CN105451024B - Digital hologram coding transmission method adopting compressed sensing - Google Patents
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Abstract
The invention discloses a digital hologram coding and transmitting method adopting compressed sensing, which compresses, transmits and decodes a digital hologram based on the compressed sensing, and reconstructs the digital hologram in a wavelet domain in a targeted manner by an integral variation method, thereby improving the quality of a reproduced image. Specifically, a variable density sampling matrix is used for carrying out down-sampling on the digital hologram at a sampling rate lower than the Nyquist law so as to achieve the purpose of reducing the data volume of subsequent coding transmission; further compressing and coding the sampled data by a Huffman lossless coding method; the iterative reconstruction is a multi-stage block iterative reconstruction method. Compared with the common method for measuring the matrix and reducing the measured value, the method further improves the compression ratio and reduces the computation amount of the sending end and the system complexity; improving the quality of the reproduced image; after decompression, the digital hologram is reconstructed, and three-dimensional display can be performed by applying optical systems such as a spatial light modulator and the like.
Description
Technical Field
The invention belongs to the field of digital image processing, relates to a digital hologram coding transmission method adopting compressed sensing, and particularly relates to related methods such as manufacturing and reproducing of a color digital hologram, variable density sampling of a compressed sensing technology, integral variation reconstruction and the like.
Background
In 2006, candies et al are described in the literature "Emmanuel J. candies, Justin Romberg and Terence Tao," Robust uncartaint principles: the method comprises the steps of firstly providing a compressed sensing technology in actual signal reception from high level Information, namely IEEE Transactions on Information Theory, Vol.52, No.2, pp.489-509, 2006, providing a prototype and possible application of a compressed sensing Theory, and providing a method for carrying out high-precision reconstruction on highly undersampled data through nonlinear estimation.
The hologram records amplitude and phase information of a three-dimensional object, and the amount of data is very large, and compression processing is required for encoding and transmission. The main problem to be studied when applying the compressed sensing technology to the compressed transmission of digital holograms is how to improve the compression rate of the compression process and improve the quality of the reproduced image. Document two, "y.rivenson, a.stem, and b.javidi," Compressive Fresnel holographics, "j.display technol.vol.6, No.10, pp.506-509, 2010" describes a solution: and performing down-sampling on the digital hologram by using a low-sampling-rate matrix, and directly obtaining a reproduced image of the hologram by using less sampling data through a whole variation minimization method under a wavelet sparse basis. However, this method has a problem that the reconstruction of the digital hologram is not performed, and it cannot be used for the optical stereoscopic display system to perform the three-dimensional stereoscopic display of the object. Document three, "lie, li jun. hologram compression research based on compressive sensing [ J ]. university of south china proceedings: science edition, 2013, 44 (4): 61-65 and article four "king lemna, chen bao shen, blatthy blue, et al. 37-38 "all describe compression methods for reconstructing digital holograms under the structure of compressed sensing techniques, which use measurement matrices to obtain partial measurements for compression purposes, but they have the problem that: the measurement matrix needs a large amount of matrix operation for measuring the hologram, the system operation complexity is high, and meanwhile, the measured value is a floating point number, which brings extra storage and transmission data quantity and reduces the data compression rate.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a digital hologram coding transmission method adopting compressed sensing, which performs compressed transmission on a digital hologram based on the compressed sensing so as to achieve the purposes of high compression rate and low information loss.
In the present invention, the following terms are agreed:
compressed sensing: compressive sensing; digital hologram: digital hologram.
The principle of the invention is as follows: the invention applies the compression sensing technology to the compression transmission of the digital hologram, and because the digital hologram is an interference fringe image, each pixel carries partial information of other pixels, and the whole information of the digital hologram can be estimated through partial pixel information, the digital hologram can be down-sampled by a sampling rate far lower than the Nyquist law, the data amount processed by a compression transmission system is greatly reduced, and the compression rate of the image is improved. Meanwhile, no complex operation is introduced in the sampling compression process, so that the system complexity and power consumption of the compression transmitting end can be effectively reduced. Because the interference process of the object light and the reference light stores the object information in a higher frequency part during the recording of the digital hologram, and the blocked holograms have similar spectral distribution in a frequency domain, the digital hologram is reconstructed in a targeted manner by adopting the integral variation of multi-stage blocking iteration and an L1 mode minimization method in the frequency domain, and the quality of a reproduced image is improved. After decompression, the digital hologram is reconstructed, and three-dimensional display can be performed by applying optical systems such as a spatial light modulator and the like. The method provided by the invention can achieve better level on compression rate and image recovery quality for the digital hologram compression technology.
The technical scheme provided by the invention is as follows:
a digital hologram coding transmission method adopting compressed sensing is characterized in that the digital hologram is compressed, transmitted and decoded based on the compressed sensing, and the digital hologram is reconstructed pertinently by adopting a multilevel block iterative integral variation and L1 mode minimization method in a frequency domain, so that the purposes of high compression rate, low information loss and improvement of quality of a reconstructed image are achieved, and the reconstructed image can be applied to three-dimensional display; the digital hologram encoding and transmitting method specifically comprises the following steps:
1) converting an original color three-dimensional object into an RGB space, and recording the original color three-dimensional object as a digital hologram by a Fresnel off-axis holographic calculation method; or an optical platform is adopted to build a Fresnel off-axis hologram recording light path, and a CCD camera is used for recording to obtain a digital hologram;
2) compressing the digital hologram obtained in step 1), comprising: down-sampling the digital hologram, and then performing compression coding on the sampled data to obtain compressed data;
3) transmitting the compressed data obtained in the step 2) between a transmitting end and a receiving end;
4) decompressing the compressed data received by the receiving end, including decoding at the receiving end, and reconstructing the decoded data by an integral variable and L1 modular minimization method of multi-stage block iteration to obtain a reconstructed hologram;
5) reconstructing the reconstructed hologram obtained in the step 4) to obtain a reconstructed image.
