Three-channel compression imaging system and image reconstruction method

Abstract

The present invention discloses a three-channel compression imaging system and an image reconstruction method. The three-channel compression imaging system includes a dual-channel recording component. By adding a diffraction optical element and a streak camera without a lens, the parameters of the diffraction optical element and the lens are set so that two light paths are imaged at different positions of the streak camera sensor, and the photosensitive areas of the pixel points are staggered relative to the image, thereby doubling the sampling rate. Then, an integral channel recording component is added, and the integral image is recorded using a CMOS camera. The combination of the dual-channel recording component and the integral channel recording component achieves a three-fold increase in the sampling rate, overcoming the problem of spatial information loss and insufficient dynamic range of the streak camera in traditional single-channel ultrafast compression imaging system technology. The image reconstruction method can reconstruct extremely high-quality two-dimensional images to avoid distortion in the depiction of shock wave characteristics and improve the accuracy of velocity field analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of image communication, and in particular to a three-channel compression imaging system and an image reconstruction method. Background Art

[0002] See Figure 1 The existing ultrafast compressed imaging system (CUP) for velocity interferometry (VISAR) of arbitrary reflecting surfaces (VISAR) is an ultrafast two-dimensional imaging and recording system that combines compressed sensing technology with a streak camera. This system reconstructs the original ultrafast dynamic scene from the compressed image by encoding, compressing, sampling, and image inversion of non-repeatable ultrafast dynamic scenes. Existing ultrafast compressed imaging systems generally use a single-channel optical path design. The optical system first images the object point onto a transmissive encoding plate, which then encodes the image. Finally, the image is imaged through a series of lenses onto the wide slit of the optical streak camera. Finally, using compressed sampling data reconstruction methods, dozens of time-resolved two-dimensional images containing object or shock wave velocity information are obtained.

[0003] At present, the two-dimensional images obtained by the compressed sampling data reconstruction method of the single-channel ultrafast compressed imaging system generally have the problem of low image reconstruction quality. One of the important reasons is the high compression frame rate. In the observation of the two-dimensional shock wave velocity field of inertial confinement fusion, it is necessary to observe the transient process with high time resolution, which will make the compressed sampling process longer. It is usually necessary to record no less than 50 frames of transient images, that is, the sampling rate is less than 2%. In the mathematical model, it belongs to the problem of solving a super ill-conditioned set of equations. The current encoding sampling position points are as follows: Figure 2 As shown in the figure, the gaps between sampling points are very large, making it difficult for compressed sensing reconstruction algorithms to support high-quality 2D images at such a low sampling rate. This leads to distortion in the depiction of shock wave characteristics, resulting in insufficient accuracy in velocity field analysis. Therefore, solving the poor quality of reconstructed data caused by low sampling rates is a key issue in the research of ultrafast compressed imaging systems. Summary of the Invention

[0004] In view of this, the present invention provides a three-channel compression imaging system and an image reconstruction method.

[0005] The technical solution is as follows:

[0006] A first aspect of the present application relates to a three-channel compressive imaging system, comprising a spectroscopic assembly, a dual-channel recording assembly, and an integrating channel recording assembly. The spectroscopic assembly comprises at least a spectroscope BS3. The dual-channel recording assembly comprises a streak camera C1 without a lens, and a transmissive encoder plate OED, a filter F3a, a lens L3b, a diffractive optical element DOE, and a lens L3c, which are sequentially arranged between the transmissive surface of the spectroscope BS3 and the cathode of the streak camera C1. The integrating channel recording assembly comprises a CMOS camera C2 and a filter F3b arranged between the reflective surface of the spectroscope BS3 and the lens of the CMOS camera C2.

[0007] The incident Doppler interference fringe image is split into two by the beam splitter BS3. The beam reflected by the beam splitter BS3 is light path 3. The image of light path 3 passes through filter F3b and is recorded by CMOS camera C2. The beam that passes through the beam splitter BS3 passes through the transmission encoder plate OED, filter F3a, and lens L3b in sequence, and is then split into two by the diffractive optical element DOE to form light path 1 and light path 2. The images of light path 1 and light path 2 are imaged by lens L3c and are formed on the exposed cathode of streak camera C1.

