Sparse sample mixed detection method and system based on sparse ternary Bernoulli matrix

Abstract

The present invention discloses a sparse sample mixed inspection method and system based on a sparse three-value Bernoulli matrix, which belongs to the field of early epidemic infection screening. The method is: numbering a plurality of samples to be tested collected, and preparing multiple copies of equal amount for each sample; setting the number of mixing operations, and setting the generation probability of elements in the sampling sequence; setting two mixing groups for each mixing operation, randomly generating a sampling sequence according to the set probability, and performing grouping operations on each sample according to the sampling sequence. After all samples are grouped, the virus concentration of the two mixed samples is detected and the virus concentration difference is recorded; sparse three-value Bernoulli matrix modeling is performed according to the adopted mixing operation and the corresponding virus concentration detection results; the detection problem is converted into a sparse reconstruction problem, and a sparse signal recovery algorithm is used to obtain a sparse solution to determine the virus infected person. The present invention is suitable for large-scale virus detection scenarios, and has the characteristics of low detection cost, strong operability and high accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of early epidemic infection screening, and specifically relates to a sparse sample mixed testing method and system based on a sparse three-valued Bernoulli matrix. Background Art

[0002] In the prevention and control of the epidemic, timely detection of infected people is extremely important, but the realization of this goal faces huge challenges and also requires a high price. Even if some costs are reduced through mixed testing, a large amount of funds and manpower are still required, and a lot of social resources and time costs are consumed.

[0003] In the early stages of a pandemic, there are very few infected people, which can be regarded as a sparse signal. Virus samples from subjects, of which the number of positive samples does not exceed ( ), in order to reduce reagent consumption and detection costs, and to detect with high probability The most direct mixing strategy is to select an appropriate number of samples to mix (10 mixed with 1), and then test the mixed samples, which can reduce the number of tests to This essentially corresponds to an observation matrix ( ), Each row of represents a mixed sample, and the mixed test sample is , a total of If the measurement matrix is ​​a Bernoulli matrix, since the Bernoulli random matrix has the restricted isometry property (RIP), according to the compressed sensing theory, High probability of detection with one test positive samples. When it is very big, , which means that the number of tests is greatly reduced, the consumption of test reagents is greatly reduced, and thus the cost of testing is greatly reduced; and the sparsity of the Bernoulli matrix also makes the mixing operation feasible. Summary of the invention

[0004] In order to solve the problems in the prior art, the present invention proposes a sparse sample mixed detection method and system based on a sparse three-valued Bernoulli matrix.

[0005] The technical solution adopted by the present invention is as follows:

[0006] In a first aspect, the present invention discloses a hybrid detection method for large-scale sparse samples based on a Bernoulli matrix, comprising the following steps:

[0007] S1: Number the collected samples to be tested and prepare multiple copies of equal amount for each sample;

[0008] S2: Set the number of mixing operations M, perform mixing operations and virus concentration detection;

[0009] Among them, two mixing groups are set for each mixing operation, and the sampling sequence of the mixing operation is randomly generated according to the set probability. Each sample is assigned to two mixing groups or does not participate in the mixing according to the sampling sequence. After the sample grouping is completed, the samples in the first group are mixed to obtain a first mixed sample, and the samples in the second group are mixed to obtain a second mixed sample. The virus concentration of the two mixed samples is detected and the virus concentration difference is recorded;

[0010] S3: Perform mathematical modeling based on the mixing operation adopted in S2 and the corresponding virus concentration detection results;

[0011] S4: Based on the results of mathematical modeling, the detection problem is converted into a sparse reconstruction problem, and a sparse signal recovery algorithm is used to obtain a sparse solution to identify virus-infected persons.

[0012] In the second aspect, the present invention provides a large-scale sparse sample mixing detection system for implementing the above method, which includes: a sample preprocessing module to be tested, a sample mixing module, a virus concentration detection, a mathematical modeling module and an infected person determination module; the sample preprocessing module to be tested is used to number the collected samples to be tested and prepare multiple equal copies of each sample; the sample mixing module performs sample mixing operations according to a set mixing scheme, and for each mixing operation, randomly generates a sampling sequence according to a set probability, and assigns each sample to two mixing groups or does not participate in the mixing according to the sampling sequence. After the sample grouping is completed, the samples in the first group are mixed to obtain a first mixed sample, and the samples in the second group are mixed to obtain a second mixed sample; the virus concentration detection is used to detect the virus concentration of the two mixed samples obtained by each mixing operation and record the virus concentration difference; the mathematical modeling module performs mathematical modeling according to the mixing operation adopted by the sample mixing module and the detection results of the virus concentration detection; the infected person determination module obtains a model based on the mathematical modeling module, converts the detection problem into a sparse reconstruction problem, adopts a sparse signal recovery algorithm to obtain a sparse solution, and determines the virus infected person.

