CN111179367B - A Deterministic Weighted Coding Method - Google Patents

Abstract

In order to solve the technical problem that the reconstruction quality of the compressed ultrafast imaging technology has uncertainty due to the uncertain state of the traditional encoding mode, the invention provides a deterministic weighting encoding method for the compressed ultrafast imaging technology, which comprises the following steps: 1) presetting encoding; 2) weighting the preset codes; 3) and manufacturing a coding board, and performing deterministic weighted coding on the information. Under the premise of adopting the same reconstruction algorithm, the peak signal-to-noise ratio and the structural similarity of the simulation reconstruction based on the coding mode of the invention are improved to a certain extent compared with the reconstruction result based on the existing (0-1) pseudo-random coding mode.

Description

A Deterministic Weighted Coding Method

technical field

The invention belongs to the technical field of signal and information processing, and relates to a deterministic weighted coding method for compressed ultrafast imaging technology.

Background technique

Compressed ultrafast imaging technology is a combination of compressed sensing theory and streak camera to realize two-dimensional imaging technology with time resolution ranging from picoseconds to femtoseconds. The realization process of two-dimensional imaging is shown in Figure 1. The time resolution of traditional streak cameras can reach the order of picoseconds to minutes and seconds, but its narrow slit (about 5mm) limits its imaging to a line. When the slit is opened, information at different times will intersect on the CCD. stack. The combination of compressive sensing theory and streak camera can separate overlapping two-dimensional scenes through the method of coding and compressive sensing algorithm reconstruction, and realize the purpose of two-dimensional imaging under a single exposure of streak camera. The process can be simply described as:

E(m,n)=TSCI(x,y,t) (1)

Among them: E(m,n) represents the overlapping 2D scene recorded by the CCD of the streak camera; I(x,y,t) represents the original dynamic scene, C represents the external code of DMD (Digital Micro Mirror), S represents The deflection operator of the scanning voltage of the streak camera, T represents the overlapping process of the two-dimensional dynamic scene on the CCD. The whole process can be described by the following mathematical formula

Among them: d" is the pixel size of the CCD. In order to reconstruct the overlapping two-dimensional image, the compressed sensing algorithm framework needs to be used. The inverse problem solution form can be expressed as follows:

为正则项函数。相较于传统的压缩感知算法，该重构算法框架中的正则项采用全变差(TV)模型，同时使其形式满足三维平滑的先验条件要求，具体公式描述如下：Among them: O is the linear operator (O=TSC), β is the regular term parameter,

is the regular term function. Compared with the traditional compressed sensing algorithm, the regular term in the reconstruction algorithm framework adopts the Total Variation (TV) model, and at the same time its form meets the prior requirements of three-dimensional smoothness. The specific formula is described as follows:

Among them: the index h represents the horizontal direction of each plane in the three-dimensional information, the index v represents the vertical direction of each plane in the three-dimensional information, N represents the dimension of the three-dimensional matrix, I represents the intensity of the information, x, y, t respectively Indicates the size of the three dimensions of the three-dimensional information. For a detailed description, see the document "Single-shot compressed ultrafast photography at one hundred billion frames per second".

The emergence of compressed ultrafast imaging technology has greatly reduced the application limitations of streak cameras in the field of ultrafast diagnosis, and provided a new diagnostic method for ultrafast optical characteristics research and laser inertial fusion and other fields, but the reconstruction of compressed sensing theory The result itself is a probabilistic solution. The reconstruction result of the existing algorithm can only have an ideal effect when reconstructing about 20 pictures. How to effectively ensure the accuracy and effectiveness of the solution is a challenge faced by the compressed ultrafast imaging technology. big problem. Among them, the encoding state is a key factor affecting the quality of reconstruction. The traditional encoding method uses a pseudo-random matrix containing only "0" and "1" elements, "1" represents the reflection of the digital micro-mirror, and "0" represents the digital Micromirrors discard information without reflecting. However, the uncertain state of pseudo-random coding often leads to uncertainty about the reconstruction quality of different scenes. East China Normal University once proposed to use a genetic algorithm to obtain the optimal coding state only corresponding to a specific scene to improve the reconstruction quality of compressed ultrafast imaging, but this method is cumbersome. See "Optimizing codes for compressed ultrafastphotography by the genetic algorithm" for details. Therefore, how to adopt a simple and efficient coding design method needs further research.

SUMMARY OF THE INVENTION

In order to solve the technical problem that the reconstruction quality of the compressed ultrafast imaging technology is uncertain due to the uncertain state of the traditional encoding method, the present invention provides a deterministic weighted encoding method of the compressed ultrafast imaging technology, which avoids the optimal encoding. Based on the coding method of the present invention, the reconstruction quality of the compressed ultrafast imaging technology can be effectively improved, and the local pseudo-information phenomenon of the reconstructed image can be improved.