[0008] Among them, by setting the parameters of the diffraction optical element DOE and lens L3c, each pixel point of the optical path 2 is offset by 1 / 2 pixel diagonally toward the next row and column on the image, so as to be staggered and distributed between the pixel points of the optical path 1 without overlapping.

[0009] The above three-channel compressed imaging system is adopted. By adding a diffractive optical element (DOE) to the dual-channel recording component and coordinating it with a streak camera C1 without a lens, the parameters of the diffractive optical element (DOE) and lens L3c are set so that optical path 1 and optical path 2 are imaged at different positions of the streak camera sensor, and the photosensitive areas of the pixels are staggered relative to the image. This enables the cathode of the streak camera C1 to record two dynamic encoded images, thereby doubling the sampling rate. Then, an integral channel recording component is added, and the integral image is recorded using the CMOS camera C2. The combined dual-channel recording component and the integral channel recording component achieve a three-fold increase in the sampling rate, overcoming the problem of spatial information loss and insufficient dynamic range of the streak camera in traditional single-channel ultrafast compressed imaging system technology.

[0010] A second aspect of the present application relates to an image reconstruction method for the above-mentioned three-channel compression imaging system, comprising the following steps:

[0011] The two dynamic coded images E1 and E2 recorded by streak camera C1 on light path 1 and light path 2 are expressed as:

[0012] , ;

[0013] In the above formula, T represents the time integration, C represents the spatial mask, and I(x, y, t) represents the incident light intensity information. and Represent the horizontal and vertical coordinates of the spatial dimension respectively, represents the time dimension coordinate, S represents the shearing coefficient caused by the cathode of streak camera C1 when scanning and recording two dynamic coded images, and M represents the acquisition area of ​​the compressed image of optical path 2 offset by 1 / 2 pixel by streak camera C1;

[0014] The dynamic coded image E1 is represented as a three-dimensional dynamic scene I containing t frames modulated by the dynamic code A. The dynamic coded image E1 is represented as:

[0015] ;

[0016] In the above formula, and Represent the b-th frame mask of the dynamic coded image E1 and the corresponding dynamic scene, stands for Hadamard dot product;

[0017] Write the above formula into matrix form and vectorize the corresponding matrix columns, let , , represents the operator that vectorizes the matrix columns, then:

[0018] ;

[0019] In the above formula, , ; H represents the sensing matrix, which is the cascade of diagonal matrices. The expression of the sensing matrix H is ,in, , , represents an operator that constructs a column vector into a diagonal matrix;

[0020] Similarly, for the dynamic coded image E2, we have:

[0021] ;

[0022] In the above formula, , ; Sensing matrix The expression is ,in, , , represents the b-th frame mask corresponding to the dynamic coded image E2;

[0023] The integral image E3 recorded by the CMOS camera C2 on the optical path 3 is expressed as:

[0024] ;

[0025] Then express the integral image E3 as the augmented matrix and The product of , where , , is the identity matrix, Representation matrix Each column of is shifted right by b-1 bits, and the matrix With the matrix are diagonal matrix blocks with the same number of columns, and the matrix The elements on the diagonal are all 1;

[0026] The sampling data of optical path 1, optical path 2 and optical path 3 Expressed as:

[0027] ;

[0028] In the above formula, represents the sampling matrix of optical path 1, optical path 2 and optical path 3, Represents the vectorized arrangement of matrix columns;

[0029] because Satisfying the sparsity condition, the solution of the above equation is transformed into an unconstrained optimization problem:

[0030] ;

[0031] In the above formula, represents the best estimate of the original signal, , , is the data fidelity item, is the regular term for adding constraints, is the regularization parameter, Indicates the value of the variable x when the following formula reaches the minimum value;

[0032] Introducing intermediate variables , so the problem is transformed into the following optimization problem:

[0033] ;

[0034] Write the above formula in the form of augmented Lagrangian function:

[0035] ;

[0036] In the above formula, represents the Lagrange factor, represents the penalty function factor;

[0037] The above optimization problem is decomposed into the following three sub-problems:

[0038] ;

[0039]

[0040] ;

[0041] In the above formula, represents the scaled dual variable, and its expression is ; Indicates the number of iterations;

[0042] Iterate the solution formulas of the above three sub-problems, then determine whether the current solution meets the convergence conditions and update the number of iterations. If it meets the conditions or the number of iterations is not less than the preset maximum number of iterations, output the reconstructed dynamic scene 3D data, otherwise continue the iterative solution.