[0013] In a third aspect, the present invention discloses an electronic device, including a processor and a memory, wherein the memory stores machine executable instructions that can be executed by the processor, and the processor executes the machine executable instructions to implement the hybrid detection method of large-scale sparse samples based on the Bernoulli matrix.

[0014] In a fourth aspect, the present invention discloses a machine-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, they are used to implement the hybrid detection method of large-scale sparse samples based on the Bernoulli matrix.

[0015] Compared with the prior art, the beneficial effects of the present invention include:

[0016] The present invention adopts a sparse three-valued Bernoulli matrix as the observation matrix, and the non-zero elements of each row of the matrix ( and ) is approximately Compared with the random Gaussian matrix, it reduces the complexity of data operation and improves the operability of sample mixing.

[0017] Compared with the binary Bernoulli matrix (matrix elements are 0 and 1), the sparse ternary Bernoulli matrix performs better in signal recovery accuracy. In compressed sensing, the low correlation between the columns of the observation matrix is ​​an important factor in ensuring the reconstruction of sparse signals. The binary Bernoulli matrix may produce high correlation in the columns due to the single element (0 and 1), resulting in measurement redundancy. The randomness and symbol diversity of the ternary Bernoulli matrix ( ,0, ) can significantly reduce column correlation. In addition, the theoretical research on compressed sensing shows that the elements of the sparse three-valued Bernoulli matrix are zero-mean random variables with a symmetric distribution (i.e. and The probability of occurrence of the same), so that it can achieve the same signal recovery performance as the random Gaussian matrix, while the sparse binary Bernoulli matrix lacks strict theoretical guarantees, especially in satisfying the restricted isometry property (RIP). Therefore, compared with the sparse binary Bernoulli matrix, the sparse ternary Bernoulli matrix used in the present invention can provide higher accuracy in the recovery of sparse signals.

[0018] In a sparse three-valued Bernoulli matrix (matrix elements are 0, and ), by setting two mixing groups, the effective allocation of samples is achieved. In the corresponding mixing operation, the element 1 in the sampling sequence indicates that the corresponding sample is assigned to the first mixing group, the element -1 indicates that the corresponding sample is assigned to the second mixing group, and the element 0 indicates that the corresponding sample does not participate in this mixing operation. Through this design, the matrix element The corresponding inverse virus concentration weighted operation fully utilizes the advantages of the three-valued Bernoulli matrix in the detection process, especially its superior performance in sparse signal recovery.

[0019] Therefore, the present invention has the characteristics of low detection cost, strong operability and high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A flow chart of mixed detection of large-scale sparse samples based on Bernoulli matrix described in the present invention.

[0021] Figure 2 Different probabilities for the embodiments of the present invention Different mixing operations The corresponding reconstruction accuracy plot.

[0022] Figure 3 These are the experimental results of using sparse binary Bernoulli matrix as mixing matrix under the same experimental conditions.

[0023] Figure 4 This is an attempt to implement a hybrid detection system for large-scale sparse samples in the present invention. DETAILED DESCRIPTION

[0024] The present invention is further described and illustrated below in conjunction with specific embodiments. The technical features of each embodiment of the present invention can be combined accordingly without conflicting with each other.

[0025] The above-mentioned embodiments only express several implementation methods of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the attached claims.

[0026] like Figure 1 The figure shows a mixed detection flow chart in a specific embodiment of the present invention. Virus samples were collected from subjects, and the virus concentration was , where the number of positive samples does not exceed ( ), usually, in order to ensure the number of mixing operations Small number of positive samples It should be less than , which is consistent with the characteristics of the early stage of the epidemic, so the method of the present invention is suitable for screening infected persons in the early stage of the epidemic. The specific process of the embodiment of the present invention is as follows:

[0027] from Virus samples were collected from subjects to ensure that each sample was not contaminated by the outside world during the collection process. The virus samples of the subjects are numbered The virus concentration of all samples was ,in , prepare multiple equal portions of each sample, each with the same virus concentration, for subsequent mixing operations.