The technical scheme of the present invention is:

A deterministic weighted coding method for compressing an ultrafast imaging system, which is special in that it includes the steps:

1) Encoding preset

1.1) Let the column vector a=[1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 01 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1];

1.2) Set the size of the precoding matrix Phi to be m×n, and construct a column vector b with the column vector a as the repeating unit, and the number of repetitions is d, where d satisfies m≤48*d≤m+48;

1.3) Let the n _i -th column (i=1, 2.., n) of the precoding matrix Phi be represented by a vector consisting of the first m elements after the column vector b is inversely cyclically shifted by 2×(i-1) elements , thereby constructing the precoding matrix Phi;

2) Weighting the preset coding

2.1) Obtain the local sparsity distribution state S in the precoding matrix Phi by convolving the precoding matrix Phi with the 3×3 all-one matrix w, where S=Phi*w;

2.2) According to the local sparsity distribution state S, calculate the global average sparsity S _a , where

2.3) Compare the local sparsity distribution state S with the global average sparsity S _a , and perform corresponding weighting processing on the element "1" at different local sparsity:

For _a local matrix whose local sparsity distribution state S is less than the global average sparsity Sa, that is, when S(i,j)≤S _a , the corresponding element Phi(i,j) is added with a smaller weight;

A larger weight is added to the corresponding element Phi( _i ,j) when the local sparsity distribution state S is greater than the global average sparsity Sa, that is, the corresponding element Phi(i,j) in the case of S( _i ,j)>Sa;

3) Make a coding board and perform deterministic weighted coding on the information

3.1) According to the preset coding after the weighting process in step 2), design coding plates with different light transmittance apertures, and different light transmittances represent different weighted states of the coding;

3.2) Use the prepared coding board as the coding device, and set it at the front end of the compression ultrafast imaging system, so as to realize the deterministic weighted coding of the information.

Further, the coding plate described in step 3.1) adopts an optical reticle.

Further, the principle of changing the weight in step 2.3) is that when the element Phi(i,j) is a non-zero element, the element value increases/decreases by 0.03.

Compared with the prior art, the beneficial effects of the present invention are:

1. The present invention uses deterministic weighted coding to replace the existing (0-1) pseudo-random coding, which avoids the randomness of image reconstruction quality caused by the randomness of pseudo-random coding, and effectively improves the ultra-fast compression. Reconstruction accuracy of imaging techniques.

2. Under the premise of using the same reconstruction algorithm, the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) of the simulation reconstruction based on the coding method of the present invention are better than those based on the existing (0-1) pseudo-random coding. The refactoring result of the method has been improved to a certain extent.

3. The present invention is also applicable to other technologies combined with compressed sensing theory, such as single-pixel camera imaging, coded aperture-based hyperspectral imaging, and the like.

Description of drawings

Figure 1 shows the realization process of 2D imaging of the compressed ultrafast imaging system.

2 is a comparison of the compression and reconstruction results of the classic image Pepper using the existing pseudo-random coding and the deterministic weighted coding method of the present invention, wherein: (a) is the original image of Pepper, and (b) is the existing pseudo-random coding re-encoding. Composition, (c) is the deterministic weighted coding reconstruction map of the present invention.

FIG. 3 is a comparison of PSNR and SSIM data of the compression and reconstruction results of the classic pictures lena and Pepper respectively using different existing pseudo-random coding and the deterministic weighted coding method of the present invention.

FIG. 4 is a flow chart of the deterministic weighted coding method of the present invention.

Detailed ways

As shown in Figure 4, the deterministic weighted coding method provided by the present invention comprises the following steps:

Step 1: Encoding Preset

In order to avoid the excessive difference in local sparsity of pseudo-random coding resulting in excessive weight range, we preset a standard triangular distribution coding method, as follows:

1.1) Let the column vector a=[1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 01 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1], the feature of this column vector is that the number of elements '0' is triangularly distributed under the condition of ensuring a certain coding sparsity;

1.2) Set the size of the precoding matrix Phi to be m×n, and construct a column vector b with the column vector a as the repeating unit, and the number of repetitions is d, where d satisfies m≤48*d≤m+48;

1.3) Let the n _i -th column (i=1, 2.., n) of the precoding matrix Phi be represented by a vector consisting of the first m elements after the column vector b is inversely cyclically shifted by 2×(i-1) elements , thereby constructing the precoding matrix Phi. For example: vector b=[1 3 5 79], the first two columns of vectors after the reverse cyclic shift operation are [7 9 1 3 5; 3 5 7 9 1], and then take the first m elements of each column, namely The first two columns of the matrix to be set.

Step 2: Weighting the preset encoding

2.1 Obtain the local sparsity distribution state S in the precoding matrix Phi by convolving the precoding matrix Phi with the 3×3 all-one matrix w, S=Phi*w;

2.2 According to the local sparsity distribution state S, calculate the global average sparsity S _a , where

2.3 Compare the local sparsity distribution state S with the global average sparsity S _a , and perform corresponding weighting processing on the element "1" at different local sparsity:

For _a local matrix whose local sparsity distribution state S is less than the global average sparsity Sa, that is, when S(i,j)≤S _a , the corresponding element Phi(i,j) is added with a smaller weight;

A larger weight is added to the corresponding element Phi( _i ,j) when the local sparsity distribution state S is greater than the global average sparsity Sa, that is, when S( _i ,j)>Sa.