[0043] The above image reconstruction method not only has all the advantages of the above three-channel compressed imaging system, but also can reconstruct extremely high-quality two-dimensional images to avoid distortion in the depiction of shock wave characteristics and improve the accuracy of velocity field analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is the schematic diagram of a single-channel ultrafast compression imaging system;

[0045] Figure 2 Schematic diagram of the encoding sampling position points recorded by the single-channel ultrafast compression imaging system;

[0046] Figure 3 This is the schematic diagram of the three-channel ultrafast compression imaging system;

[0047] Figure 4 The schematic diagram of the arbitrary reflecting surface velocity interferometer based on the three-channel ultrafast compressive imaging system;

[0048] Figure 5 Schematic diagram of the encoded sampling locations recorded by the dual-channel recording component of the three-channel ultrafast compression imaging system;

[0049] Figure 6 Schematic diagram of the encoding sampling position points recorded by the dual-channel recording component and the integral channel recording component of the three-channel ultrafast compression imaging system. DETAILED DESCRIPTION

[0050] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0051] Example 1:

[0052] like Figure 3 As shown, a three-channel compression imaging system mainly includes a spectroscopic component, a dual-channel recording component and an integral channel recording component.

[0053] The beam splitting assembly includes at least a beam splitter BS3, which is used to split the incident Doppler interference fringe image into two. In this embodiment, the beam splitting assembly also includes a reflector M3 and a lens L3a. The reflector M3 and the lens L3a are arranged in sequence toward the beam splitter BS3. Therefore, the incident Doppler interference fringe image is first reflected by the reflector M3, then emitted by the lens L3a, and then emitted by the lens L3a to the beam splitter BS3.

[0054] The dual-channel recording assembly comprises a lensless streak camera C1, along with a transmissive encoder plate OED, filter F3a, lens L3b, diffractive optical element (DOE), and lens L3c, positioned sequentially between the transmissive surface of beam splitter BS3 and the exposed cathode of streak camera C1. The diffractive optical element (DOE) splits the incident Doppler interference fringe image into two. Specifically, a beam transmitted through beam splitter BS3 passes through the transmissive encoder plate OED, filter F3a, and lens L3b before being split by the diffractive optical element (DOE) into two paths, optical path 1 and optical path 2. The images of optical paths 1 and 2 are imaged onto the exposed cathode of streak camera C1 via lens L3c. Since streak camera C1 lacks a lens, it can directly record the amplified coded signal on the cathode, maximizing the maximum resolution of CUP technology (approximately 100μm) and further exploring the potential of the system.

[0055] The integration channel recording component includes a CMOS camera C2 and a filter F3b arranged between the reflective surface of the spectroscope BS3 and the lens of the CMOS camera C2. The beam reflected by the spectroscope BS3 is the light path 3. The image of the light path 3 is recorded by the CMOS camera C2 after passing through the filter F3b.

[0056] Most importantly, see Figure 5 By setting the parameters of the diffractive optical element (DOE) and lens L3c, each pixel of optical path 2 is offset by 1 / 2 pixel diagonally toward the next row and column on the image, so that it is staggered and non-overlapping between the pixels of optical path 1. That is, the pixels of optical path 2 are staggered and non-overlapping between the pixels of optical path 1. This allows the cathode of streak camera C1 to record two dynamic encoded images (E1 and E2), doubling the sampling rate. Then, an integral channel recording component is added, and the integral image is recorded using CMOS camera C2. See [1] for details. Figure 6The integrated dual-channel recording component and the integral channel recording component achieved a 3-fold increase in the sampling rate, overcoming the problem of loss of spatial information in traditional single-channel ultrafast compression imaging system technology and the problem of insufficient dynamic range of streak cameras.

