CN112802135A - Ultrathin lens-free separable compression imaging system and calibration and reconstruction method thereof - Google Patents

Abstract

The invention provides an ultra-thin lensless separable compression imaging system and a calibration and reconstruction method thereof. The imaging system includes a random coded aperture mask, an image sensor, a hollow box with openings at the front and rear ends, and an opaque fixed plate. The coded aperture mask is sealed at the front opening of the hollow box, the image sensor and the hollow box are both fixed on the opaque fixing plate, and the image sensor is located in the rear opening of the hollow box. The invention realizes imaging by using random coded aperture, which not only maximizes the luminous flux, but also greatly reduces the thickness, volume and weight of the imaging system, reduces the cost, and has the advantages of compact structure, light weight and low cost; According to the separable compressed sensing theory, the invention applies the separable matrix to the measurement matrix of the imaging system, which significantly reduces the difficulty of calibration and reconstruction of the imaging system, and has the advantages of optical realization and calculation feasibility.

Description

An ultra-thin lensless separable compression imaging system and its calibration and reconstruction method

technical field

The invention relates to the technical field of coded aperture imaging, in particular to an ultra-thin lensless separable compression imaging system and a calibration and reconstruction method thereof.

Background technique

The existing imaging systems are generally lens-based imaging systems, which are affected by factors such as the number, thickness, and focusing space of lenses, and have problems such as large volume, high price, cumbersome assembly, and limited installation space. For example, lens-based imaging The system's lenses for visible light can be made from inexpensive materials such as glass and plastic, but lenses for the infrared and ultraviolet spectrum are very expensive; lens-based imaging systems always require assembly, reducing manufacturing efficiency.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide an ultra-thin lensless separable compression imaging system and a calibration and reconstruction method thereof. The imaging system has the advantages of compact structure, light weight and low cost, and by adopting a separable design, it can reduce the Difficulty of imaging system calibration and reconstruction.

The technical scheme of the present invention is:

An ultra-thin lensless separable compression imaging system, the imaging system includes a random coded aperture mask, an image sensor, a hollow box with openings at the front and rear ends, and an opaque fixed plate, the random coded aperture mask is sealed and covered at the At the front opening of the hollow box, the image sensor and the hollow box are both fixed on the opaque fixing plate, and the image sensor is located in the rear opening of the hollow box, and the image sensor and the random The center points of the coded aperture mask are collinear, and the random coded aperture mask is composed of opaque elements and transparent elements, the opaque elements are used for blocking light, and the transparent elements are used for transmitting light.

In the ultra-thin lensless separable compression imaging system, the opaque fixed plate is a black plate.

In the ultra-thin lensless separable compression imaging system, the hollow box is a cuboid structure composed of opaque isolation plates.

A method for calibrating an ultra-thin lensless separable compression imaging system, the measurement matrix of the imaging system adopts a separable matrix, and the method comprises the following steps:

(1) calibrating the left separation matrix of the measurement matrix, specifically including:

(11) Select N calibration images C _k =h _k 1 ^T , k=1,2,...,N, where h _k represents the kth column of the Hadamard matrix H of N×N order, and 1 represents the N-dimensional full 1 column vector, 1 ^T represents the transpose of 1;

和

并分别投影到显示器上，其中

表示将C_k中所有+1元素保留、-1元素设置为0得到的图像，

表示将-C_k中所有+1元素保留、-1元素设置为0得到的图像；(12) Divide the calibration image C _k , k=1,2,...,N into two images

and

and projected onto the monitor respectively, where

represents the image obtained by keeping all +1 elements in C _k and setting -1 elements to 0,

Indicates the image obtained by keeping all +1 elements in -C _k and setting -1 elements to 0;

和

在图像传感器上得到的M×M阶的测量值

和

相减，得到标定图像C_k的测量值Y_k；(13) Combine the two images

and

Measured values of order M×M obtained on the image sensor

and

Subtraction to obtain the measured value Y _{k of the calibration image C k ;}

(14) Perform a rank-one approximation on the measured values Y _k , k=1,2,...,N to obtain a matrix

进行奇异值分解，并将分解得到的包含左奇异向量的正交矩阵与包含奇异值的对角矩阵相乘，将相乘得到的矩阵的第1列记为u_k,k＝1,2,…,N，则u_k为M维列向量；(15) Pair matrix

