemeal in new center, repeat this restructuring procedure, until complete the reconstruct of whole digital hologram information.

For the digital hologram coding and transmission method of above-mentioned employing compressed sensing, further, step 5) described reconstructed hologram to be reproduced, specifically according to Fresnel off-axis gaussian beam algorithm, by irradiating and Fresel diffraction two processes from axle reference light, realize digital hologram to be reproduced as initial three-dimensional object;

Wherein, reproduce formula, i.e. formula 10 according to off-axis gaussian beam, utilize the playback light R (x, y) consistent with reference light to irradiate hologram I _h(x, y) reproduces:

I _H(x，y)×R(x，y)＝(|R(x，y)| ²+|U(x，y)| ²)R(x，y)+|R(x，y)| ²U(x，y)+R ²(x，y)U ^*(x，y)

(formula 10)

In formula 10, I _hthe light intensity that (x, y) is hologram record, R (x, y) is reference light and playback light wavefront function, and U (x, y) is original objects reproduction wavefront function, U ^*the conjugation item that (x, y) is reproduction image;

Diffraction process through reproducing light-struck digital hologram light wave is calculated by means of Fresnel diffraction (formula 2 ~ formula 3), obtains the 3-d reproduction picture of original objects at diffraction plane.

The digital hologram coding and transmission method of above-mentioned employing compressed sensing uses change density sampling matrix down-sampled to digital hologram with the sample rate lower than Nyquist law, reduce the data volume of next code transmission, further data compressed by Huffman coding method and encode; After receiving terminal decoding, by total variational and the L1 mould Method for minimization reconstructed number hologram of Multilevel Block iteration.This scheme reduces system complexity and the power consumption of compression transmitting terminal, improve compression speed and compression ratio, the quality of reproduced image after receiving terminal improves compression, the image reproducing that can regulate grade can be provided, applied optics system the hologram of reconstruct can be carried out 3 D stereo display simultaneously.

Compared with prior art, the invention has the beneficial effects as follows:

The invention provides a kind of digital hologram coding and transmission method adopting compressed sensing, compression transmission is carried out for digital hologram based on compressed sensing, because digital hologram is interference fringe image, each pixel all carries the partial information of other pixel, the Global Information of digital hologram can be inferred by part Pixel Information, therefore, can carry out down-sampled to digital hologram by the sample rate far below Nyquist law, greatly reduce the data volume of compression transmission system process, and improve the compression ratio of image.Meanwhile, because Sampling Compression process does not introduce complex calculation, system complexity and the power consumption of compression transmitting terminal effectively can be reduced.Because object information is stored in upper frequency part by the interventional procedures of object light during digital hologram record and reference light, and the hologram of piecemeal has similar spectrum distribution at frequency domain, adopt total variational and the L1 mould Method for minimization specific aim reconstructed number hologram of Multilevel Block iteration in frequency domain, improve the quality of reproduced image.Be reconstructed digital hologram after decompression, the optical system such as application space optical modulator can carry out 3 D stereo display.Advantage of the present invention is mainly reflected in following several respects:

(1) change density sampling matrix is used directly to carry out down-sampled to digital hologram in spatial domain with the sample rate lower than Nyquist law, reduce the data volume of compression transmission system process, compare the method that general measure matrix reduces measured value, further raising compression ratio, reduces operand and the system complexity of transmitting terminal;

(2) object information is stored in upper frequency part by interventional procedures during digital hologram record, and the hologram of piecemeal has similar spectrum distribution at frequency domain, adopt total variational and the L1 mould Method for minimization specific aim reconstructed number hologram of Multilevel Block iteration in frequency domain, improve the quality of reproduced image.

(3) be reconstructed digital hologram after decompressing, the optical system such as application space optical modulator can carry out 3 D stereo display.

Accompanying drawing explanation

Fig. 1 is the FB(flow block) of the digital hologram compression transmitting method of employing compressed sensing provided by the invention.

Fig. 2 is the schematic diagram of three-dimensional body and composition diagram picture;

Wherein, (a) is initial three-dimensional object; B () is lena image; C () is USAF image; D () is PM5544 resolution chart.

Fig. 3 is the comparison diagram of original image and compressed images;

Wherein, (a) is original hologram; B () is hologram after compression; C the reproduction figure of () original hologram (a), reproduces distance 500mm; D after () compression, the reproduction figure of hologram (b), reproduces distance 500mm; E the reproduction figure of () original hologram (a), reproduces distance 505mm; F the reproduction figure of () original hologram (b), reproduces distance 505mm; G the reproduction figure of () original hologram (a), reproduces distance 510mm; H the reproduction figure of () original hologram (a), reproduces distance 500mm;

Fig. 4 is the present invention program and JPEG compression method reproduced image PSNR figure-of-merit curve figure under different compression ratio.

Fig. 5 is the present invention program's reproduced image NCC under different compression ratio, K, Q figure-of-merit curve figure.

Fig. 6 is the schematic diagram of the oblique spatial filter matrices in the embodiment of the present invention; In figure, 0,1 ,-1 is the numerical value of matrix element.

Wherein, the numerical value of 0,1 ,-1 representing matrix element.