[0057] It should be pointed out that the parameters of the diffractive optical element DOE and the lens L3c mainly include the angle, f-number, depth of field parameters, etc. of the diffractive optical element DOE, so that the dual-channel recording component can supplement some of the lost information.

[0058] Example 2:

[0059] See Figure 4 An arbitrary reflecting surface velocity interferometer based on the three-channel compressive imaging system of Example 1 includes a probe light emitting and receiving module and an interference module. The probe light emitting and receiving module is configured to emit probe light toward a target surface and direct Doppler signal light reflecting from the target surface, which carries target surface velocity information, to the interference module. The interference module is configured to form a Doppler interference fringe image and direct the generated Doppler interference fringe image toward the reflector M3 of the spectroscopic assembly.

[0060] The probe light emitting and receiving module includes a probe light source and a lens L1a, a beam splitter BS1 and a lens L1b which are sequentially arranged between the probe light source and the target surface.

[0061] The probe light emitted by the probe light source acts on the target surface through lens L1a, spectrometer BS1 and lens L1b in sequence. The target surface reflects back Doppler signal light carrying target surface velocity information, which is then emitted to the interference module through lens L1b and spectrometer BS1 in sequence.

[0062] The interference module includes a reflector M2a, a reflector M2e, and an interference assembly disposed between the reflectors M2a and M2e. The interference assembly includes a delay reflector M2d and a beam splitter BS2a, a beam splitter BS2b, a reflector M2b, and a reflector M2c arranged in a parallelogram. BS2a and BS2b are disposed at opposite ends of the short diagonal of the parallelogram, while M2b and M2c are disposed at opposite ends of the long diagonal of the parallelogram.

[0063] The Doppler signal light carrying target surface velocity information, emitted by the probe light emitting and receiving modules, passes through reflector M2a and is directed to spectroscope BS2a. BS2a splits the Doppler signal light into two beams. The Doppler signal light beam that passes through spectroscope BS2a passes through reflector M2b and is directed to spectroscope BS2b. The Doppler signal light beam reflected by spectroscope BS2a passes through reflector M2c and is directed to spectroscope BS2b. After being reflected by spectroscope BS2b and directed to reflector M2d, it is returned to spectroscope BS2b by reflector M2d. Finally, spectroscope BS2b converges the two Doppler signal light beams incident on reflectors M2b and M2d to form a Doppler interference fringe image. This image is then directed to reflector M3 of the spectroscope assembly via reflector M2e. The provision of reflector M2d forms a delayed optical path, functioning similarly to the etalon of a conventional arbitrary-reflecting-surface velocity interferometer.

[0064] Example 3:

[0065] An image reconstruction method for a three-channel compression imaging system according to embodiment 1 comprises the following steps:

[0066] If the influence of noise is not considered, the low-dimensional two-dimensional observation image recorded by the streak camera C1 or the CMOS camera C2 can be expressed as:

[0067]

[0068] In the above formula, E represents the image collected by the streak camera C1 or the CMOS camera C2, A represents the combined linear observation operator, Represents the incident light intensity information, and Represent the horizontal and vertical coordinates of the spatial dimension respectively, Represents the time dimension coordinate.

[0069] Therefore, the two dynamic coded images E1 and E2 recorded by streak camera C1 on light path 1 and light path 2 are expressed as:

[0070] , ;

[0071] In the above formula, T represents the time integration; C represents the spatial mask, which is determined by the transmission code plate OED; S represents the shear effect coefficient caused by the cathode of the streak camera C1 when scanning and recording two dynamic coding images; M represents the acquisition area of ​​the compressed image of optical path 2 offset by 1 / 2 pixel by the streak camera C1.

[0072] The dynamic coded image E1 is represented as a three-dimensional dynamic scene I containing t frames modulated by the dynamic code A. The dynamic coded image E1 is represented as:

[0073]

[0074] In the above formula, and Represent the b-th frame mask of the dynamic coded image E1 and the corresponding dynamic scene, stands for Hadamard dot product.

[0075] Write the above formula into matrix form and vectorize the corresponding matrix columns, let , , represents the operator that vectorizes the matrix columns, then:

[0076] ;

[0077] In the above formula, , ; H represents the sensing matrix, which is the cascade of diagonal matrices. The expression of the sensing matrix H is ,in, , , Represents the operator that constructs a diagonal matrix from a column vector.