Perform singular value decomposition, multiply the obtained orthogonal matrix containing left singular vectors with the diagonal matrix containing singular values, and denote the first column of the multiplied matrix as u _k , k=1,2, ...,N, then _uk is an M-dimensional column vector;

(16) Combine the M-dimensional column vectors u _k , k=1, 2,...,N together to form an M×N-order matrix [u ₁ ; u ₂ ;...;u _N ];

(17) Use the following formula to calibrate the left separation matrix:

表示左分离矩阵Φ_L的标定矩阵，H^-1＝H^T/N，H^T表示H的转置；in,

Represents the calibration matrix of the left separation matrix Φ _L , H ^-1 =H ^T /N, H ^T represents the transpose of H;

(2) calibrating the right separation matrix of the measurement matrix, specifically including:

(21) Select N calibration images C′ _k =1h _k ^T , k=1,2,...,N, where 1 represents an N-dimensional all-one column vector, and h _k represents the Hadamard matrix H of N×N order In the kth column, h _k ^T represents the transpose of h _k ;

和

并分别投影到显示器上，其中

表示将C′_k中所有+1元素保留、-1元素设置为0得到的图像，

表示将-C′_k中所有+1元素保留、-1元素设置为0得到的图像；(22) Divide the calibration image C′ _k , k=1,2,...,N into two images

and

and projected onto the monitor respectively, where

represents the image obtained by keeping all +1 elements in C′ _k and setting the -1 elements to 0,

Indicates the image obtained by retaining all +1 elements in -C' _k and setting -1 elements to 0;

和

在图像传感器上得到的M×M阶的测量值

和

相减，得到标定图像C′_k的测量值Y′_k；(23) Combine the two images

and

Measured values of order M×M obtained on the image sensor

and

Subtraction to obtain the measured value Y' _{k of the calibration image C' k ;}

(24) Perform a rank-one approximation on the measured values Y′ _k , k=1,2,...,N to obtain a matrix

进行奇异值分解，并将分解得到的包含奇异值的对角矩阵与包含右奇异向量的正交矩阵的转置相乘，将相乘得到的矩阵的第1列记为v_k,k＝1,2,…,N，则v_k为M维列向量；(25) Pair matrix

Perform singular value decomposition, multiply the obtained diagonal matrix containing singular values by the transpose of the orthogonal matrix containing the right singular vector, and denote the first column of the multiplied matrix as v _k , k=1 ,2,...,N, then v _k is an M-dimensional column vector;

(26) Combine M-dimensional column vectors v _k , k=1, 2,...,N to form a matrix of M×N order [v ₁ ; v ₂ ;...;v _N ];

(27) Use the following formula to calibrate the right separation matrix:

表示右分离矩阵Φ_R的标定矩阵，H^-1＝H^T/N，H^T表示H的转置。in,

Represents the calibration matrix of the right separation matrix Φ _R , H ^-1 =H ^T /N, and H ^T represents the transpose of H.

A reconstruction method of an ultra-thin lensless separable compression imaging system, the measurement matrix of the imaging system adopts a separable matrix, and the method comprises the following steps:

(1) Perform singular value decomposition on the calibration matrix of the left separation matrix of the measurement matrix and the calibration matrix of the right separation matrix, and use the following formula to calculate its pseudo-inverse:

表示左分离矩阵Φ_L的标定矩阵

的伪逆，

表示右分离矩阵Φ_R的标定矩阵

的伪逆，U_L表示对

进行奇异值分解得到的包含左奇异向量的正交矩阵，Σ_L表示对

进行奇异值分解得到的包含奇异值的对角矩阵，V_L表示对

进行奇异值分解得到的包含右奇异向量的正交矩阵，

表示U_L的转置，

表示Σ_L的逆矩阵，U_R表示对

进行奇异值分解得到的包含左奇异向量的正交矩阵，Σ_R表示对

进行奇异值分解得到的包含奇异值的对角矩阵，V_R表示对

进行奇异值分解得到的包含右奇异向量的正交矩阵，

表示U_R的转置，

表示Σ_R的逆矩阵；in,

The calibration matrix representing the left separation matrix Φ _L

The pseudo-inverse of ,

The calibration matrix representing the right separation matrix Φ _R

The pseudo-inverse of , U _L denotes the pair

Orthogonal matrix containing left singular vectors obtained by singular value decomposition, Σ _L represents the pair