Fig. 7 is the hardware system figure adopting optical means record digital hologram;

Wherein, Laser represents laser, and Spatialfilter represents spatial filter, and BS1, BS2 represent beam splitter, M ₁, M ₂, M ₃represent speculum, lens1, lens2 represent beam expanding lens, and Object representative is recorded object, and CCD represents light-sensitive element; PC1, PC2 represent receiving terminal and transmitting terminal, and Network represents transmitting procedure, and output represents follow-up output system.

Embodiment

Below in conjunction with accompanying drawing, further describe the present invention by embodiment, but the scope do not limited the present invention in any way.

Compression sensing method is used for compressed image and comprises two basic processes: one is when compressing, and reduces data number and reaches compression object; Two is when decompressing, and is used in one the date restoring image compressing and obtain; Multiple implementation method is had in concrete process.Such as: in compression, can by the pixel of down-sampled mode Direct Sampling part image; Also can be multiplied with image by calculation matrix, project image onto low-dimensional (can be understood as and multiple pixel values of image are become a measured value by certain Combination of Methods); When decompressing, the method for above-mentioned document two, have employed the processing procedure of hologram-> sampling-> reproduction image; The method of document three is that hologram-> measures-> (method of measurement data reconstructed hologram must be used to be reconstructed)-> hologram-> reproduction image >; The method of document four is hologram-> sampling-> (must use the method for sampled data reconstruction render picture)-> reproduction image; And method employing provided by the invention is that hologram-> sampling-> uses the method for sampled data reconstructed hologram to obtain the processing procedure of hologram-> reproduction image.

The FB(flow block) of the digital hologram compression transmitting method of employing compressed sensing provided by the invention as shown in Figure 1, the method is applicable to process Fresnel off-axis hologram, comprise produced by Computer Simulation or by optical system record, be not limited to digital hologram.In embodiments of the present invention, the invention provides method specifically to comprise the steps:

1) original color three-dimensional body is transformed into rgb space and carries out process calculating; By Fresnel off-axis gaussian beam algorithm, initial three-dimensional object is recorded as digital hologram; Or adopt optical table to build Fresnel off-axis hologram recording beam path, use ccd video camera record digital hologram;

The method of use computer recording digital hologram is: according to Fresnel off-axis gaussian beam algorithm, initial three-dimensional object is recorded as digital hologram.Fresnel off-axis hologram record interferes two parts to form by Fresel diffraction with from axle reference light.

Wherein, Fresel diffraction (Fresneldiffraction) refers to the diffraction of light wave at near-field region.Fresnel Diffraction Integral formula can be used for calculating the propagation of light wave at near-field region.Calculate and superposed to the Fresel diffraction of holographic recording plane by three-dimensional body every bit institute outgoing light wave, three-dimensional body can be calculated before the Object light wave of holographic recording plane.

When axle reference light is interfered and referred to hologram reconstruction, have reproduction image and twin image and Zero-order diffractive speck simultaneously, overlappedly affect reproduced image quality.Introduce and exist before Object light wave the reference light of certain angle when hologram record, different order diffraction picture can be separated, obtain separately reproduced image clearly.

According to off-axis gaussian beam formula, complex amplitude function before interfering record object light diffracted wave is utilized to form hologram I _h(x, y):

I _H(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, I _hthe light intensity that (x, y) is hologram record, R (x, y) is function before reference light wave, and U (x, y) is original objects wavefront function.R ^*(x, y) and U ^*(x, y) is respectively the conjugation item of R (x, y) and U (x, y).

The diffraction process of object light wave is calculated by means of Fresnel diffraction (formula 2):

$U(x,y)\&ap;\frac{\exp \left(jkd\right)}{j\mathrm{\&lambda;}d}\underset{\mathrm{\&Sigma;}}{\&Integral;\&Integral;}O(x_0,y_0)\exp \&lsqb;jk\frac{{(x-x_0)}^2+{(y-y_0)}^2}{2d}\&rsqb;{\mathrm{dx}}_0{\mathrm{dy}}_0$ (formula 2)

In formula 2, d is diffraction distance, and k is wave number, and j is imaginary unit; (x ₀, y ₀) be initial object wave plane, (x, y) is diffraction plane; O (x ₀, y ₀) be initial object wave plane information, U (x, y) is complex amplitude function before diffraction distance is the Object light wave of d.Use computer to calculate this diffraction integral, fast Fourier transform can be carried out by through type 3:

$\begin{array}{c}U\left(p\mathrm{\&Delta;}x,q\mathrm{\&Delta;}y\right)=\frac{\exp \left(jkd\right)}{j\mathrm{\&lambda;}d}\exp \&lsqb;\frac{jk}{2d}\left({\left(p\mathrm{\&Delta;}x\right)}^2+{\left(q\mathrm{\&Delta;}y\right)}^2\right)\&rsqb;\\ \&times;F{\left\{O\left({\mathrm{m\&Delta;x}}_0,{\mathrm{n\&Delta;y}}_0\right)\exp \&lsqb;\frac{jk}{2d}{\left({\mathrm{m\&Delta;x}}_0\right)}^2+{\left({\mathrm{n\&Delta;y}}_0\right)}^2\&rsqb;\right\}}_{\frac{p\mathrm{\&Delta;}x}{\mathrm{\&lambda;}d},\frac{q\mathrm{\&Delta;}y}{\mathrm{\&lambda;}d}}\\ \left(p,q,m,n=-\frac{N}{2},-\frac{N}{2}+1,\mathrm{...},\frac{N}{2}-1\right)\end{array}$ (formula 3)