[0078] Similarly, the dynamic coded image E2 is represented as a three-dimensional dynamic scene I containing t frames modulated by the dynamic code A. Then the dynamic coded image E2 is represented as:

[0079] ;

[0080] In the above formula, Also represents the sensor matrix, sensor matrix The expression is ,in, , , Indicates the b-th frame mask corresponding to the dynamic coded image E2.

[0081] The integral image E3 recorded by the CMOS camera C2 on the optical path 3 is expressed as:

[0082] ;

[0083] For the recording operation of the CMOS camera C2, the integral image E3 can be expressed as the augmented matrix and The product of , where , , is the identity matrix, Representation matrix Each column of is shifted right by b-1 bits, and the matrix With the matrix are diagonal matrix blocks with the same number of columns, and the matrix The elements on the diagonal are all 1, that is, the CMOS camera C2 is regarded as a full-1 encoding. This method can be used to deal with the time marking problem of the integral branch and the dynamic branch.

[0084] Therefore, the sampling data of optical path 1, optical path 2 and optical path 3 are Expressed as:

[0085] ;

[0086] In the above formula, represents the sampling matrix of optical path 1, optical path 2 and optical path 3, = represents the matrix column vectorization arrangement. Therefore, the sampling data of this embodiment is The dimension is compared with the sampling data of the single-channel ultrafast compression imaging system For example, having more rows can effectively increase the sampling rate by 3 times. Completed The unsampled part can effectively improve the resolution of the inverted image.

[0087] Solving the above equation is an NP-hard problem, because Satisfying the sparsity condition, the solution of the above equation is transformed into an unconstrained optimization problem:

[0088] ;

[0089] In the above formula, represents the best estimate of the original signal; ; ; It is the data fidelity term, which is used to ensure that the difference between the estimated value and the original signal is minimal; A regular term for adding constraints; is the regularization parameter, which is used to balance these two weights; It represents the value of the variable x when the following equation reaches its minimum value.

[0090] Therefore, this embodiment uses optimization theory to solve , to achieve the reconstruction of dynamic scenes, as follows:

[0091] In order to solve the above unconstrained optimization problem, a step-by-step optimization method can be adopted and the alternating direction multiplier framework can be used for solution.

[0092] First, introduce intermediate variables , so the problem is transformed into the following optimization problem:

[0093] ; ;

[0094] Then, write the above formula as the augmented Lagrangian function form:

[0095] ;

[0096] In the above formula, represents the Lagrange factor, Represents the penalty function factor.

[0097] Finally, the above optimization problem is decomposed into the following three sub-problems:

[0098] ;

[0099] ;

[0100] ;

[0101] In the above formula, represents the scaled dual variable, and its expression is ; Indicates the number of iterations.

[0102] For sub-problems , which is about For the quadratic optimization problem, according to the Lagrange first-order optimality condition, the iterative update formula of x is obtained:

[0103] ;

[0104] In the above formula, represents the identity matrix;

[0105] In order to speed up the matrix calculation process, the conjugate gradient method is used to solve the above equation.

[0106] The problem of sub- Expressed as a noise reduction problem:

[0107] ;

[0108] In the above formula, Indicates that it has parameters The denoiser, where , which means the The standard deviation of the Gaussian white noise of the denoising operator in iterations.

[0109] The total variation regularization is used to solve the above equation. This is because the data compression ratio and the size of the coded aperture collected in the ultrafast compression imaging system are large, resulting in a strong aliasing effect of the compressed image, and the total variation regularization can play a certain inhibitory role.

[0110] Among them, the expression of total variation regularization is:

[0111] ;

[0112] In the above formula, Represents total variation regularization, assuming that the image The dimension is ; m, n, p are the discretization of the image Index in three dimensions; x m 、x n 、x p Two-dimensional matrices corresponding to m, n, and p dimensions respectively; and Represent the first-order difference operators in the horizontal and vertical directions on the two-dimensional plane, respectively. In addition, in order to improve the ability to suppress aliasing effects, a deep denoiser can be combined to enhance the quality of compressed image reconstruction.