Aiming at the digital hologram coding transmission method adopting compressed sensing, further, the step 2) specifically uses a variable density sampling matrix to perform down-sampling on the digital hologram at a sampling rate lower than the Nyquist law so as to achieve the purpose of reducing the data volume of subsequent coding transmission; and further compressing and coding the sampled data by a Huffman lossless coding method.
For the above digital hologram encoding and transmitting method using compressed sensing, further, the step 2) of downsampling the digital hologram specifically includes the following steps:
211) a signal f of length N is represented as a linear combination of a set of orthonormal bases, as shown in equation 4:
f ═ Ψ θ (formula 4)
In formula 4, Ψ ═ ψ1ψ2…ψN]And theta is psiiThe weighting coefficient of (2); if theta only has K (K < N) nonzero elements, the signal f is called to have K sparsity in the domain psi;
212) after the signal f is transformed to a certain transform domain to obtain a sparse representation, the M multiplied by N (K < M < N) dimensional measurement matrix is used for projecting the transformation coefficient theta through the formula 5 to obtain M measurement values y, so as to achieve the purpose of reducing the number of the measurement values:
In the formula 5, the first step is,
is an M × N dimensional observation matrix, and can be selected as Gaussian random matrixAn array, a binary random matrix, or a structured random matrix; Ψ-1Is the inverse matrix of Ψ; the measured value y is a compressed representation of the signal to be acquired; the transform is a fourier transform, a DCT transform, or a wavelet transform.
Aiming at the digital hologram coding transmission method adopting compressed sensing, in step 212), the matrix is observed
Is a random binary matrix, so that the data format of the measured values is consistent with the image pixel data format, thereby not introducing extra compression rate loss.
Aiming at the digital hologram coding transmission method adopting compressed sensing, in step 212), the matrix is observed
In order to improve the random binary matrix, the density sampling matrix is changed, and a random binary matrix with uneven distribution is generated through equations 6 to 7, wherein the distribution density is in negative correlation with the distance from the center of the image:
In the formulas 6 to 7, g (x, y) is a random matrix composed of element values satisfying uniform random distribution between [0, 1], r (x, y) is a matrix composed of normalized distances of pixel coordinates thereof from the center of the image, (x, y) is a matrix pixel coordinate, and m, n are the sizes of the image and the sampling matrix; the hologram is masked with the observation matrix g (x, y) to extract some of the sample values, thereby further reducing the sampling rate.
In view of the above-mentioned digital hologram encoding transmission method using compressed sensing, further, step 3) specifically uses a TCP/IP transmission protocol to transmit compressed data between the transmitting end and the receiving end.
For the digital hologram encoding and transmitting method using compressed sensing, further, in step 4), the iterative reconstruction is performed on the decoded data by using an overall variation and L1-mode minimization method of multi-level block iteration to obtain a reconstructed hologram, specifically, a process of reconstructing a measurement signal y with a length M to obtain a measurement signal f with a length N includes the following steps:
421) solving for the minimum L as shown in equation 80Norm:
In formula 8, Ψ ═ ψ1ψ2…ψN]Denotes a set of orthonormal bases, theta is psiiThe weighting coefficient of (a) is determined,
representing the reconstructed signal pair psiiWeight coefficient of (2) ("psi-1Is the inverse matrix of Ψ, Φ Ψ-1Is an observation matrix, y is a measured value, and f is an original signal; | θ | non-woven phosphorpIs LpAnd (4) defining norm.
422) Will solve the equation 8 minimum L0Norm by using L1Norm to equivalent L0Norm to convert to optimized L1Solving L by combining minimum norm with integral variation minimization method1Norm minimization problem;
423) solving for the integral variation and L1And (3) reconstructing the compressed sensing signal to obtain a reconstructed hologram according to the norm minimization problem:
In formula 9, Ψ ═ ψ1ψ2…ψN]Representing a set of orthonormal bases as the basis of Fourier transform, theta being phiiThe weighting coefficient of (a) is determined,
representing the reconstructed signal pair psiiWeight coefficient of (2) ("psi-1Is the inverse matrix of Ψ, Φ Ψ-1The method comprises the steps of (1) obtaining an observation matrix, namely a random binary matrix of variable density, wherein y is a measured value, and f is an original signal; | θ | non-woven phosphor1Represents L1Norm, TV represents the definition of integral variation, and alpha represents L1The norm and the overall variance.
Since each pixel of the digital hologram carries part of the information of the other pixels, L1The norm can ensure the consistency of the reconstructed hologram and the original hologram image, and simultaneously, the interference process of the object light and the reference light stores the object information in a higher frequency part when the digital hologram is recorded, the integral variation extracts the high-frequency information of the image, and the consistency of the details of the reconstructed hologram and the original hologram image can be ensured.
For the above digital hologram encoding and transmitting method using compressed sensing, further, in step 423), a block iteration method is used to reconstruct the digital hologram in blocks. Multi-stage blocking of the hologram, starting with the central minimum block, using the global variation and L described in step 423)1A mode minimizing method of reconstructing the hologram of the block portion; secondly, the frequency domain information of the block is reconstructed
Performing iterative reconstruction on 8 neighborhood blocks of the central block as initial conditions of frequency domain sparsity estimation and iteration; and combining the reconstructed 9 blocks into a new central minimum block, and repeating the reconstruction process until the reconstruction of all the digital hologram information is completed.