In formula 3, F represents Fourier transform, and d is diffraction distance, and k is wave number, and j is imaginary unit; L ₀for initial object wave plane sample range; The sampling number of initial object wave plane is N × N, i.e. the number of pixels of initial pictures; Initial object wave plane sampled point be spaced apart Δ x ₀=Δ y ₀=L ₀/ N; Δ x=Δ y is initial object wave plane discrete Fourier transform (DFT) post-sampling interval, and in spatial domain, corresponding is with it sampling interval of diffraction plane.

Make the method optically recording digital hologram be: employing be that optoelectronic detection device (ccd video camera) records the interference fringe of object light wave and reference light wave and is stored in computer.

As shown in Figure 7, wherein, Laser represents laser, and Spatialfilter represents spatial filter, and BS1, BS2 represent beam splitter, M ₁, M ₂, M ₃represent speculum, lens1, lens2 represent beam expanding lens, and Object representative is recorded object, and CCD represents light-sensitive element; PC1, PC2 represent receiving terminal and transmitting terminal, and Network represents transmitting procedure, and output represents follow-up output system; The light that laser sends is divided into two bundles by beam splitter BS1; A branch ofly to reflect through mirror M 2, enter beam expanding lens lens1 and expand and collimate, become directional light, be irradiated to be recorded on object and form object wave, object wave is irradiated to the light-sensitive element surface of digital camera through beam splitter BS2; Another bundle becomes directional light through beam expanding lens collimating mirror and mirror M 1, then turns to through beam splitter BS2, forms reference light, and superpose in CMOS (or CCD) photoelectric device plane with object wave and interfere, formation hologram.

2) use change density sampling matrix to carry out down-sampled to hologram, by Huffman lossless coding method, compressed encoding is carried out to sampled data;

Compression process is made up of random observation matrix sampling and Huffman lossless coding.

2.1 random observation matrix samplings

The design of random observation matrix is the key of compressed sensing technique compresses sampling.Observing matrix carries out dimensionality reduction observation to original signal and obtains a small amount of sampled data, in order to guarantee from measured value accurate reconstruction signal, and demand fulfillment and the limited equidistant character of the sparse base of original signal.

A length is the signal f of N, can be expressed as the linear combination of one group of orthonormal basis, as shown in Equation 4:

F=Ψ θ (formula 4)

In formula 4, Ψ=[ψ ₁ψ ₂ψ _n], θ is ψ _iweight coefficient.If θ only has K (K < < N) individual nonzero element, signal f is claimed to have K degree of rarefication at territory Ψ.This provides the foundation for compression measurement afterwards.

Signal f is transformed to after certain transform domain obtains its rarefaction representation, ties up projection matrix by M × N (K < M < < N) and conversion coefficient θ is projected, obtain M measured value y, namely

$y=\mathrm{\&Phi;}\mathrm{\&theta;}={\mathrm{\&Phi;\&Psi;}}^{-1}f=\widehat{\mathrm{\&Phi;}}f$ (formula 5)

In formula 5, for M × N ties up observing matrix, Ψ ^-1for the inverse matrix of Ψ, measured value y is exactly that the required Signal Compression obtained represents.In compression measuring process, in must ensureing that calculation matrix can not be gathered 2 different sparse signal element map to same sampling.Therefore, observing matrix the constraints that demand fulfillment is certain, as retrained equidistant condition (RestrictedIsometryProperty, RIP) etc.Conventional observing matrix be chosen as gaussian random matrix, two-value random matrix, structuring random matrix etc.

In order to reach the object of compression, can not realize only by the quantity reducing measured value, what the design of observing matrix also needed to consider measurement field chooses the data type with measured value.In a computer, digital hologram generally stores with bitmap form, and each pixel of image can use the shaping records of values represented by certain bit number.In transform domain process, as Fourier transform, dct transform, wavelet transformation etc., the coefficient after conversion needs to use floating number record.In general, the bit number that the bit number in computer needed for floating number record will be several times as much as needed for the record of shaping number scale.Same, adopt the observing matrix of the floating number compositions such as gaussian random matrix, measured value also needs to use floating number record.This will bring extra compression ratio loss.Meanwhile, the method adopting the column vector of calculation matrix and hologram or hologram to be multiplied is measured, and will bring huge operation time and space cost.