[0113] For the sub-problem , obtained by iteratively updating the formula of the above two sub-problems and , we can solve it by taking the residual (i.e. the difference between the actual observed value and the estimated value).

[0114] Iterate the solution formulas of the above three sub-problems, then determine whether the current solution meets the convergence conditions and update the number of iterations. If it meets the conditions or the number of iterations is not less than the preset maximum number of iterations, output the reconstructed dynamic scene 3D data, otherwise continue the iterative solution.

[0115] Finally, it should be noted that the above description is only a preferred embodiment of the present invention. Under the guidance of the present invention, ordinary technicians in this field can make various similar expressions without violating the purpose and claims of the present invention. Such changes fall within the scope of protection of the present invention.

Claims

1. A three-channel compression imaging system, characterized in that: The system comprises a spectroscopic component, a dual-channel recording component, and an integral channel recording component. The spectroscopic component comprises at least a spectroscope BS3. The dual-channel recording component comprises a streak camera C1 without a lens, and a transmissive encoder plate OED, a filter F3a, a lens L3b, a diffractive optical element DOE, and a lens L3c sequentially arranged between the transmissive surface of the spectroscope BS3 and the cathode of the streak camera C1. The integral channel recording component comprises a CMOS camera C2 and a filter F3b arranged between the reflective surface of the spectroscope BS3 and the lens of the CMOS camera C2. The incident Doppler interference fringe image is split into two by the beam splitter BS3. The beam reflected by the beam splitter BS3 is light path 3. The image of light path 3 passes through filter F3b and is recorded by CMOS camera C2. The beam that passes through the beam splitter BS3 passes through the transmission encoder plate OED, filter F3a, and lens L3b in sequence, and is then split into two by the diffractive optical element DOE to form light path 1 and light path 2. The images of light path 1 and light path 2 are imaged by lens L3c and are formed on the exposed cathode of streak camera C1. Among them, by setting the parameters of the diffraction optical element DOE and lens L3c, each pixel point of the optical path 2 is offset by 1 / 2 pixel diagonally toward the next row and column on the image, so as to be staggered and distributed between the pixel points of the optical path 1 without overlapping.

2. The three-channel compression imaging system according to claim 1, characterized in that: The light splitting component also includes a reflector M3 and a lens L3a; The incident Doppler interference fringe image is sequentially projected onto the beam splitter BS3 via the reflector M3 and lens L3a.

3. The three-channel compression imaging system according to claim 1 or 2, characterized in that: It also includes a probe light emitting and receiving module and an interference module, wherein the probe light emitting and receiving module is used to emit probe light toward the target surface and introduce the Doppler signal light carrying the target surface velocity information reflected by the target surface into the interference module, and the interference module is used to form a Doppler interference fringe image and introduce the Doppler interference fringe image into the spectroscopic component; The probe light emitting and receiving module includes a probe light source and a lens L1a, a beam splitter BS1 and a lens L1b which are sequentially arranged between the probe light source and the target surface; The probe light emitted by the probe light source sequentially passes through lens L1a, spectroscope BS1 and lens L1b to act on the target surface. The Doppler signal light carrying target surface velocity information reflected back by the target surface sequentially passes through lens L1b and spectroscope BS1 to the interference module.

4. The three-channel compression imaging system according to claim 3, characterized in that: The interference module includes a reflector M2a, a reflector M2e, and an interference component arranged between the reflector M2a and the reflector M2e. The interference component includes a delay reflector M2d and a beam splitter BS2a, a beam splitter BS2b, a reflector M2b, and a reflector M2c arranged in a parallelogram. The Doppler signal light carrying the target surface velocity information emitted by the probe light emitting and receiving module is emitted to the spectrometer BS2a through the reflector M2a and split into two by the spectrometer BS2a. The Doppler signal light beam that passes through the spectrometer BS2a is emitted to the spectrometer BS2b through the reflector M2b. The Doppler signal light beam reflected by the spectrometer BS2a is emitted to the spectrometer BS2b through the reflector M2c. The spectrometer BS2b is then reflected to the reflector M2d and then returned to the spectrometer BS2b by the reflector M2d. Finally, the spectrometer BS2b converges the two Doppler signal lights incident on the reflectors M2b and M2d to form a Doppler interference fringe image, which is then emitted to the spectrometer component through the reflector M2e.