The diagonal matrix containing singular values obtained by singular value decomposition, V _L represents the pair

The orthonormal matrix containing the right singular vector obtained by singular value decomposition,

represents the _transpose of UL,

represents the inverse of Σ _L , and _UR represents the pair

Orthogonal matrix containing left singular vectors obtained by singular value decomposition, Σ _R represents the pair

The diagonal matrix containing singular values obtained by singular value decomposition, VR _represents the pair

The orthonormal matrix containing the right singular vector obtained by singular value decomposition,

represents the transpose of _UR ,

represents the inverse matrix of Σ _R ;

(2) Judging whether the left separation matrix and the right separation matrix are well calibrated, if so, jump to step (3), if not, jump to step (4);

(3) According to the measured value of the target image, the reconstructed target image is obtained by calculating the following formula:

表示重建的目标图像，Y表示目标图像的测量值；in,

represents the reconstructed target image, and Y represents the measured value of the target image;

(4) According to the measured value of the target image, the following formula is used to calculate the reconstructed target image:

表示重建的目标图像，Y表示目标图像的测量值，σ_L和σ_R为中间变量，σ_L＝(Σ_L)²，σ_R＝(Σ_R)²,

表示σ_R的转置，τ表示正则化参数，1表示N维全1列向量，1^T表示1的转置，

表示V_R的转置，·/表示点除。in,

represents the reconstructed target image, Y represents the measured value of the target image, σ _L and σ _R are intermediate variables, σ _L =(Σ _L ) ² , σ _R =(Σ _R ) ² ,

represents the transpose of σ _R , τ represents the regularization parameter, 1 represents an N-dimensional all-one column vector, 1 ^T represents the transpose of 1,

Represents the transpose of _VR , ·/ represents point division.

It can be seen from the above technical solutions that the present invention realizes imaging by using random coded apertures, which not only maximizes the luminous flux, but also greatly reduces the thickness, volume and weight of the imaging system, and reduces the cost, and has the advantages of compact structure, light weight and low cost. In addition, according to the theory of separable compressed sensing, the present invention applies the separable matrix to the measurement matrix of the imaging system, which significantly reduces the difficulty of the calibration and reconstruction of the imaging system, and has the advantages of optical implementation and computational feasibility.

Description of drawings

FIG. 1 is a schematic structural diagram of an imaging system of the present invention.

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

As shown in FIG. 1 , an ultra-thin lensless separable compression imaging system includes a randomly coded aperture mask 1 , an image sensor 2 , a hollow box 3 with openings at the front and rear ends, and an opaque fixing plate 4 . The random coded aperture mask 1 is sealed and covered on the front opening of the hollow box 3 , the image sensor 2 and the hollow box 3 are both fixed on the opaque fixing plate 4 , and the image sensor 2 is located in the rear opening of the hollow box 3 . , the image sensor 2 is collinear with the center point of the random coded aperture mask 1.

The imaging system of the present invention is mainly composed of a random coded aperture mask 1 and an image sensor 2 . The introduction of the hollow box 3 and the opaque fixing plate 4 can keep the distance between the random coded aperture mask 1 and the image sensor 2 fixed, and can also block stray light to ensure that the light will not bypass the random coded aperture mask 1 from the two. The side irradiates onto the image sensor 2 so that the measured value noise is as small as possible. The hollow box body 3 is of a rectangular parallelepiped structure and is composed of an opaque isolation plate, and the opaque fixed plate 4 is a black plate.

The randomly coded aperture mask 1 and the image sensor 2 are considered to be planar and parallel to each other. A randomly coded aperture mask 1 is placed in front of the image sensor at a distance d (typically measured on the order of microns). The random coded aperture mask 1 is binary and consists of opaque elements and transparent elements. The opaque elements are used to block light and the transparent elements are used to transmit light. The ideal random code aperture mask 1 can maximize the light flux. The present invention can be imaged under incoherent light, and the object can be imaged under natural light.

The design of the coded aperture plays an important role in imaging. An ideal design would maximize luminous flux while providing a well-conditioned scene-to-image sensor transfer function for easy inversion. The main purpose of random coded apertures is to provide a more randomized modulation of information, preserving as much information as possible.