Therefore, the present invention adopts random binary matrix directly to sample to digital hologram in spatial domain.Namely, in formula 5, get for random binary matrix, getting f is digital hologram matrix, and the two corresponding element carries out point multiplication operation.Random binary matrix is by 0 of random distribution, 1 value composition.Use the sampling of random binary logm word hologram, the data format of measured value will be consistent with image pixel data form, can not introduce the loss of additional compression rate.Simultaneously, the present invention is directed to the characteristic of diffraction process during digital hologram record, general random two values matrix is improved, adopt change density sampling matrix, produce a random binary matrix pockety, wherein distribution density becomes negative correlation with range image centre distance:

$mask(x,y)=\left\{\begin{array}{cc}1,& r(x,y)\&GreaterEqual;g(x,y)\\ 0,& r(x,y)<g(x,y)\end{array}\right.$ (formula 6)

$r(x,y)=1-\frac{\sqrt{{(x-m/2)}^2+{(y-n/2)}^2}}{\sqrt{{(m/2)}^2+{(n/2)}^2}}$ (formula 7)

In formula 6 ~ formula 7, g (x, y) be by meeting [0,1] random matrix of the element value composition of even random distribution between, the matrix that r (x, y) is made up of apart from picture centre normalized cumulant its pixel coordinate, (x, y) be matrix pixel coordinate, m, n are the size of image and sampling matrix.Act on hologram with this observing matrix for mask, extract wherein fractional-sample value, reduce sample rate further.

2.2 Huffman lossless codings

Huffman coding (HuffmanCoding) is a kind of entropy code for lossless data compression (power coding) algorithm.Huffman coding uses variable length coding table to source encoding symbols, occur that the letter that probability is high uses shorter coding, otherwise occur probability low then use longer coding, this just make coding after the average length of character string, desired value reduce, thus reach the object of Lossless Compression data.

By source symbol by the descending order arrangement of the probability occurred, the source symbol of two minimum probability is carried out combination be added, and repeat this step, all the time larger probability branch is placed on top, until only surplus next source symbol and probability reaches 1.0; 1 is appointed as to one, the top of often pair of combination, is appointed as 0 for following one, draws by the path of each source symbol to probability 1.0, write down 1 and 0 along path; 1,0 sequence is write out for each source symbol, then just obtains non-isometric Huffman code from right to left.

Data after sampling matrix is down-sampled, its span is centrifugal pump limited between 0 ~ 255, and meanwhile, value interval probability near hologram pixel mean value is higher, and the probability away from mean value reduces gradually.Therefore, use huffman coding can carry out further compressed encoding to sampled data, reduce transmitted data amount.

3) TCP/IP host-host protocol is used to be transmitted between transmitting terminal and receiving terminal by packed data;

Transmission Control Protocol is commonly called Connection-oriented Protocol, and this agreement ensures reliably effectively data to be sent to receiving terminal from transmitting terminal.Before main frame uses Transmission Control Protocol to send data to another main frame, transport layer can start a process, for creating linking between destination host.By this link, the session between main frame or communication data stream can be followed the tracks of.Meanwhile, this process also guarantees that every platform main frame is all known and carried out communication preparation.Complete TCP Dialog request creates bi-directional session between main frame.

The reliability of TCP communication is to employ connection-oriented session.Before transmitting terminal uses Transmission Control Protocol to send data to receiving terminal, transport layer can start a process, for creating linking between receiving terminal.By this link, the session between main frame or communication data stream can be followed the tracks of.Meanwhile, this process also guarantees that every platform main frame is all known and carried out communication preparation.Complete TCP Dialog request creates bi-directional session between main frame.After conversation establishing, receiving terminal sends confirmation for the data segment received to transmitting terminal.In TCP session, these confirmations constitute the basis of reliability.Transmitting terminal sends the data segment comprising verification value, and the sequential value that its value equals to receive adds 1, and adds the synchronizing sequence value of self.By this verification value, response and the last data segment being sent to transmitting terminal can couple together by receiving terminal.The receiving terminal sent with verification value responds, and its value equals Receiving Order train value and adds 1, completes whole connection procedure with this.

4) decoding data is received to receiving terminal, use total variational method to carry out iterative reconstruction to decoded data, obtain the hologram after reconstructing;

4.1 Hofmann decodings: according to the coding schedule used in cataloged procedure, circulate a reading bit from the bit stream received, and forms new code word, inquire about this code word in coding schedule, effective for correspondence code word decoded.Observing matrix sampled data is obtained after decoding.

The total variational of 4.2 Multilevel Block iteration and L1 mould Method for minimization pin

The measuring-signal y that namely compressed sensing technology signal reconstruction is M by length reconstructs the process that length is the measuring-signal f of N.This process can by solving minimum L ₀norm Resolving probiems, that is:

$\begin{array}{c}\begin{array}{ccc}\widehat{\mathrm{\&theta;}}={\min }_{\mathrm{\&theta;}}\left|\right|\mathrm{\&theta;}|{|}_0& s.t.& y=\mathrm{\&Phi;}\mathrm{\&theta;}={\mathrm{\&Phi;\&Psi;}}^{-1}f,\end{array}\\ \left|\right|\mathrm{\&theta;}|{|}_p={\left({\mathrm{\&Sigma;}}_{i=1}^N{\left|{\mathrm{\&theta;}}_i\right|}^p\right)}^{1/p}\end{array}$ (formula 8)

In formula 8, Ψ=[ψ ₁ψ ₂ψ _n], represent one group of orthonormal basis; θ is ψ _iweight coefficient; represent that the signal of reconstruct is to ψ _iweight coefficient; Ψ ^-1for the inverse matrix of Ψ; Φ Ψ ^-1for observing matrix; Y is measured value; F is primary signal; || θ || _pfor L _pthe definition of norm.