5. An image reconstruction method for a three-channel compression imaging system according to any one of claims 1 to 4, characterized in that: The following steps are involved: The two dynamic coded images E1 and E2 recorded by streak camera C1 on light path 1 and light path 2 are expressed as: ， ； In the above formula, T represents the time integration, C represents the spatial mask, and I(x, y, t) represents the incident light intensity information. and Represent the horizontal and vertical coordinates of the spatial dimension respectively, represents the time dimension coordinate, S represents the shearing coefficient caused by the cathode of streak camera C1 when scanning and recording two dynamic coded images, and M represents the acquisition area of ​​the compressed image of optical path 2 offset by 1 / 2 pixel by streak camera C1; The dynamic coded image E1 is represented as a three-dimensional dynamic scene I containing t frames modulated by the dynamic code A. The dynamic coded image E1 is represented as: ； In the above formula, and Represent the b-th frame mask of the dynamic coded image E1 and the corresponding dynamic scene, stands for Hadamard dot product; Write the above formula into matrix form and vectorize the corresponding matrix columns, let , , represents the operator that vectorizes the matrix columns, then: ； In the above formula, , ; H represents the sensing matrix, which is the cascade of diagonal matrices. The expression of the sensing matrix H is ,in, , , represents an operator that constructs a column vector into a diagonal matrix; Similarly, for the dynamic coded image E2, we have: ； In the above formula, the sensing matrix The expression is ,in, , , represents the b-th frame mask corresponding to the dynamic coded image E2; The integral image E3 recorded by the CMOS camera C2 on the optical path 3 is expressed as: ； Then express the integral image E3 as the augmented matrix and The product of , where , , is the identity matrix, Representation matrix Each column of is shifted right by b-1 bits, and the matrix With the matrix are diagonal matrix blocks with the same number of columns, and the matrix The elements on the diagonal are all 1; The sampling data of optical path 1, optical path 2 and optical path 3 Expressed as: ； In the above formula, represents the sampling matrix of optical path 1, optical path 2 and optical path 3, Represents the vectorized arrangement of matrix columns; because Satisfying the sparsity condition, the solution of the above equation is transformed into an unconstrained optimization problem: ； In the above formula, represents the best estimate of the original signal, , , is the data fidelity item, is the regular term for adding constraints, is the regularization parameter, Indicates the value of the variable x when the following formula reaches the minimum value; Introducing intermediate variables , so the problem is transformed into the following optimization problem: ； ； Write the above formula in the form of augmented Lagrangian function: ； In the above formula, represents the Lagrange factor, represents the penalty function factor; The above optimization problem is decomposed into the following three sub-problems: ； ； ； In the above formula, represents the scaled dual variable, and its expression is ; Indicates the number of iterations; Iterate the solution formulas of the above three sub-problems, then determine whether the current solution meets the convergence conditions and update the number of iterations. If it meets the conditions or the number of iterations is not less than the preset maximum number of iterations, output the reconstructed dynamic scene 3D data, otherwise continue the iterative solution.

6. The image reconstruction method according to claim 5, characterized in that: For sub-problems , according to the Lagrange first-order optimality condition, the iterative update formula of x is obtained: ； In the above formula, represents the identity matrix; The conjugate gradient method is used to solve the above equation.

7. The image reconstruction method according to claim 5, characterized in that: The problem of sub- Expressed as a noise reduction problem: ； In the above formula, Indicates that it has parameters The denoiser, where , which means the The standard deviation of the Gaussian white noise of the denoising operator in the iteration; The total variation regularization is used to solve the above equation.

8. The image reconstruction method according to claim 7, characterized in that: The expression of the total variation regularization is: ； In the above formula, Represents total variation regularization, assuming that the image The dimension is ; m, n, p are the discretization of the image Index in three dimensions; x m 、x n 、x p Two-dimensional matrices corresponding to m, n, and p dimensions respectively; and represent the first-order difference operators in the horizontal and vertical directions on the two-dimensional plane, respectively.

Images