Aiming at the digital hologram coding and transmitting method adopting compressed sensing, further, in the step 5), the reconstruction hologram is reconstructed, and the digital hologram is reconstructed into an original three-dimensional object through two processes of off-axis reference light irradiation and Fresnel diffraction specifically according to a Fresnel off-axis holographic algorithm;
wherein the reproduction light corresponding to the reference light is used according to an off-axis holographic reproduction formula, that is, formula 10R (x, y) illuminating hologram IH(x, y) reproducing:
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 10)
In the formula 10, IH(x, y) is the light intensity of hologram record, R (x, y) is the wave front function of reference light and reproduced light, U (x, y) is the reproduced wave front function of original object*(x, y) is the conjugate term of the reconstructed image;
the diffraction process of the digital hologram light wave irradiated with the reproduced light is calculated by fresnel diffraction formulas (formulas 2 to 3), and a three-dimensional reproduced image of the original object is obtained on the diffraction plane.
The digital hologram coding and transmitting method adopting compressed sensing uses a variable density sampling matrix to carry out down-sampling on the digital hologram at a sampling rate lower than the Nyquist law, reduces the data volume of subsequent coding and transmission, and further compresses and codes data by a Huffman coding method; after decoding at the receiving end, the digital hologram is reconstructed by the overall variation and L1 modulus minimization method of multi-stage block iteration. The scheme reduces the system complexity and power consumption of a compression sending end, improves the compression rate and compression ratio, improves the quality of the compressed reproduced image at a receiving end, can provide an adjustable image reproduction grade, and can simultaneously use an optical system to carry out three-dimensional display on the reconstructed hologram.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a digital hologram coding transmission method adopting compressed sensing, which is used for carrying out compressed transmission on a digital hologram based on the compressed sensing, and because the digital hologram is an interference fringe image, each pixel carries partial information of other pixels, and the whole information of the digital hologram can be estimated through partial pixel information, the digital hologram can be subjected to down-sampling by a sampling rate far lower than the Nyquist law, the data volume processed by a compressed transmission system is greatly reduced, and the compression ratio of the image is improved. Meanwhile, no complex operation is introduced in the sampling compression process, so that the system complexity and power consumption of the compression transmitting end can be effectively reduced. Because the interference process of the object light and the reference light stores the object information in a higher frequency part during the recording of the digital hologram, and the blocked holograms have similar spectral distribution in a frequency domain, the digital hologram is reconstructed in a targeted manner by adopting the integral variation of multi-stage blocking iteration and an L1 mode minimization method in the frequency domain, and the quality of a reproduced image is improved. After decompression, the digital hologram is reconstructed, and three-dimensional display can be performed by applying optical systems such as a spatial light modulator and the like. The advantages of the invention are mainly embodied in the following aspects:
the digital hologram is directly subjected to down-sampling in a spatial domain by using a variable density sampling matrix at a sampling rate lower than the Nyquist law, so that the data amount processed by a compression transmission system is reduced, compared with a method for reducing measurement values by using a common measurement matrix, the compression rate is further improved, and the operation amount and the system complexity of a transmitting end are reduced;
and (II) the interference process during the recording of the digital hologram stores the object information in a higher frequency part, the blocked holograms have similar spectral distribution in a frequency domain, and the digital hologram is reconstructed in the frequency domain by adopting the integral variation of multi-stage blocking iteration and an L1 mode minimization method in a targeted manner, so that the quality of a reproduced image is improved.
And thirdly, the digital hologram is reconstructed after decompression, and three-dimensional display can be carried out by applying optical systems such as a spatial light modulator and the like.
Drawings
Fig. 1 is a flow chart of a digital hologram compression transmission method using compressed sensing according to the present invention.
FIG. 2 is a schematic illustration of a three-dimensional object and a component image;
wherein (a) is an original three-dimensional object; (b) is a lens image; (c) is a USAF image; (d) the test chart is a PM5544 test chart.
FIG. 3 is a comparison of an original image and a compressed image;
wherein, (a) is an original hologram; (b) is a compressed hologram; (c) a reproduction of the original hologram (a) at a reproduction distance of 500 mm; (d) a reconstructed image of the compressed hologram (b), the reconstruction distance being 500 mm; (e) a reproduction of the original hologram (a), reproduction distance 505 mm; (f) a reproduction of the original hologram (b), reproduction distance 505 mm; (g) a reproduction of the original hologram (a), the reproduction distance being 510 mm; (h) a reproduction of the original hologram (a) at a reproduction distance of 500 mm;
FIG. 4 is a graph showing the PSNR quality of reproduced images by the scheme of the present invention and the JPEG compression method at different compression rates.
Figure 5 is a graph of the quality of NCC, K, Q images reproduced by the inventive arrangement at different compression rates.
FIG. 6 is a schematic diagram of a diagonal spatial filter matrix in an embodiment of the present invention; in the figure 0, 1, -1 are the values of the matrix elements.
Where 0, 1, -1 represent the values of the matrix elements.
FIG. 7 is a diagram of a hardware system for optically recording a digital hologram;
wherein Laser represents a Laser, Spatial filter represents a Spatial filter, BS1 and BS2 represent beam splitters, M1、M2、M3Representing a mirror, lens1, lens2 representing a beam expander, Object representing a recorded Object, and CCD representing a photosensitive element; PC1 and PC2 represent the receiving end and the transmitting end, Network represents the transmission process, and output represents the subsequent output system.
Detailed Description
The invention will be further described by way of examples, without in any way limiting the scope of the invention, with reference to the accompanying drawings.