Because solving of formula 8 is a np hard problem, is difficult to solve in polynomial time, even cannot verifies the reliability of solution.L ₁under minimum norm under compressed sensing assumed condition and L ₀minimum norm has equivalence, can obtain identical solution.So above formula is converted into L ₁optimization problem under minimum norm.L ₁norm minimum is by with L ₁norm carrys out approximate 0 norm, L ₁norm minimum is convex optimization problem, solution procedure can have been changed into a linear programming problem.

Total variation method be by Rudin, Osher and Fatemi propose solve L ₁norm minimum method, the method becomes the most successful method in image restoration now.In the present invention, total variational is minimized and L ₁norm minimum combines, for compressed sensing signal reconstruction:

$\begin{array}{c}\begin{array}{ccc}\widehat{\mathrm{\&theta;}}=\underset{\mathrm{\&theta;}}{min}\left(\right|\left|\mathrm{\&theta;}\right|{|}_1+\mathrm{\&alpha;}TV\left(f\right))& s.t.& y=\mathrm{\&Phi;}\mathrm{\&theta;}={\mathrm{\&Phi;\&Psi;}}^{-1}f\end{array},\\ whichTV\left(f\right)=\sqrt{{\left(f_{i+1,j}-f_{i,j}\right)}^2+{\left(f_{i,j+1}-f_{i,j}\right)}^2}\end{array}$ (formula 9)

In formula 9, Ψ=[ψ ₁ψ ₂ψ _n], represent one group of orthonormal basis; θ is ψ _iweight coefficient; represent that the signal of reconstruct is to ψ _iweight coefficient; Ψ ^-1for the inverse matrix of Ψ; Φ Ψ ^-1for observing matrix; Y is measured value; F is primary signal; || θ || ₁represent L ₁norm; TV represents the definition of total variational; α represents L ₁weight between norm and total variational.

Because each pixel of digital hologram all carries the partial information of other pixel, therefore, L ₁norm can ensure the consistency of reconstructed hologram and original hologram image, simultaneously, during digital hologram record, object information is stored in upper frequency part by the interventional procedures of object light and reference light, total variational is extracted the high-frequency information of image, can ensure the consistency of reconstructed hologram and original hologram image detail.

Because the hologram of piecemeal has similar spectrum distribution at frequency domain, the present invention adopts the reconstructing method of Multilevel Block iteration.The mode of digital hologram according to central partition and 8 neighborhoods thereof split, these 9 piecemeal spectrum distribution have consistency.Central piecemeal is split further with same partitioning scheme, obtains the Multilevel Block of digital hologram.In sampling process, central partition takes more sampled value, and first, reconstruction center piecemeal can obtain reconstructed image more accurately; Secondly, utilize the central partition frequency domain information after reconstruct as the openness estimation of its 8 neighborhood and iteration initial condition, can with less sampled value more accurate reconstructed residual information.After obtaining these 9 piecemeal reconfiguration information, be combined into new central piecemeal, continued 8 partition neighborhood of the new central piecemeal of reconstruct, until obtain whole digital hologram reconfiguration information.

5) reconstructed hologram is reproduced, compare with original hologram reproduced image, adopt objective evaluation Standard Judgement compression algorithm quality;

Reconstructed hologram being reproduced, specifically according to Fresnel off-axis gaussian beam algorithm, digital hologram is reproduced as initial three-dimensional object, needing to reproduce with Fresel diffraction two process implementation Fresnel off-axis holograms by irradiating from axle reference light.

Reproduce formula according to off-axis gaussian beam, utilize the playback light R (x, y) consistent with reference light to irradiate hologram I _h(x, y) reproduces:

I _H(x，y)×R(x，y)＝(|R(x，y)| ²+|U(x，y)| ²)R(x，y)+|R(x，y)| ²U(x，y)+R ²(x，y)U ^*(x，y)

(formula 10)

In formula 10, I _hthe light intensity that (x, y) is hologram record, R (x, y) is reference light and playback light wavefront function, and U (x, y) is original objects reproduction wavefront function, U ^*the conjugation item that (x, y) is reproduction image.

Diffraction process through reproducing light-struck digital hologram light wave is calculated by means of Fresnel diffraction (formula 2 ~ formula 3), can obtain the 3-d reproduction picture of original objects at diffraction plane.

In order to test compression ratio and the reproduced image quality of this programme, the evaluation methods such as Y-PSNR (PSNR), normalization relative coefficient (NCC), fuzzy coefficient (K) and quality factor (Q) are adopted to weigh the quality of reproduced image respectively.

5.1 Y-PSNRs (PSNR)

Y-PSNR (PSNR) is for weighing the image reconstruction quality after losing compressed encoding, and its computational methods are:

$PSNR=10\&times;{\log }_{10}\&lsqb;\frac{{(2^b-1)}^2}{MSE}\&rsqb;$ (formula 11)

$MSE=\frac{1}{m\&times;n}\underset{i=1,j=1}{\overset{m,n}{\&Sigma;}}{\&lsqb;X\left(i,j\right)-Y\left(i,j\right)\&rsqb;}^2$ (formula 12)

Wherein, MSE represents mean square error, the bit number of each pixel of b representative image, X (i, j) represent the pixel value of original image at point (i, j), Y (i, j) represents original image at point (i, j) pixel value, m, n representative image size.