[0028] Set the number of mixing operations Each mixing operation corresponds to a one-dimensional sampling sequence. The length of the sampling sequence is the same as the total number of samples to be tested. Each position in the sequence corresponds to a sample to be tested. The value of the element in the sampling sequence is -1, 1 or 0, indicating the mixing method of the corresponding sample to be tested. The probability of generating an element value of 1 or -1 in the sampling sequence is set to , the probability of generating an element value of 0 is , two mixing groups are set for each mixing operation.

[0029] In order to further improve the effectiveness of the method of the present invention, improve the detection efficiency and detection accuracy, the present invention proposes The value range is , Should be greater than ,in is a hyperparameter and should satisfy ,in .

[0030] For Mixing operation, where , according to the set probability The randomly generated length is The sampling sequence ,in , further preferably, the sampling sequence Requirements and The sampling sequences are all different. If they are the same, they are regenerated. Each sample is operated according to the sampling sequence. The sample corresponding to the position where the element is 1 is assigned to the first mixing group, the sample corresponding to the position where the element is -1 is assigned to the second mixing group, and the sample corresponding to the position where the element is 0 does not participate in this mixing.

[0031] After all samples are grouped, the samples in the first group are mixed to obtain mixed samples. , mix the samples in the second group to get a mixed sample , the virus concentrations of the two mixed samples were tested, respectively and , record the difference in virus concentration of the mixed sample as .

[0032] Repeat the above steps Each operation will generate two independent mixed samples, a total of Mixed samples The virus concentrations were and ,in express The virus concentration of all the first group of mixed samples in this operation, express The virus concentration of all the second group of mixed samples in this operation, the difference in virus concentration of the mixed samples is:

[0033] (1)

[0034] In formula (1): Represents two mixed samples , The virus concentration difference is .

[0035] The above sample mixing scheme is used by matrix express, Each row of corresponds to an operation.

[0036] for No. Row, element is The position corresponds to the The sample number assigned to the first group in the operation, where Indicates The number of samples in the first group in the operation; the elements are The position corresponds to the The sample number assigned to the second group in the operation, where Indicates The number of samples in the second group in the operation; the position of the element 0 indicates the In this mixing operation, the sample corresponding to this position does not participate in the mixing.

[0037] The difference in virus concentration of the mixed test samples can be expressed as:

[0038] (2)

[0039] In formula (2): Matrix Corresponding to the sample mixing scheme, the dimension is , which is essentially a Bernoulli matrix,

[0040] Represents the virus concentration of all samples, with dimensions .

[0041] The detection problem is converted into a sparse reconstruction problem, the goal is to find a sparse solution satisfy:

[0042] (3)

[0043] In formula (3): represents the sparse signal to be reconstructed, Indicates the allowed noise threshold.

[0044] The orthogonal matching pursuit algorithm is used to obtain the sparsest , The positions of the non-zero elements in correspond to the numbers of the people infected with the virus.

[0045] In order to verify the feasibility and effectiveness of the technical solution proposed in this invention, a simulation experiment was conducted. samples to be tested (recorded as sample numbers 1 to 1000), randomly set samples were positive, and the rest were negative. The virus concentration of positive samples followed a log-normal distribution. The virus concentration of negative samples is usually set to 0. Considering the presence of detection noise, it is set to a value close to 0. . In order to meet the mixing operation times In the case of mixed sample concentration difference Reconstruct the sparse , that is, to identify those infected with the virus, among which represents the hyperparameter, Represents the reconstructed sparse signal.

[0046] Figure 2 is the experimental result of the embodiment of the present invention, which gives different probabilities Different mixing operations The corresponding reconstruction accuracy, where the reconstruction accuracy means the number of times all virus-infected people can be accurately located by repeating the above process 500 times. Figure 3 is the experimental result of using sparse binary Bernoulli matrix as mixing matrix under the same experimental conditions. It corresponds to the case of setting only one mixing group. The probability of each sample participating in the mixing in each operation is . Figure 2 and Figure 3 The experimental results show that under the same distribution probability and reconstruction accuracy, the detection times of the embodiment of the present invention are less. Therefore, the sample mixing detection method of the embodiment of the present invention not only has good detection performance, but also can significantly reduce the detection times.