In the imaging system of the present invention, the random coded aperture plays the role of measuring the scene in the real world and mapping it to the image sensor 2, and its mathematical model can be represented by the measurement matrix (ie the scene-image sensor transfer function matrix) Φ as A projection matrix of order M×N. Before conducting real experiments using the imaging system of the present invention, the measurement matrix Φ must be calibrated to determine the mapping between the scene and the measurement values of the image sensor 2 so that scene recovery can be achieved from the measurement values of the image sensor 2 .

In order to reduce the storage dimension of the measurement matrix Φ, a separable design idea is adopted to improve the measurement matrix Φ of the imaging system of the present invention, thereby reducing the difficulty of calibration and reconstruction of the imaging system. The measurement matrix Φ can be expressed as:

表示Kronecker积，可以是直接乘积或张量积。Among them, Φ _L and Φ _R represent the left separation matrix and the right separation matrix of the measurement matrix Φ, respectively,

Represents the Kronecker product, which can be a direct product or a tensor product.

Therefore, the calibration of the measurement matrix Φ is transformed into the calibration of its left separation matrix Φ _L and right separation matrix Φ _R.

A method for calibrating an ultra-thin lensless separable compression imaging system, comprising the following steps:

S1, calibrate the left separation matrix Φ _L of the measurement matrix Φ, which specifically includes:

S11. Select N calibration images C _k =h _k 1 ^T , _k =1, 2, . Column vector, 1 ^T represents the transpose of 1.

和

并分别投影到显示器上，其中

表示将C_k中所有+1元素保留、-1元素设置为0得到的图像，

表示将-C_k中所有+1元素保留、-1元素设置为0得到的图像。S12. Divide the calibration image C _k , k=1,2,...,N into two images

and

and projected onto the monitor respectively, where

represents the image obtained by keeping all +1 elements in C _k and setting -1 elements to 0,

Represents the image obtained by keeping all +1 elements in -C _k and setting -1 elements to 0.

和

The Hadamard matrix H consists of elements +1 and -1, resulting in that each calibration image C _k , k=1,2,...,N generated by Hadamard mode needs to be split into two images

and

和

在图像传感器上得到的M×M阶的测量值

和

相减，得到标定图像C_k的测量值Y_k：S13. Combine the two images

and

Measured values of order M×M obtained on the image sensor

and

Subtraction to obtain the measured value Y _{k of the calibration image C k :}

S14. Perform a rank-one approximation on the measured values y _k , k=1, 2, ..., N to obtain a matrix

进行奇异值分解，并将分解得到的包含左奇异向量的正交矩阵U与包含奇异值的对角矩阵Σ(该对角矩阵只有第一个元素不为0，其它元素均为0)相乘，将相乘得到的矩阵的第1列记为u_k,k＝1,2,…,N，则u_k为M维列向量，令：S15, pair matrix

Perform singular value decomposition, and multiply the resulting orthogonal matrix U containing left singular vectors with a diagonal matrix Σ containing singular values (only the first element of the diagonal matrix is not 0, and other elements are 0) , denote the first column of the multiplied matrix as u _k , k=1,2,...,N, then u _k is an M-dimensional column vector, let:

Since Y _k =Φ _L C _k (Φ _R ) ^T =(Φ _L h _k )(Φ _R 1) ^T , then:

u _k =Φ _L h _k

S16. Combine the M-dimensional column vectors u _k , k=1, 2,...,N together to form an M×N-order matrix [u ₁ ; u ₂ ;...; u _N ], there are:

[u ₁ ; u ₂ ;...;u _N ]=Φ _L [h ₁ ;h ₂ ;...;h _N ]=Φ _L H

S17. Use the following formula to calibrate the left separation matrix Φ _L :

表示左分离矩阵Φ_L的标定矩阵，H^-1＝H^T/N，H^T表示H的转置。in,

Represents the calibration matrix of the left separation matrix Φ _L , H ^-1 =H ^T /N, and H ^T represents the transpose of H.

S2, calibrate the right separation matrix Φ _R of the measurement matrix Φ, specifically including:

S21. Select N calibration images C′ _k = 1h _k ^T , _k =1, 2, . Column k, h _k ^T represents the transpose of h _k .