5.2 normalized-cross-correlation function (NCC)

Normalized-cross-correlation function (NCC) is used for weighing the correlation of the image after Compress softwares and former figure.Formula is:

$NCC=\frac{1}{m\&times;n}\underset{i,j}{\&Sigma;}\frac{\&lsqb;X(i,j)-\stackrel{\&OverBar;}{X}\&rsqb;\&lsqb;Y(i,j)-\stackrel{\&OverBar;}{Y}\&rsqb;}{{\mathrm{\&sigma;}}_X{\mathrm{\&sigma;}}_Y}$ (formula 13)

In formula 13, X (i, j) represents the pixel value of original image at point (i, j), and Y (i, j) represents the pixel value of original image at point (i, j), and X, Y are respectively their mean value, σ _xand σ _ytheir standard deviation of difference, m, n representative image size.NCC value is more close to 1, and image difference is less, and the quality namely after image compression decompress(ion) is better.

5.3 fuzzy coefficients (K)

Fuzzy coefficient K is defined as the ratio of the HFS of the image zooming-out after original image and Compress softwares.Consider that the transmission of image delivering system edge and details is generally direction-free, therefore tilted direction edge and the transmission coefficient of details can represent details transmission that is vertical, horizontal direction, and mix due to the level of output image, vertical detail and blocking artifact, not easily represent fog-level, therefore choose the derivative-type spatial filter (as shown in Figure 6) of tilted direction, only compare the transmission of tilted direction edge and details, the transmission coefficient of whole image border and details can be represented, i.e. fuzzy coefficient:

$K_{blur}=\frac{S_{i,out}}{S_{i,in}},S_i=\underset{i}{\&Sigma;}\underset{j}{\&Sigma;}{y}_f^{\&prime;}(i,j)$ (formula 14)

Wherein S _ibe defined as edge energy feature, y ' _f(i, j) is the value that pixel value that (i, j) puts obtains after the process of tilted direction derivative-type spatial filter, K _blurfor edge energy and the input edge energy ratio of output.Close to 1, K value more represents that the picture quality after Compress softwares is better.

5.3 quality factors (Q)

Quality factor (Q) combines three image faults and weighs factor: impairment correlations, average distortion and contrast distortion.Be specifically defined as:

$Q=\frac{4{\mathrm{\&sigma;}}_{xy}XY}{({\mathrm{\&sigma;}}_x^2+{\mathrm{\&sigma;}}_y^2)(X^2+Y^2)}$ (formula 15)

Wherein { x _i| i=1,2 ... N} and { y _i| i=1,2 ... N} represents the sets of pixel values of image after former figure and Compress softwares respectively, and X, Y are respectively their mean value.σ _xand σ _ytheir standard deviation of difference.The general range of Q value is [-1,1], and more represent that the image after Compress softwares is more similar to original image close to 1, the picture quality namely after Compress softwares is better.

Fig. 2 is the schematic diagram of three-dimensional body and composition diagram picture.In the present embodiment, record object by being placed in different distance, three pictures of different angles form, as Fig. 2 (a), bulk is 10mm × 10mm × 10mm; Lena image recording distance in Fig. 2 (b) is 510mm; 1951 USAF resolution detected image (Fig. 2 (c), USAF image) recording distances are 500mm to 510mm; PM5544 colour TV signal resolution chart (Fig. 2 (d), PM5544 test pattern) recording distance is 500mm to 510mm.Fig. 3 is the comparison diagram of original image and compressed images; The original hologram of record is as shown in Fig. 3 (a); Hologram after overcompression transmission is as shown in Fig. 3 (b), and compression ratio is 10%; Fig. 3 (c) and Fig. 3 (d) contrast apart from for 500mm reproduced image reproducing for hologram after original hologram and compression; Fig. 3 (e) and Fig. 3 (f) contrast apart from for 500mm reproduced image reproducing for hologram after original hologram and compression; Fig. 3 (g) and Fig. 3 (h) contrast apart from for 500mm reproduced image reproducing for hologram after original hologram and compression.

Digital hologram based on compressed sensing compression transmission plan provided by the invention uses change density sampling matrix down-sampled to digital hologram with the sample rate lower than Nyquist law, reduce the data volume of next code transmission, further data compressed by Huffman coding method and encode; After receiving terminal decoding, by total variational method reconstructed number hologram.This scheme reduces system complexity and the power consumption of compression transmitting terminal, improve compression speed and compression ratio, the quality of reproduced image after receiving terminal improves compression, the image reproducing that can regulate grade can be provided, applied optics system the hologram of reconstruct can be carried out 3 D stereo display simultaneously.Table 1 is the objective evaluation quality versus that the invention provides method and JPEG compression method reproduced image under different compression ratio:

Table 1 is the objective evaluation quality versus that the invention provides method and JPEG compression method reproduced image under different compression ratio

Fig. 4 is the present invention program and JPEG compression method reproduced image PSNR figure-of-merit curve figure under different compression ratio.Fig. 5 is the present invention program's reproduced image NCC under different compression ratio, K, Q figure-of-merit curve figure.