[0047] like Figure 4 FIG. 1 is a schematic diagram of a hybrid detection system for large-scale sparse samples of the present invention. The hybrid detection system of the present invention is used to implement the hybrid detection method in the aforementioned embodiment, and includes:

[0048] The sample preprocessing module is used to number the collected samples and prepare multiple copies of each sample in equal amounts;

[0049] The sample mixing module performs sample mixing operations according to the set mixing scheme. A mixing operation is performed to randomly generate a sampling sequence according to a set probability, and each sample is assigned to two mixing groups or not mixed according to the sampling sequence. After the sample grouping is completed, the samples in the first group are mixed to obtain a first mixed sample, and the samples in the second group are mixed to obtain a second mixed sample;

[0050] Virus concentration detection, used to detect the virus concentration of the two mixed samples obtained in each mixing operation and record the virus concentration difference;

[0051] A mathematical modeling module, which performs mathematical modeling based on the mixing operation adopted by the sample mixing module and the test results of the virus concentration test;

[0052] The infected person identification module obtains a model based on the mathematical modeling module, converts the detection problem into a sparse reconstruction problem, and uses a sparse signal recovery algorithm to obtain a sparse solution to identify the virus infected person.

[0053] An embodiment of the present invention further provides an electronic device, including a memory and a processor;

[0054] The memory is used to store computer programs;

[0055] The processor is used to implement the above-mentioned mixed detection process of large-scale sparse samples based on the Bernoulli matrix when executing the computer program.

[0056] An embodiment of the present invention further provides a computer-readable storage medium on which a program is stored. When the program is executed by a processor, the above-mentioned mixed detection process of large-scale sparse samples based on the Bernoulli matrix is ​​implemented.

[0057] The computer-readable storage medium may be an internal storage unit of any device with data processing capability described in any of the aforementioned embodiments, such as a hard disk or a memory. The computer-readable storage medium may also be an external storage device of any device with data processing capability, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card, etc. equipped on the device. Furthermore, the computer-readable storage medium may also include both an internal storage unit and an external storage device of any device with data processing capability. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capability, and may also be used to temporarily store data that has been output or is to be output.

[0058] Obviously, the above-described embodiments and drawings are only some examples of the present application. For those of ordinary skill in the art, the present application can also be applied to other similar situations based on these drawings without creative work. In addition, it is understandable that, although the work done in this development process may be complicated and lengthy, for those of ordinary skill in the art, certain changes in design, manufacturing or production based on the technical content disclosed in this application are only conventional technical means and should not be regarded as insufficient content disclosed in this application. Without departing from the concept of the present application, several variations and improvements can also be made, which all belong to the scope of protection of the present application. Therefore, the scope of protection of the present application shall be subject to the attached claims.

Claims

1. A sparse sample mixed inspection method based on a sparse three-valued Bernoulli matrix, characterized in that: The following steps are involved: S1: Number the collected samples to be tested and prepare multiple copies of equal amount for each sample; S2: Set the number of mixing operations M, perform mixing operations and virus concentration detection; The step S2 comprises: S21: Set the number of mixing operations M. Each mixing operation corresponds to a one-dimensional sampling sequence. The length of the sampling sequence is the same as the total number of samples to be tested. Each position in the sequence corresponds to a sample to be tested. The value of the element in the sampling sequence is -1, 1 or 0, indicating the mixing method of the corresponding sample to be tested. The probability of generating an element value of 1 or -1 in the sampling sequence is set to , the probability of generating an element value of 0 is ; S22: For Mixing operation, where , randomly generate length according to the probability in S21 The sampling sequence ,in , perform a mixing operation on each sample to be tested according to the sampling sequence, the sample corresponding to the position where the element is 1 is assigned to the first mixed group, the sample corresponding to the position where the element is -1 is assigned to the second mixed group, and the sample corresponding to the position where the element is 0 does not participate in this mixing; after all samples are grouped, mix the samples in the first group to obtain a mixed sample , mix the samples in the second group to get a mixed sample , the virus concentrations of the two mixed samples were tested, respectively and , record the difference in virus concentration of the mixed sample as ; S23: Repeat step S22 until completed Each mixing operation generates two independent mixed samples. Mixed samples The virus concentrations were and ,in express The virus concentration of all the first group of mixed samples in this operation, express The virus concentration of all the second group of mixed samples in this operation, the difference in virus concentration of the mixed samples is: ; Where: Represents a mixed sample , The virus concentration difference is ; Among them, two mixing groups are set for each mixing operation, and the sampling sequence of the mixing operation is randomly generated according to the set probability. Each sample is assigned to two mixing groups or does not participate in the mixing according to the sampling sequence. After the sample grouping is completed, the samples in the first group are mixed to obtain a first mixed sample, and the samples in the second group are mixed to obtain a second mixed sample. The virus concentration of the two mixed samples is detected and the virus concentration difference is recorded; S3: Sparse three-valued Bernoulli matrix modeling is performed based on the mixing operation adopted in S2 and the corresponding virus concentration detection results; The step S3 comprises the following specific steps: The sample mixing scheme in step S2 is converted into a matrix express, Each row of corresponds to a mixing operation; for No. Row, element is The position corresponds to the The sample number assigned to the first group in the operation, where Indicates The number of samples in the first group in the operation; the elements are The position corresponds to the The sample number assigned to the second group in the operation, where Indicates The number of samples in the second group in the operation; the position of the element 0 indicates the In this mixing operation, the sample corresponding to this position does not participate in the mixing; The difference in virus concentration of the mixed test samples is expressed as: ; Where: Matrix Corresponding to the sample mixing scheme, the dimension is , which is essentially a sparse three-valued Bernoulli matrix, Represents the virus concentration of all samples, with dimensions ; S4: Based on the results of mathematical modeling, the detection problem is converted into a sparse reconstruction problem, and a sparse signal recovery algorithm is used to obtain a sparse solution to identify virus-infected persons.