The use of the compressed sensing method for compressing images involves two basic processes: firstly, during compression, the number of data is reduced to achieve the purpose of compression; when decompressing, restoring the image by the data obtained by compressing in the first step; there are various ways to implement this in a particular process. For example: in compression, pixel points of a part of images can be directly sampled in a down-sampling mode; the image may also be projected to a lower dimension by multiplying the measurement matrix with the image (which may be understood as combining a number of pixel values of the image into one measurement by some method); in decompression, the method of the second document adopts the processing process of hologram- > sampling- > reproducing the image; the method of document three is hologram- > measurement- > (reconstruction must be done using the method of measuring data to reconstruct the hologram) > hologram- > reconstructed image >; the method of document four is hologram- > sample- > (a method in which a reconstructed image must be reconstructed using sample data) > reconstructed image; the method provided by the invention adopts the processing process of obtaining the hologram- > sampling- > reconstructing the hologram by using the sampling data.
The flow chart of the compressed transmission method of the digital hologram adopting the compressed sensing provided by the invention is shown in fig. 1, and the method is suitable for processing Fresnel off-axis holograms, including those generated by computer simulation or recorded by an optical system, and is not limited to digital holograms. In the embodiment of the present invention, the method provided by the present invention specifically includes the following steps:
1) converting the original color three-dimensional object into an RGB space for processing and calculation; recording an original three-dimensional object as a digital hologram by a Fresnel off-axis holographic algorithm; or an optical platform is adopted to build a Fresnel off-axis hologram recording light path, and a CCD camera is used to record a digital hologram;
the method of recording a digital hologram using a computer is: according to the fresnel off-axis holographic algorithm, the original three-dimensional object is recorded as a digital hologram. The Fresnel off-axis hologram recording is composed of Fresnel diffraction and off-axis reference light interference.
Here, Fresnel diffraction (Fresnel diffraction) refers to diffraction of light waves in the near field region. Fresnel diffraction integral can be used to calculate the propagation of light waves in the near field region. And calculating Fresnel diffraction of light emitted from each point of the three-dimensional object to the holographic recording plane and superposing the light, so that the object light wave front of the three-dimensional object on the holographic recording plane can be calculated.
The off-axis reference light interference means that when the hologram is reproduced, a reproduced image, a twin image and a zero-order diffraction bright spot exist at the same time, and the reproduced image quality is influenced by mutual overlapping. When the hologram is recorded, reference light with a certain included angle with the wavefront of object light is introduced, so that different-order diffraction images can be separated to obtain a single clear reproduced image.
According to the off-axis holographic formula, the hologram I is formed by using the complex amplitude function of the diffraction wave front of the interference record object lightH(x，y)：
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 the formula 1, IH(x, y) is the intensity of the hologram recording, R (x, y) is the reference wavefront function, and U (x, y) is the original object wavefront function. R*(x, y) and U*And (x, y) are conjugate terms of R (x, y) and U (x, y) respectively.
The diffraction process of the object light wave is calculated by the fresnel diffraction formula (equation 2):
In formula 2, d is the diffraction distance, k is the wave number, and j is the imaginary unit; (x)0，y0) Is the initial object wave plane, and (x, y) is the diffraction plane; o (x)0，y0) For initial object wave plane information, U (x, y) is the complex amplitude function of the object wavefront with a diffraction distance d. Using a computer to calculate this diffraction integral, a fast fourier transform can be performed by equation 3:
In formula 3, F represents Fourier transform, d represents diffraction distance, k represents wave number, and j represents imaginary unit; l is0The initial object wave plane sampling range is obtained; the number of sampling points of the initial object wave plane is NXN, namely the number of pixels of the initial image; the interval of the initial object wave plane sampling points is Deltax0＝Δy0＝L0N; Δ x ═ Δ y is the sampling interval after the initial object wave plane discrete fourier transform, and in the spatial domain, the corresponding sampling interval is the diffraction plane.
The method of recording a digital hologram using an optical method is: the interference fringes of object light waves and reference light waves are recorded by a photoelectronic detector (CCD camera) and stored in a computer.
As shown in FIG. 7, where Laser represents a Laser, Spatial filter represents a Spatial filter, BS1 and BS2 represent beam splitters, and M represents1、M2、M3Representing a mirror, lens1, lens2 representing a beam expander, Object representing a recorded Object, and CCD representing a photosensitive element; PC1 and PC2 represent a receiving end and a sending end, Network represents a transmission process, and output represents a subsequent output system; the light emitted by the laser is split into two beams by a beam splitter BS 1; one beam is reflected by a reflector M2, enters a beam expanding lens (lens 1), is expanded and collimated to be parallel light, and irradiates a recorded object to form object waves, and the object waves penetrate through a beam splitter BS2 to irradiate the surface of a photosensitive element of the digital camera; the other beam is converted into parallel light by the beam expander collimating mirror and the reflecting mirror M1, and then is turned by the beam splitter BS2 to form reference light, and the reference light and object waves are overlapped and interfered on the plane of a CMOS (or CCD) photoelectric device to form a hologram.
2) Down-sampling the hologram by using a variable density sampling matrix, and performing compression coding on sampling data by using a Huffman lossless coding method;
the compression process consists of random observation matrix sampling and Huffman lossless coding.
2.1 random Observation matrix sampling
The design of the random observation matrix is the key of compressed sampling of the compressed sensing technology. The observation matrix performs dimensionality reduction observation on the original signal to obtain a small amount of sampling data, and in order to ensure that the signal can be accurately reconstructed from an observation value, the finite equidistant property of the original signal sparse basis needs to be met.
A signal f of length N can be expressed as a linear combination of a set of orthonormal bases, as shown in equation 4:
f ═ Ψ θ (formula 4)
In formula 4, Ψ ═ ψ1ψ2…ψN]And theta is psiiThe weighting coefficient of (2). If θ has only K (K < N) nonzero elements, signal f is said to have K sparsity in domain Ψ. This is followed byThe compression measurement provides the basis.