In sum, this programme has a good application prospect in the transmission of 3D hologram Information Compression.This programme thinking all can reach more excellent level for digital hologram compress technique qualitatively in compression ratio and Postprocessing technique.

It should be noted that the object publicizing and implementing example is to help to understand the present invention further, but it will be appreciated by those skilled in the art that: in the spirit and scope not departing from the present invention and claims, various substitutions and modifications are all possible.Therefore, the present invention should not be limited to the content disclosed in embodiment, and the scope that the scope of protection of present invention defines with claims is as the criterion.

Claims (9)

1. one kind adopts the digital hologram coding and transmission method of compressed sensing, described method is compressed digital hologram based on compressed sensing, transmits and is decoded, in wavelet field by total variational method reconstructed number hologram pointedly, improve the quality of reproduced image, reproduced image can be applicable to 3 D stereo display; Described digital hologram coding and transmission method specifically comprises the steps:

1) original color three-dimensional body is transformed into rgb space, by Fresnel off-axis gaussian beam computational methods, original color three-dimensional body is recorded as digital hologram; Or adopt optical table to build Fresnel off-axis hologram recording beam path, use ccd video camera record to obtain digital hologram;

2) sampling process: to step 1) digital hologram that obtains compresses, comprising: carry out down-sampled to described digital hologram, then carry out compressed encoding to sampled data, obtains packed data;

3) transmitting procedure: by step 2) packed data that obtains transmits between transmitting terminal and receiving terminal;

4) restructuring procedure: decompress to the packed data that receiving terminal receives, is included in receiving terminal and decodes, then carries out iterative reconstruction by total variational method to decoded data, obtains the hologram after reconstructing;

5) to step 4) hologram after the reconstruct that obtains reproduces, and obtains reproduction image.

2. adopt the digital hologram coding and transmission method of compressed sensing as claimed in claim 1, it is characterized in that, step 2) specifically use change density sampling matrix to carry out down-sampled with the sample rate lower than Nyquist law to digital hologram, to reach the object of the data volume reducing next code transmission; Further sampled data compressed by Huffman lossless coding method again and encode.

3. adopt the digital hologram coding and transmission method of compressed sensing as claimed in claim 1, it is characterized in that, step 2) describedly carry out down-sampled to digital hologram, specifically comprise the steps:

211) by a length be the signal f of N, be expressed as the linear combination of one group of orthonormal basis, as shown in Equation 4:

F=ψ θ (formula 4)

In formula 4, ψ=[ψ ₁ψ ₂ψ _n], θ is ψ _iweight coefficient; If θ only has K (K < < N) individual nonzero element, signal f is claimed to have K degree of rarefication at territory ψ;

212) signal f is transformed to after certain transform domain obtains its rarefaction representation, M × N (K < M < < N) is tieed up calculation matrix and projects to conversion coefficient θ by through type 5, obtain M measured value y, to reach the object of the quantity reducing measured value:

$y=\mathrm{\&Phi;\&theta;}=\mathrm{\&Phi;}{\mathrm{\&psi;}}^{-1}f=\widehat{\mathrm{\&Phi;}}f$ (formula 5)

In formula 5, for M × N ties up observing matrix, be chosen as gaussian random matrix, two-value random matrix or structuring random matrix; ψ ^-1for the inverse matrix of ψ; Measured value y is that the Signal Compression of required acquisition represents; Describedly be transformed to Fourier transform, dct transform or wavelet transformation.

4. adopt the digital hologram coding and transmission method of compressed sensing as claimed in claim 3, it is characterized in that, step 212) in, observing matrix for random binary matrix, the data format of measured value and image pixel data form are consistent, thus the loss of additional compression rate can not be introduced.

5. adopt the digital hologram coding and transmission method of compressed sensing as claimed in claim 4, it is characterized in that, step 212) in, observing matrix for the change density sampling matrix improved random binary matrix, through type 6 ~ formula 7 produces a random binary matrix pockety, and wherein distribution density and range image centre distance are inversely proportional to:

$\mathrm{mask}(x,y)=\left\{\begin{array}{cc}1,& r(x,y)\&GreaterEqual;g(x,y)\\ 0,& r(x,y)<g(x,y)\end{array}\right.$ (formula 6)

$r(x,y)=\frac{\sqrt{{(x-m/2)}^2+{(y-n/2)}^2}}{\sqrt{{(m/2)}^2+{(n/2)}^2}}$ (formula 7)

In formula 6 ~ formula 7, g (x, y) be by meeting [0,1] random matrix of the element value composition of even random distribution between, the matrix that r (x, y) is made up of apart from picture centre normalized cumulant its pixel coordinate, (x, y) be matrix pixel coordinate, m, n are the size of image and sampling matrix; Act on hologram with observing matrix g (x, y) for mask, extract wherein fractional-sample value, thus reduce sample rate further.

6. adopt the digital hologram coding and transmission method of compressed sensing as claimed in claim 1, it is characterized in that, step 3) specifically use TCP/IP host-host protocol to be transmitted between transmitting terminal and receiving terminal by packed data.