和

并分别投影到显示器上，其中

表示将C′_k中所有+1元素保留、-1元素设置为0得到的图像，

表示将-C′_k中所有+1元素保留、-1元素设置为0得到的图像。S22. Divide the calibration image C′ _k , k=1,2,...,N into two images

and

and projected onto the monitor respectively, where

represents the image obtained by keeping all +1 elements in C′ _k and setting the -1 elements to 0,

Represents the image obtained by keeping all +1 elements in -C' _k and setting -1 elements to 0.

和

The Hadamard matrix H consists of elements +1 and -1, resulting in that each calibration image C′ _k , k=1,2,...,N generated by Hadamard mode needs to be divided into two images

and

和

在图像传感器上得到的M×M阶的测量值

和

相减，得到标定图像C′_k的测量值Y′_k：S23. Combine the two images

and

Measured values of order M×M obtained on the image sensor

and

Subtraction to obtain the measured value Y' _{k of the calibration image C' k :}

S24. Perform a rank-one approximation on the measured values Y′ _k , k=1, 2, ..., N to obtain a matrix

进行奇异值分解，并将分解得到的包含奇异值的对角矩阵Σ′(该对角矩阵只有第一个元素不为0，其它元素均为0)与包含右奇异向量的正交矩阵V′的转置(V′)^T相乘，将相乘得到的矩阵的第1列记为v_k,k＝1,2,…,N，则v_k为M维列向量，令：S25, pair matrix

Perform singular value decomposition, and decompose the diagonal matrix Σ' containing singular values (only the first element of the diagonal matrix is not 0, and other elements are 0) and the orthogonal matrix V' containing the right singular vector Multiply the transpose (V′) ^T of , and denote the first column of the multiplied matrix as v _k , k=1,2,...,N, then v _k is an M-dimensional column vector, let:

Since Y′ _k =Φ _L C′ _k (Φ _R ) ^T =(Φ _L 1)(Φ _R h _k ) ^T , then:

v _k =Φ _R h _k

S26. Combine the M-dimensional column vectors v _k , k=1, 2,...,N together to form an M×N-order matrix [v ₁ ; v ₂ ;...; v _N ], there are:

[v ₁ ; v ₂ ;...;v _N ]=Φ _R [h ₁ ;h ₂ ;...;h _N ]=Φ _R H

S27. Use the following formula to calibrate the right separation matrix Φ _R :

表示右分离矩阵Φ_R的标定矩阵，H^-1＝H^T/N，H^T表示H的转置。in,

Represents the calibration matrix of the right separation matrix Φ _R , H ^-1 =H ^T /N, and H ^T represents the transpose of H.

A reconstruction method of an ultra-thin lensless separable compression imaging system, comprising the following steps:

和

进行奇异值分解，并采用以下公式计算其伪逆：s1, the calibration matrix for the left separation matrix Φ _L of the measurement matrix Φ and the right separation matrix Φ _R

and

Perform singular value decomposition and compute its pseudoinverse using the following formula:

表示左分离矩阵Φ_L的标定矩阵

的伪逆，

表示右分离矩阵Φ_R的标定矩阵

的伪逆，U_L表示对

进行奇异值分解得到的包含左奇异向量的正交矩阵，Σ_L表示对

进行奇异值分解得到的包含奇异值的对角矩阵，V_L表示对

进行奇异值分解得到的包含右奇异向量的正交矩阵，

表示U_L的转置，

表示Σ_L的逆矩阵，U_R表示对

进行奇异值分解得到的包含左奇异向量的正交矩阵，Σ_R表示对

进行奇异值分解得到的包含奇异值的对角矩阵，V_R表示对

进行奇异值分解得到的包含右奇异向量的正交矩阵，

表示U_R的转置，

表示Σ_R的逆矩阵。in,

The calibration matrix representing the left separation matrix Φ _L

The pseudo-inverse of ,

The calibration matrix representing the right separation matrix Φ _R

The pseudo-inverse of , U _L denotes the pair

Orthogonal matrix containing left singular vectors obtained by singular value decomposition, Σ _L represents the pair

The diagonal matrix containing singular values obtained by singular value decomposition, V _L represents the pair

The orthonormal matrix containing the right singular vector obtained by singular value decomposition,

represents the _transpose of UL,

represents the inverse of Σ _L , and _UR represents the pair

Orthogonal matrix containing left singular vectors obtained by singular value decomposition, Σ _R represents the pair