Transforming the signal f to a certain transform domain to obtain a sparse representation, and projecting the transformation coefficient theta through a projection matrix of dimension M multiplied by N (K < M < N) to obtain M measurement values y, namely
In the formula 5, the first step is,
for an M x N dimensional observation matrix, Ψ-1The measurement y is a compressed representation of the signal that needs to be acquired, which is the inverse of Ψ. In the compression measurement process, it must be ensured that the measurement matrix does not map 2 different sparse signal elements into the same sampling set. Thus, the observation matrix
Certain constraints, such as a constrained Isometry Property (RIP), need to be satisfied. Commonly used observation matrix
The random matrix can be selected from a Gaussian random matrix, a binary random matrix, a structured random matrix and the like.
For compression purposes, this cannot be achieved by merely reducing the number of measurement values, and the design of the observation matrix also needs to consider the selection of the measurement field and the data type of the measurement values. In computers, digital holograms are typically stored in the form of a bitmap, and each pixel of the image may be recorded using a reshaped value represented by a certain number of bits. In the process of transforming domain, such as fourier transform, DCT transform, wavelet transform, etc., the transformed coefficients need to be recorded using floating point numbers. Generally, the number of bits required for floating point number recording in a computer will be several times the number of bits required for reshaped number recording. Similarly, the measurement value is recorded by using an observation matrix composed of floating point numbers such as a gaussian random matrix. This will bring extra compression loss. Meanwhile, the method of multiplying the measurement matrix by the hologram or the column vector of the hologram is adopted for measurement, which brings huge operation time and space cost.
Therefore, the invention adopts the random binary matrix to directly sample the digital hologram in the space domain. That is, in formula 5, take
And f is taken as a digital hologram matrix for the random binary matrix, and the corresponding elements of the two matrixes are subjected to dot multiplication operation. The random binary matrix consists of randomly distributed 0, 1 values. The digital hologram is sampled by using the random binary matrix, and the data format of the measured value is kept consistent with the data format of the image pixel, so that the loss of extra compression rate is not introduced. Meanwhile, aiming at the characteristics of the diffraction process during the recording of the digital hologram, the invention improves a general random binary matrix, adopts a variable density sampling matrix to generate a random binary matrix with uneven distribution, wherein the distribution density is in negative correlation with the distance from the center of an image:
In the formulas 6 to 7, g (x, y) is a random matrix composed of element values satisfying uniform random distribution between [0, 1], r (x, y) is a matrix composed of normalized distances of pixel coordinates thereof from the center of the image, (x, y) is a matrix pixel coordinate, and m, n are the sizes of the image and the sampling matrix. The observation matrix is used as a mask to act on the hologram, partial sampling values are extracted, and the sampling rate is further reduced.
2.2 Huffman lossless coding
Huffman Coding (Huffman Coding) is an entropy Coding (weight Coding) algorithm used for lossless data compression. The Huffman coding uses a variable length coding table to code the source symbols, letters with high occurrence probability use shorter codes, and letters with low occurrence probability use longer codes, so that the average length and the expected value of the character strings after coding are reduced, and the aim of lossless data compression is fulfilled.
Arranging the information source symbols in the descending order of the probability of occurrence, combining and adding the two information source symbols with the minimum probability, repeating the step, and always placing a higher probability branch in the upper part until only one information source symbol is left and the probability reaches 1.0; assigning the upper one of each pair of combinations as a 1 and the lower one as a 0, obtaining a path from each source symbol to a position with a probability of 1.0, and recording 1 and 0 along the path; and writing a 1 and 0 sequence for each source symbol, and obtaining the Huffman codes with unequal lengths from right to left.
The data after being subjected to down-sampling by the sampling matrix has a limited discrete value in a value range of 0-255, and meanwhile, the probability of a value in an interval near the average value of the pixels of the holographic image is high, and the probability of a value far away from the average value is gradually reduced. Therefore, the sampled data can be further compression-encoded using huffman coding, reducing the amount of transmitted data.
3) Transmitting the compressed data between the transmitting end and the receiving end by using a TCP/IP transmission protocol;
the TCP protocol is commonly referred to as a connection-oriented protocol that ensures reliable and efficient transfer of data from a sender to a recipient. Before a host sends data to another host using the TCP protocol, the transport layer initiates a process for creating a link with the destination host. Through this link, sessions or communication data flows between hosts can be tracked. At the same time, the process also ensures that each host knows and is ready for communication. A full TCP session requires a bi-directional session to be created between the hosts.
The reliability of TCP communication is that a connection-oriented session is used. Before the sender sends data to the receiver using the TCP protocol, the transport layer starts a process for creating a link with the receiver. Through this link, sessions or communication data flows between hosts can be tracked. At the same time, the process also ensures that each host knows and is ready for communication. A full TCP session requires a bi-directional session to be created between the hosts. After the session is established, the receiving end sends confirmation information to the sending end aiming at the received data segment. In a TCP session, these acknowledgements form the basis for reliability. The sending end sends a data segment containing an acknowledgement value, wherein the value of the data segment is equal to the sum of the received sequence value and 1, and the self synchronous sequence value is added. With this acknowledgement value, the receiving end can concatenate the response with the data segment last sent to the transmitting end. And sending a receiving end response with an acknowledgement value, wherein the value of the receiving end response is equal to the value of the receiving sequence plus 1, thereby completing the whole connection process.
4) Decoding the data received by the receiving end, and performing iterative reconstruction on the decoded data by using an integral variation method to obtain a reconstructed hologram;
4.1 Huffman decoding: according to an encoding table used in the encoding process, one bit is read from a received bit stream circularly to form a new code word, the code word is inquired in the encoding table, and the corresponding effective code word is decoded. And obtaining observation matrix sampling data after decoding.