7. adopt the digital hologram coding and transmission method of compressed sensing as claimed in claim 1, it is characterized in that, step 4) described by total variational method, iterative reconstruction is carried out to decoded data, obtain the hologram after reconstructing, the measuring-signal y being specifically M by length reconstructs and obtains the process that length is the measuring-signal f of N, comprises the steps:

421) minimum L is as shown in Equation 8 solved ₀norm:

$\widehat{\mathrm{\&theta;}}={\min }_{\mathrm{\&theta;}}{\left|\right|\mathrm{\&theta;}\left|\right|}_0\mathrm{}s.t.\mathrm{}y=\mathrm{\&Phi;\&theta;}=\mathrm{\&Phi;}{\mathrm{\&Psi;}}^{-1}f,$

${\left|\right|\mathrm{\&theta;}\left|\right|}_p={\left({\mathrm{\&Sigma;}}_{i=1}^N{\left|{\mathrm{\&theta;}}_i\right|}^p\right)}^{1/p}$ (formula 8)

In formula 8, ψ=[ψ ₁ψ ₂ψ _n], represent one group of orthonormal basis; θ is ψ _iweight coefficient; represent that the signal of reconstruct is to ψ _iweight coefficient; ψ ^-1for the inverse matrix of ψ; Φ ψ ^-1for observing matrix; Y is measured value; F is primary signal; || θ || _pfor L _pthe definition of norm;

422) the minimum L of formula 8 will be solved ₀norm, by with L ₁norm carrys out approximate L ₀norm is converted into optimization L ₁minimum norm, solves L by linear programming method ₁norm minimum problem;

423) L is solved ₁norm minimum problem, minimizes total variational and L ₁norm minimum combines reconstruct compressed sensing signal, obtains the hologram after reconstructing:

$\widehat{\mathrm{\&theta;}}=\underset{\mathrm{\&theta;}}{\min }({\left|\right|\mathrm{\&theta;}\left|\right|}_1+\mathrm{\&alpha;TV}\left(f\right))\mathrm{}s.t.\mathrm{}y=\mathrm{\&Phi;\&theta;}=\mathrm{\&Phi;}{\mathrm{\&Psi;}}^{-1}f,$

$\mathrm{which}\mathrm{}\mathrm{TV}\left(f\right)=\sqrt{{(f_{i+1,j}-f_{i,j})}^2+{(f_{i,j+1}-f_{i,j})}^2}$ (formula 9)

In formula 9, ψ=[ψ ₁ψ ₂ψ _n], represent one group of orthonormal basis; θ is ψ _iweight coefficient; represent that the signal of reconstruct is to ψ _iweight coefficient; ψ ^-1for the inverse matrix of ψ; Φ ψ ^-1for observing matrix; Y is measured value; F is primary signal; || θ || ₁represent L ₁norm; TV represents the definition of total variational; α represents L ₁weight between norm and total variational.

8. adopt the digital hologram coding and transmission method of compressed sensing as claimed in claim 7, it is characterized in that, described iterative reconstruction is Multilevel Block iterative reconstruction method, specifically:

Digital hologram is carried out segmentation according to the partitioned mode of center and eight neighborhood and obtains nine piecemeals, the spectrum distribution of described nine piecemeals has consistency;

Central partition is split further with above-mentioned partitioning scheme, obtains the Multilevel Block of digital hologram;

In sampling process, the sampled value that central partition obtains is more than the piecemeal of eight neighborhood;

In restructuring procedure, first reconstruction center piecemeal obtains reconstructed image; Central partition frequency domain information after recycling reconstruct, as openness estimation and the iteration initial condition of its eight neighborhood, reconstructs the information obtaining eight neighborhood; After obtaining above-mentioned nine piecemeal reconfiguration information, be combined into new central piecemeal; Continue the eight neighborhood piecemeal of the described central piecemeal newly of reconstruct, until obtain whole digital hologram reconfiguration information.

9. adopt the digital hologram coding and transmission method of compressed sensing as claimed in claim 1, it is characterized in that, step 5) described reconstructed hologram to be reproduced, specifically according to Fresnel off-axis gaussian beam algorithm, by irradiating and Fresel diffraction two processes from axle reference light, realize digital hologram to be reproduced as initial three-dimensional object;

Wherein, reproduce formula, i.e. formula 10 according to off-axis gaussian beam, utilize the playback light R (x, y) consistent with reference light to irradiate hologram I _h(x, y) reproduces:

I _H(x，y)×R(x，y)＝(|R(x，y)| ²+|U(x，y)| ²)R(x，y)+|R(x，y)| ²U(x，y)+R ²(x，y)U ^*(x，y)

(formula 10)

In formula 10, I _hthe light intensity that (x, y) is hologram record, R (x, y) is reference light and playback light wavefront function, and U (x, y) is original objects reproduction wavefront function, U ^*the conjugation item that (x, y) is reproduction image;

Diffraction process through reproducing light-struck digital hologram light wave is calculated by means of Fresnel diffraction, obtains the 3-d reproduction picture of original objects at diffraction plane.