The diagonal matrix containing singular values obtained by singular value decomposition, VR _represents the pair

The orthonormal matrix containing the right singular vector obtained by singular value decomposition,

represents the transpose of _UR ,

represents the inverse of Σ _R.

s2. Determine whether the left separation matrix Φ _L and the right separation matrix Φ _R are well calibrated, if so, jump to step s3, and if not, jump to step s4.

s3. According to the measurement value of the target image, use the following formula to calculate the reconstructed target image:

表示重建的目标图像，Y表示目标图像的测量值。in,

represents the reconstructed target image, and Y represents the measured value of the target image.

s4. According to the measured value of the target image, use the following formula to calculate the reconstructed target image:

表示重建的目标图像，Y表示目标图像的测量值，σ_L和σ_R为中间变量，σ_L＝(Σ_L)²，σ_R＝(Σ_R)²,

表示σ_R的转置，τ表示正则化参数，1表示N维全1列向量，1^T表示1的转置，

表示V_R的转置，·/表示点除。in,

represents the reconstructed target image, Y represents the measured value of the target image, σ _L and σ _R are intermediate variables, σ _L =(Σ _L ) ² , σ _R =(Σ _R ) ² ,

represents the transpose of σ _R , τ represents the regularization parameter, 1 represents an N-dimensional all-one column vector, 1 ^T represents the transpose of 1,

Represents the transpose of _VR , ·/ represents point division.

It can be seen from the above reconstruction method that if Φ _L and Φ _R are both well-calibrated, then the unknown scene X can be estimated by solving a least squares problem:

The solution is in closed form:

噪声放大的影响，减小噪声的一个简单方法是在最小二乘法问题中增加正则化项：If the calibration conditions of Φ _L and Φ _R are not good or insufficient, it is necessary to consider the least squares estimation

The effect of noise amplification, a simple way to reduce the noise is to add a regularization term to the least squares problem:

和

的SVD明确写出：where τ > 0, the solution of the above equation can also be used

and

The SVD explicitly writes:

The above-mentioned embodiments are only to describe the preferred embodiments of the present invention, and do not limit the scope of the present invention. On the premise of not departing from the design spirit of the present invention, various modifications made by those of ordinary skill in the art to the technical solutions of the present invention and improvements, all should fall within the protection scope determined by the claims of the present invention.

Claims (5)

1. An ultra-thin lensless separable compression imaging system, characterized in that: the imaging system comprises a random coded aperture mask, an image sensor, a hollow box body and an opaque fixed plate opened at the front and rear ends, and the random coded aperture mask The film is sealed and covered at the front opening of the hollow box, the image sensor and the hollow box are both fixed on the opaque fixing plate, and the image sensor is located in the rear opening of the hollow box, the The image sensor is collinear with the center point of the random coded aperture mask, the random coded aperture mask is composed of opaque elements and transparent elements, the opaque elements are used to block light, and the transparent elements are used to transmit light. 2 . The ultra-thin lensless separable compression imaging system according to claim 1 , wherein the opaque fixed plate is a black plate. 3 . 3 . The ultra-thin lensless separable compression imaging system according to claim 1 , wherein the hollow box is a cuboid structure composed of opaque isolation plates. 4 . 4. A calibration method of an ultra-thin lensless separable compression imaging system, the measurement matrix of the imaging system adopts a separable matrix, and it is characterized in that, the method comprises the following steps: (1) calibrating the left separation matrix of the measurement matrix, specifically including: (11) Select N calibration images C _k =h _k 1 ^T , k=1,2,...,N, where h _k represents the kth column of the Hadamard matrix H of N×N order, and 1 represents the N-dimensional full 1 column vector, 1 ^T represents the transpose of 1; (12) Divide the calibration image C _k , k=1,2,...,N into two images

and

and projected onto the monitor respectively, where

represents the image obtained by keeping all +1 elements in C _k and setting -1 elements to 0,

Indicates the image obtained by keeping all +1 elements in -C _k and setting -1 elements to 0; (13) Combine the two images

and

Measured values of order M×M obtained on the image sensor

and

Subtraction to obtain the measured value Y _{k of the calibration image C k ;} (14) Perform a rank-one approximation on the measured values Y _k , k=1,2,...,N to obtain a matrix