Among them, the principle of changing the weight is that when the element Phi(i,j) is a non-zero element, the element value increases/decreases by about 0.03.

Step 3: Make a coding board to perform deterministic weighted coding on the information

According to the preset coding after the weighting process in step 2, coding plates with different light transmittance apertures are designed. The coding board adopts an optical mask, and different light transmittances represent different weighted states of the coding.

The digital micro-mirror is replaced by the prepared coding plate, which is used as the coding device of the compressed ultrafast imaging system, and is set at the front end of the compressed ultrafast imaging system, thereby realizing the deterministic weighted coding of the information.

The basic principle of the present invention:

The problem solved by the compressed sensing algorithm is a linear underdetermined equation. When different weights are added according to different local sparsity of the encoding, it also satisfies the following inverse problem solution form:

Among them: I _s is the set of variables with relatively strong encoding local sparsity (that is, greater than the global average sparsity), τ _s is the weighting coefficient matrix corresponding to Is _; I _c is the encoding local sparsity is weak (that is, less than the global average sparsity) ) of the variable set, τ _c is the weighting coefficient matrix corresponding to I _c ; the specific weighting method refers to the above step 2.

Simulation:

The example is applied to the two classic legends of Pepper and lena with a resolution of 128×128. The original image preprocessing method is as follows: multiply the designed weighted code with the preset image M to obtain the encoded image Phi′ , Phi′=Phi.*M. The pixel size of the preset image M is 128×128, and the encoded 10 identical images are relatively shifted by one pixel value and superimposed. This modeling process is equivalent to the encoding of the reticle, the deflection effect of the scanning voltage of the streak camera, and the compression ultrafast imaging process of superimposing the two-dimensional scene on the CCD at different times.

FIG. 2 is a comparison of the reconstruction results based on the existing (0-1) pseudo-random coding method and the present invention. It can be seen that the present invention effectively reduces the local pseudo-information phenomenon caused by the randomness of the pseudo-random coding.

Accompanying drawing 3 is after adopting 20 kinds of pseudo-random codes generated at random and the coding mode of the present invention to encode two classic pictures of Lena and Pepper respectively, and then adopt the same compression and reconstruction algorithm to obtain the result comparison, wherein the pseudo-random coding and the present invention are compared. The sampling rate is 0.25. It can be seen that the peak signal to noise ratio (PSNR) and structural similarity index (SSIM) after reconstruction based on the coding method of the present invention are obviously better than the existing methods.

Claims (3)

1. a deterministic weighted coding method for compressing ultrafast imaging system, is characterized in that, comprises the steps: 1) Encoding preset 1.1) Let the column vector a=[1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 00 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1]; 1.2) Set the size of the precoding matrix Phi to be m×n, and construct a column vector b with the column vector a as the repeating unit, and the number of repetitions is d, where d satisfies m≤48*d≤m+48; 1.3) Let the n _i -th column (i=1, 2.., n) of the precoding matrix Phi be represented by a vector consisting of the first m elements after the column vector b is inversely cyclically shifted by 2×(i-1) elements , thereby constructing the precoding matrix Phi; 2) Weighting the preset coding 2.1) Obtain the local sparsity distribution state S in the precoding matrix Phi by convolving the precoding matrix Phi with the 3×3 all-one matrix w, where S=Phi*w; 2.2) According to the local sparsity distribution state S, calculate the global average sparsity S _a , where

2.3) Compare the local sparsity distribution state S with the global average sparsity S _a , and perform corresponding weighting processing on the element "1" at different local sparsity: For _a local matrix whose local sparsity distribution state S is less than the global average sparsity Sa, that is, when S(i,j)≤S _a , the corresponding element Phi(i,j) is added with a smaller weight; A larger weight is added to the corresponding element Phi( _i ,j) when the local sparsity distribution state S is greater than the global average sparsity Sa, that is, the corresponding element Phi(i,j) in the case of S( _i ,j)>Sa; 3) Make a coding board and perform deterministic weighted coding on the information 3.1) According to the preset coding after the weighting process in step 2), design coding plates with different light transmittance apertures, and different light transmittances represent different weighted states of the coding; 3.2) Use the prepared coding board as the coding device, and set it at the front end of the compression ultrafast imaging system, so as to realize the deterministic weighted coding of the information. 2 . The deterministic weighted coding method according to claim 1 , wherein: the coding plate described in step 3.1) adopts an optical mask. 3 . 3. deterministic weighted coding method according to claim 1, is characterized in that: in step 2.3), the principle of changing weight is that in the case that element Phi(i, j) is a non-zero element, element value increases/decreases by 0.03 .

Images