4.2 Overall variation and L1 model minimization method needle for multistage blocking iteration
Compressed sensing technology signal reconstruction, namely the process of reconstructing a measuring signal f with the length of N from a measuring signal y with the length of M. This process can be done by solving for the minimum L0Norm problem solving, namely:
In formula 8, Ψ ═ ψ1ψ2…ψN]Represents a set of orthonormal bases; theta is psiiThe weighting coefficient of (2);
representing the reconstructed signal pair psiiThe weighting coefficient of (2); Ψ-1Is the inverse matrix of Ψ; phi psi-1Is an observation matrix; y is a measured value; f is an original signal; | θ | non-woven phosphorpIs LpAnd (4) defining norm.
Since the solution of equation 8 is an NP-hard problem, the method is described inThe polynomial is difficult to solve in time, and even the reliability of the solution cannot be verified. L is1Sum L under assumption of compressed sensing under minimum norm0The minimum norm has equivalence and the same solution can be obtained. Then the above formula is converted to L1Optimization problem under minimum norm. L is1Norm minimization is by using L1Norm to approximate the 0 norm, L1Norm minimization is a convex optimization problem, and the solving process can be converted into a linear programming problem.
The integral variational method is proposed by Rudin, Osher and Fatemi to solve L1Norm minimization, which is now the most successful method in image restoration. In the present invention, the overall variation is minimized with L1Norm minimization combining for compressed perceptual signal reconstruction:
In formula 9, Ψ ═ ψ1ψ2…ψN]Represents a set of orthonormal bases; theta is psiiThe weighting coefficient of (2);
representing the reconstructed signal pair psiiThe weighting coefficient of (2); Ψ-1Is the inverse matrix of Ψ; phi psi-1Is an observation matrix; y is a measured value; f is an original signal; | θ | non-woven phosphor1Represents L1A norm; TV represents the definition of the overall variation; alpha represents L1The norm and the overall variance.
Since each pixel of the digital hologram carries part of the information of the other pixels, L1The norm can ensure the consistency of the reconstructed hologram and the original hologram image, and simultaneously, the interference process of the object light and the reference light stores the object information in a higher frequency part when the digital hologram is recorded, the integral variation extracts the high-frequency information of the image, and the consistency of the details of the reconstructed hologram and the original hologram image can be ensured.
Because the partitioned holograms have similar spectral distribution in the frequency domain, the invention adopts a multi-stage partitioned iterative reconstruction method. The digital hologram is divided according to the mode of a central block and 8 neighborhoods thereof, and the frequency spectrum distribution of the 9 blocks has consistency. The central segment is further segmented in the same way to obtain multilevel segments of the digital hologram. In the sampling process, the central block takes more sampling values, and firstly, the central block is reconstructed to obtain a more accurate reconstructed image; secondly, the reconstructed center block frequency domain information is used as the sparsity estimation and iteration initial condition of the 8 neighborhoods of the center block frequency domain information, and residual information can be reconstructed more accurately by using fewer sampling values. After the 9 blocks of reconstruction information are obtained, the 9 blocks of reconstruction information are combined into a new central block, and 8 neighborhood blocks of the new central block are continuously reconstructed until all digital hologram reconstruction information is obtained.
5) Reconstructing the reconstructed hologram, comparing the reconstructed hologram with the reconstructed image of the original hologram, and judging the quality of a compression algorithm by adopting an objective evaluation standard;
and (3) reconstructing the reconstructed hologram, specifically reconstructing the digital hologram into an original three-dimensional object according to a Fresnel off-axis holographic algorithm, and realizing the reconstruction of the Fresnel off-axis hologram through two processes of off-axis reference light irradiation and Fresnel diffraction.
Illuminating the hologram I with reconstruction light R (x, y) coincident with the reference light according to an off-axis holographic reconstruction formulaH(x, y) reproducing:
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 10)
In the formula 10, IH(x, y) is the light intensity of hologram record, R (x, y) is the wave front function of reference light and reproduced light, U (x, y) is the reproduced wave front function of original object*(x, y) is a conjugate term of the reproduced image.
The diffraction process of the digital hologram light wave irradiated with the reproduction light is calculated by fresnel diffraction formulas (formulas 2 to 3), and a three-dimensional reproduction image of the original object can be obtained on the diffraction plane.
In order to test the compression rate and the quality of the reproduced image, evaluation methods such as peak signal to noise ratio (PSNR), Normalized Correlation Coefficient (NCC), fuzzy coefficient (K), quality factor (Q) and the like are respectively adopted to measure the quality of the reproduced image.
5.1 Peak Signal-to-noise ratio (PSNR)
The peak signal-to-noise ratio (PSNR) is used for measuring the image reconstruction quality after loss compression coding, and the calculation method comprises the following steps:
Where MSE represents the mean square error, b represents the number of bits per pixel of the image, X (i, j) represents the pixel value of the original image at point (i, j), Y (i, j) represents the pixel value of the original image at point (i, j), and m, n represent the image size.
5.2 normalized Cross correlation coefficient (NCC)
The normalized cross-correlation coefficient (NCC) is used to measure the correlation between the decompressed image and the original image. The formula is as follows:
In equation 13, X (i, j) represents the pixel value of the original image at the point (i, j), Y (i, j) represents the pixel value of the original image at the point (i, j), X and Y are the average values thereof, respectively, σxAnd σyTheir standard deviations, m, n, respectively, represent the image sizes. The closer the NCC value is to 1, the smaller the image difference, i.e. the better the quality of the image after compression and decompression.