2. The sparse sample mixed detection method based on the sparse three-valued Bernoulli matrix according to claim 1, characterized in that: The step S1 specifically includes: S11: The samples to be tested are numbered The virus concentration of all samples was ,in ; The number of positive samples does not exceed , ; S12: Prepare multiple equal portions of each sample, each with the same virus concentration, for subsequent mixing operations.

3. The sparse sample mixed detection method based on the sparse three-valued Bernoulli matrix according to claim 1, characterized in that: In step S2, The value range is , Should be greater than ,in is a hyperparameter and should satisfy ,in .

4. The sparse sample mixed detection method based on a sparse ternary Bernoulli matrix according to claim 1, characterized in that: In step S22, the sampling sequence generated by the i-th mixing operation is required to be consistent with the previous The sampling sequences corresponding to the mixing operations are all different. If they are the same, they are randomly generated again.

5. The sparse sample mixed detection method based on the sparse three-valued Bernoulli matrix according to claim 1, characterized in that: In the step S4, the specific steps are: The detection problem is converted into a sparse reconstruction problem, the goal is to find a sparse solution satisfy: ； Where: represents the sparse signal to be reconstructed, Indicates the allowed noise threshold; The sparse signal recovery algorithm is used to obtain the sparsest , The positions of the non-zero elements in correspond to the numbers of the people infected with the virus.

6. A hybrid detection system for sparse samples implementing the method according to any one of claims 1 to 5, characterized in that: include: The sample preprocessing module is used to number the collected samples and prepare multiple copies of each sample in equal amounts; The sample mixing module performs sample mixing operations according to the set mixing scheme. For each mixing operation, a sampling sequence is randomly generated according to the set probability. Each sample is assigned to two mixing groups or does not participate in the mixing according to the sampling sequence. After the sample grouping is completed, the samples in the first group are mixed to obtain a first mixed sample, and the samples in the second group are mixed to obtain a second mixed sample. Virus concentration detection, used to detect the virus concentration of the two mixed samples obtained in each mixing operation and record the virus concentration difference; A mathematical modeling module, which performs mathematical modeling based on the mixing operation adopted by the sample mixing module and the test results of the virus concentration test; The infected person identification module obtains a model based on the mathematical modeling module, converts the detection problem into a sparse reconstruction problem, and uses a sparse signal recovery algorithm to obtain a sparse solution to identify the virus infected person.

7. An electronic device, characterized in that: It includes a processor and a memory, wherein the memory stores machine executable instructions that can be executed by the processor, and the processor executes the machine executable instructions to implement the sparse sample mixed detection method based on a sparse three-valued Bernoulli matrix as described in any one of claims 1 to 5.

8. A machine-readable storage medium, characterized in that: The machine-readable storage medium stores machine-executable instructions, which, when called and executed by a processor, are used to implement the sparse sample mixed detection method based on a sparse three-valued Bernoulli matrix as described in any one of claims 1 to 5.

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