(15) Pair matrix

Perform singular value decomposition, multiply the obtained orthogonal matrix containing left singular vectors with the diagonal matrix containing singular values, and denote the first column of the multiplied matrix as u _k , k=1,2, ...,N, then _uk is an M-dimensional column vector; (16) Combine the M-dimensional column vectors u _k , k=1, 2,...,N together to form an M×N-order matrix [u ₁ ; u ₂ ;...;u _N ]; (17) Use the following formula to calibrate the left separation matrix:

in,

Represents the calibration matrix of the left separation matrix Φ _L , H ^-1 =H ^T /N, H ^T represents the transpose of H; (2) calibrating the right separation matrix of the measurement matrix, specifically including: (21) Select N calibration images C′ _k =1h _k ^T , k=1,2,...,N, where 1 represents an N-dimensional all-one column vector, and h _k represents the Hadamard matrix H of N×N order In the kth column, h _k ^T represents the transpose of h _k ; (22) Divide the calibration image C′ _k , k=1,2,...,N into two images

and

and projected onto the monitor respectively, where

represents the image obtained by keeping all +1 elements in C′ _k and setting the -1 elements to 0,

Indicates the image obtained by retaining all +1 elements in -C' _k and setting -1 elements to 0; (23) Combine the two images

and

Measured values of order M×M obtained on the image sensor

and

Subtraction to obtain the measured value Y' _{k of the calibration image C' k ;} (24) Perform a rank-one approximation on the measured values Y′ _k , k=1,2,...,N to obtain a matrix

(25) Pair matrix

Perform singular value decomposition, multiply the obtained diagonal matrix containing singular values by the transpose of the orthogonal matrix containing the right singular vector, and denote the first column of the multiplied matrix as v _k , k=1 ,2,...,N, then v _k is an M-dimensional column vector; (26) Combine M-dimensional column vectors v _k , k=1, 2,...,N to form a matrix of M×N order [v ₁ ; v ₂ ;...;v _N ]; (27) Use the following formula to calibrate the right separation matrix:

in,

Represents the calibration matrix of the right separation matrix Φ _R , H ^-1 =H ^T /N, and H ^T represents the transpose of H. 5. A reconstruction method of an ultra-thin lensless separable compression imaging system, the measurement matrix of the imaging system adopts a separable matrix, and it is characterized in that, the method comprises the following steps: (1) Perform singular value decomposition on the calibration matrix of the left separation matrix of the measurement matrix and the calibration matrix of the right separation matrix, and use the following formula to calculate its pseudo-inverse:

in,

The calibration matrix representing the left separation matrix Φ _L

The pseudo-inverse of ,

The calibration matrix representing the right separation matrix Φ _R

The pseudo-inverse of , U _L denotes the pair

Orthogonal matrix containing left singular vectors obtained by singular value decomposition, Σ _L represents the pair

The diagonal matrix containing singular values obtained by singular value decomposition, V _L represents the pair

The orthonormal matrix containing the right singular vector obtained by singular value decomposition,

represents the _transpose of UL,

represents the inverse of Σ _L , and _UR represents the pair

Orthogonal matrix containing left singular vectors obtained by singular value decomposition, Σ _R represents the pair

The diagonal matrix containing singular values obtained by singular value decomposition, VR _represents the pair

The orthonormal matrix containing the right singular vector obtained by singular value decomposition,

represents the transpose of _UR ,

represents the inverse matrix of Σ _R ; (2) Judging whether the left separation matrix and the right separation matrix are well calibrated, if so, jump to step (3), if not, jump to step (4); (3) According to the measured value of the target image, the reconstructed target image is obtained by calculating the following formula:

in,

represents the reconstructed target image, and Y represents the measured value of the target image; (4) According to the measured value of the target image, the following formula is used to calculate the reconstructed target image:

in,

represents the reconstructed target image, Y represents the measured value of the target image, σ _L and σ _R are intermediate variables, σ _L =(Σ _L ) ² , σ _R =(Σ _R ) ² ,

represents the transpose of σ _R , τ represents the regularization parameter, 1 represents an N-dimensional all-one column vector, 1 ^T represents the transpose of 1,

Represents the transpose of _VR , ·/ represents point division.

Images