5.3 coefficient of blur (K)
The blur coefficient K is defined as the ratio of the extracted high frequency parts of the original image and the compressed and decompressed image. Considering that the transmission of the edge and the detail by the image transmission system is generally non-directional, the transmission coefficients of the edge and the detail in the oblique direction can represent the transmission of the detail in the vertical and horizontal directions, and since the horizontal and vertical details of the output image are mixed with the block effect and are not easy to represent the blurring degree, a differential spatial filter in the oblique direction (as shown in fig. 6) is selected, and the transmission coefficients of the edge and the detail in the oblique direction are only compared, that is, the blurring coefficients:
Wherein SiIs defined as edge energy feature, y'f(i, j) is a value obtained by processing the pixel value at the point (i, j) by an oblique differential spatial filter, KblurIs the ratio of the output edge energy to the input edge energy. The closer the K value is to 1, the better the image quality after compression and decompression.
5.3 quality factor (Q)
The quality factor (Q) combines three image distortion measures: loss of correlation, average distortion and contrast distortion. The specific definition is as follows:
Where { xi1, 2 … N and yiI | -1, 2 … N } represents the pixel value set of the original image and the compressed and decompressed image, respectively, and X and Y are the average values thereof, respectively. SigmaxAnd σyTheir standard deviations, respectively. The Q value is generally in the range of [ -1, 1 [ ]]The closer to 1 indicates that the compressed and decompressed image is more similar to the original image, i.e., the image quality after compression and decompression is better.
FIG. 2 is a schematic illustration of a three-dimensional object and a component image. In this embodiment, the recording object is composed of three pictures placed at different distances and at different angles, as shown in fig. 2(a), and the spatial size is 10mm × 10mm × 10 mm; the lena image recording distance in fig. 2(b) was 510 mm; 1951 an air force resolution detection image (FIG. 2(c), USAF image) of USA is recorded at a distance of 500mm to 510 mm; the PM5544 color television signal test chart (FIG. 2(d), PM5544 test image) was recorded at a distance of 500mm to 510 mm. FIG. 3 is a comparison of an original image and a compressed image; the original hologram recorded is shown in fig. 3 (a); the hologram after compression transmission is shown in fig. 3(b), and the compression rate is 10%; FIGS. 3(c) and 3(d) are the comparison of the original hologram and the compressed hologram at a reproduction distance of 500mm for the reproduced image; FIGS. 3(e) and 3(f) are the comparison of the original hologram and the compressed hologram at a reproduction distance of 500mm for the reproduced image; FIGS. 3(g) and 3(h) show the contrast between the original hologram and the hologram after compression at a reproduction distance of 500 mm.
The digital hologram compression transmission scheme based on the compressed sensing provided by the invention uses the variable density sampling matrix to carry out down-sampling on the digital hologram at the sampling rate lower than the Nyquist law, reduces the data volume of subsequent coding transmission, and further compresses and codes the data by a Huffman coding method; and after decoding at a receiving end, reconstructing the digital hologram by an integral variation method. The scheme reduces the system complexity and power consumption of a compression sending end, improves the compression rate and compression ratio, improves the quality of the compressed reproduced image at a receiving end, can provide an adjustable image reproduction grade, and can simultaneously use an optical system to carry out three-dimensional display on the reconstructed hologram. Table 1 shows the objective evaluation quality comparison of the images reproduced by the method of the present invention and the JPEG compression method at different compression ratios:
table 1 shows the comparison of objective evaluation quality between the images reproduced by the method of the present invention and the JPEG compression method at different compression ratios
FIG. 4 is a graph showing the PSNR quality of reproduced images by the scheme of the present invention and the JPEG compression method at different compression rates. Figure 5 is a graph of the quality of NCC, K, Q images reproduced by the inventive arrangement at different compression rates.
In conclusion, the scheme has a good application prospect in three-dimensional holographic information compression and transmission. The idea of the scheme can achieve better level on the compression rate and the image recovery quality of the digital hologram compression technology.
It is noted that the disclosed embodiments are intended to aid in further understanding of the invention, but those skilled in the art will appreciate that: various substitutions and modifications are possible without departing from the spirit and scope of the invention and appended claims. Therefore, the invention should not be limited to the embodiments disclosed, but the scope of the invention is defined by the appended claims.
Claims (8)
1. A color digital hologram coding transmission method adopting compressed sensing is characterized in that the method compresses, transmits and decodes the color digital hologram based on the compressed sensing, and the color digital hologram is reconstructed in a wavelet domain by an integral variation method in a targeted manner, so that the quality of a reconstructed image is improved, and the reconstructed image can be applied to three-dimensional display; the color digital hologram encoding and transmitting method comprises the following steps:
1) converting an original color three-dimensional object into an RGB space, and recording the original color three-dimensional object as a color digital hologram by a Fresnel off-axis holographic calculation method; or an optical platform is adopted to build a Fresnel off-axis hologram recording light path, and a CCD camera is used for recording to obtain a color digital hologram;
2) sampling: compressing the color digital hologram obtained in step 1), comprising: down-sampling the color digital hologram, and then performing compression coding on the sampled data to obtain compressed data;
3) and (3) a transmission process: transmitting the compressed data obtained in the step 2) between a transmitting end and a receiving end;
4) and (3) reconstruction process: decompressing the compressed data received by the receiving end, including decoding at the receiving end, and then carrying out iterative reconstruction on the decoded data by an integral variation method to obtain a reconstructed hologram; and
5) reconstructing the reconstructed hologram obtained in the step 4) to obtain a reconstructed image,
in addition, the step 2) specifically uses a variable density sampling matrix to carry out down-sampling on the color digital hologram at a sampling rate lower than the Nyquist law so as to achieve the purpose of reducing the data volume of subsequent coding transmission; and further compressing and coding the sampled data by a Huffman lossless coding method, wherein the distribution density is inversely proportional to the distance from the center of the image.
2. The method for encoded transmission of color digital holograms using compressed sensing according to claim 1, wherein said down-sampling of color digital holograms in step 2) comprises the steps of:
211) a signal f of length N is represented as a linear combination of a set of orthonormal bases, as shown in equation 4:
f ═ Ψ θ (formula 4)
In formula 4, Ψ ═ ψ1 ψ2…ψN]Phi is phiiThe weighting coefficient of (2); if theta only has K (K < N) nonzero elements, the signal f is called to have K sparsity in the domain psi;
212) after the signal f is transformed to a certain transform domain to obtain a sparse representation, the M multiplied by N (K < M < N) dimensional measurement matrix is used for projecting the transformation coefficient theta through the formula 5 to obtain M measurement values y, so as to achieve the purpose of reducing the number of the measurement values:
in the formula 5, the first step is,
the observation matrix is an M multiplied by N dimension observation matrix, and can be selected as a Gaussian random matrix, a binary random matrix or a structured random matrix; Ψ-1Is the inverse matrix of Ψ; the measured value y is a compressed representation of the signal to be acquired; the transform is a fourier transform, a DCT transform, or a wavelet transform.
3. The method for color digital hologram encoding transmission using compressed sensing as claimed in claim 2, whereinCharacterisation, step 212), the observation matrix
Is a random binary matrix, so that the data format of the measured values is consistent with the image pixel data format, thereby not introducing extra compression rate loss.
4. The method for encoded transmission of color digital holograms using compressed sensing as claimed in claim 3, wherein in step 212) the observation matrix is observed
In order to improve the random binary matrix, the density-variable sampling matrix is generated by a random binary matrix with uneven distribution through equations 6 to 7:
in the formulas 6 to 7, g (x, y) is a random matrix composed of element values satisfying uniform random distribution between [0, 1], r (x, y) is a matrix composed of normalized distances of pixel coordinates thereof from the center of the image, (x, y) is a matrix pixel coordinate, and m, n are the sizes of the image and the sampling matrix; the hologram is masked with the observation matrix g (x, y) to extract some of the sample values, thereby further reducing the sampling rate.
5. The method for color digital hologram encoded transmission using compressed sensing according to claim 1, wherein the step 3) transmits the compressed data between the transmitting end and the receiving end using a TCP/IP transmission protocol.
6. The method for encoded transmission of color digital holograms using compressed sensing according to claim 1, wherein said step 4) of iteratively reconstructing the decoded data by the ensemble variational method to obtain the reconstructed hologram, in particular the process of reconstructing the measurement signal f with length N from the measurement signal y with length M, comprises the steps of:
421) solving for the minimum L as shown in equation 80Norm:
in formula 8, Ψ ═ ψ1 ψ2…ψN]Represents a set of orthonormal bases; theta is psiiThe weighting coefficient of (2);
representing the reconstructed signal pair psiiThe weighting coefficient of (2); Ψ-1Is the inverse matrix of Ψ; phi psi-1Is an observation matrix; y is a measured value; f is an original signal; | θ | non-woven phosphorpIs LpDefining a norm;
422) will solve the equation 8 minimum L0Norm by using L1Norm to approximate L0Norm to convert to optimized L1Minimum norm, solving for L by linear programming method1Norm minimization problem;
423) solving for L1Norm minimization problem, minimizing integral variation with L1And (3) carrying out norm minimization and reconstructing the compressed sensing signal to obtain a reconstructed hologram:
in formula 9, Ψ ═ ψ1 ψ2…ψN]Represents a set of orthonormal bases; theta is psiiThe weighting coefficient of (2);
representing the reconstructed signal pair psiiThe weighting coefficient of (2); Ψ-1Is the inverse matrix of Ψ; phi psi-1Is an observation matrix; y is a measured value; f is an original signal; | θ | non-woven phosphor1Represents L1A norm; TV represents the definition of the overall variation; alpha represents L1The norm and the overall variance.
7. The method for color digital hologram encoding and transmission using compressed sensing according to claim 6, wherein said iterative reconstruction is a multi-stage block iterative reconstruction method, specifically:
dividing the color digital hologram according to a central and eight-neighborhood partitioning mode to obtain nine partitions, wherein the frequency spectrum distribution of the nine partitions has consistency;
further dividing the central block in the dividing mode to obtain multi-level blocks of the color digital hologram;
in the sampling process, more sampling values are obtained by the central block than the eight-neighborhood blocks;
in the reconstruction process, firstly reconstructing a central block to obtain a reconstructed image; then, reconstructing to obtain the information of eight neighborhoods by using the reconstructed center block frequency domain information as the sparsity estimation and iteration initial conditions of the eight neighborhoods; after the nine block reconstruction information is obtained, combining the nine block reconstruction information into a new central block; and continuously reconstructing the eight neighborhood blocks of the new central block until all color digital hologram reconstruction information is obtained.
8. The method for encoding and transmitting color digital holograms using compressed sensing according to claim 1, wherein said reconstructing the reconstructed hologram of step 5) is implemented by two processes of off-axis reference light illumination and fresnel diffraction, in particular according to fresnel off-axis holographic algorithm;
wherein the hologram I is illuminated with a reconstruction light R (x, y) coincident with the reference light according to an off-axis holographic reconstruction formula, equation 10H(xyy) reproducing:
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 10)
In the formula 10, IH(x, y) is the light intensity of hologram record, R (x, y) is the wave front function of reference light and reproduced light, U (x, y) is the reproduced wave front function of original object*(x, y) is the conjugate term of the reconstructed image;
the diffraction process of the color digital hologram light wave irradiated by the reproduction light is calculated by a Fresnel diffraction formula, and a three-dimensional reproduction image of the original object is obtained on a diffraction plane.
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