Compressed sensing method and system based on guaranteed-dimension semi-tensor product, medium and equipment

Abstract

The invention discloses a compressed sensing method and system based on a guaranteed-dimension semi-tensor product, a medium and equipment. The method comprises the following steps: acquiring a vector expression form of an original image; converting the obtained vector into a sparse vector representation through discrete cosine transform; generating a Gaussian random matrix, and performing dimensionality-preserving semi-tensor product operation through all-one vectors with weights to construct a measurement matrix; sampling the sparse vector by using the measurement matrix to obtain a compressed transmission vector; and the Gaussian random matrix and the transmission vector are sent to a receiving end, the receiving end reconstructs and recovers the original image based on an l1 norm optimization algorithm, and compressed sensing transmission is completed. According to the method, the measurement matrix is improved based on the semi-tensor product of the guaranteed dimension, and the measurement matrix construction method can reduce the size of the generated Gaussian random matrix, so that the memory is saved, the speed in the transmission process is higher, and the bandwidth cost is saved.

Description

Technical Field

[0001] The present invention belongs to the technical field of image compression sensing, and in particular relates to a compression sensing method, system, medium and device based on dimension-preserving semi-tensor product. Background Art

[0002] The statements herein merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] With the rapid development of information technology, the amount of data generated and stored is growing exponentially. This is particularly true for the processing and transmission of multimedia data, such as images, video, and audio. Traditional signal acquisition and processing methods face significant challenges. According to a report by the International Data Corporation (IDC), global data volume is expected to continue to grow at a rate of over 20% per year for the next few years, placing higher demands on data storage, processing, and transmission. First, advances in sensor technology have made it easier to acquire high-resolution and high-frequency data. However, the resulting surge in data volume has significantly increased the complexity of data processing and transmission. In many application scenarios, particularly in wireless communications and the Internet of Things (IoT), bandwidth resources are limited. How to effectively utilize bandwidth while ensuring signal quality has become a pressing issue. Against this backdrop, compressed sensing (CS) technology has emerged as an effective means to address this issue. Despite significant progress in theory and practice, CS technology still faces several challenges in practical applications.

[0004] (1) Limitations of measurement matrix design

[0005] The design of the measurement matrix is crucial in compressed sensing applications. Traditional compressed sensing methods typically require that the columns of the measurement matrix be independent and satisfy the restricted isometry property (RIP). However, constructing a measurement matrix that satisfies these requirements is often challenging in practical applications, especially in high-dimensional signal processing and complex scenarios. This results in suboptimal compressed sensing reconstruction in some cases, failing to fully exploit the sparsity of the signal, thus affecting the quality and efficiency of signal recovery.

[0006] (2) Influence of noise and signal distortion

[0007] Compressed sensing (CS) technology is often affected by noise and signal distortion when processing real-world signals. Although CS can reconstruct signals at low sampling rates, the performance of the reconstruction algorithm can significantly degrade in high-noise environments. Noise not only degrades the quality of the reconstructed signal but can also lead to instability in the reconstruction results, especially when edge features are unclear or the signal is sparse. Therefore, improving the robustness of CS in noisy environments remains an urgent problem.

[0008] (3) Computational complexity and real-time performance

[0009] Although compressed sensing (CS) theoretically enables efficient signal reconstruction using a small number of measurements, in practice, the computational complexity of the reconstruction algorithm is often high, especially when processing large amounts of data. This makes real-time signal processing difficult, limiting the widespread adoption of CS technology in certain real-time application scenarios, such as video surveillance and medical imaging. Therefore, optimizing the reconstruction algorithm to reduce computational complexity and improve real-time processing capabilities is a key challenge facing current CS applications. Therefore, further research and improvement of CS technology, particularly in terms of algorithm optimization and adaptability to application scenarios, has important academic value and practical significance.

[0010] Currently, compressed sensing (CS) still faces many limitations in image processing, including issues such as speed and memory usage that need further resolution. In current research, the large measurement matrix often contributes significantly to memory usage, making it challenging to address this memory usage during transmission. At low sampling rates, images can exhibit a certain degree of distortion and are susceptible to noise. Further improvements in image reconstruction while conserving memory are crucial. This holds great promise in practical applications, potentially saving costs and easing transportation requirements. Currently, some researchers are using the semi-tensor product (STP) to refine the measurement matrix, thereby reducing memory usage during transmission. This approach, known as semi-tensor product-compressed sensing (STP-CS), offers a new approach to reducing memory usage. During research and development, the inventors discovered that existing methods require too many matrix conditions, making it difficult to refine the form to reduce memory usage. As image data increases in size, memory usage often quadratically, creating significant challenges in practical applications. Summary of the Invention

[0011] The purpose of the present invention is to overcome the deficiencies in the above-mentioned prior art and to provide a compressed sensing method, system, medium and device based on the dimension-preserving half-tensor product. The measurement matrix is improved based on the dimension-preserving half-tensor product. The measurement matrix construction method can reduce the size of the generated Gaussian random matrix, thereby saving memory, increasing the transmission speed and saving bandwidth costs.

[0012] In order to achieve the above object, the present invention is implemented through the following technical solutions:

[0013] On the one hand, the technical solution of the present invention provides a compressed sensing method based on dimension-preserving semi-tensor product, including:

[0014] Get the vector representation of the original image;

[0015] The obtained vector is converted into a sparse vector representation through discrete cosine transform;

[0016] Generate a Gaussian random matrix and perform a dimension-preserving semi-tensor product operation on a weighted all-one vector to construct a measurement matrix. Use the measurement matrix to sample the sparse vector to obtain a compressed transmission vector.

[0017] The Gaussian random matrix and the transmission vector are sent to the receiving end, and the receiving end reconstructs and restores the original image based on the l1 norm optimization algorithm to complete the compressed sensing transmission.

[0018] In at least one embodiment, the obtaining of the vector representation of the original image is specifically performed by performing matrix processing on the original transmission image to obtain a grayscale matrix corresponding to the original transmission image, and performing matrix-to-vectorization on the grayscale matrix to obtain the vector representation.

[0019] In at least one embodiment, the discrete cosine transform is specifically: using a discrete cosine basis Ψ to convert the obtained vector x into a sparse vector representation: x=Ψs, where s is the sparse vector.

[0020] In at least one embodiment, constructing the measurement matrix specifically involves generating a Gaussian random matrix Φ, using a weighted all-1 vector Perform dimension-preserving half-sheet vector product operation to obtain the measurement matrix in, Represents the matrix Kronecker product, and the weight value γ is a specified positive integer value, usually 2.

[0021] In at least one embodiment, the compressed transmission vector is specifically:

[0022] In at least one embodiment, the receiving end uses the Gaussian random matrix Φ and the compressed transmission vector y to perform a reconstruction operation by solving:

[0023]

[0024] Get the recovered sparse vector Using the recovered sparse vector The recovered vector representation is calculated by using the discrete cosine basis Ψ

[0025] In at least one embodiment, the recovered vector representation Perform the inverse process of matrix vectorization, convert it into image format, complete the reconstruction process, and obtain the restored original image.

[0026] On the other hand, the technical solution of the present invention further provides a compressed sensing system based on dimension-preserving semi-tensor product, comprising:

[0027] The original image processing module is configured to: obtain a vector representation of the original image;

[0028] The discrete cosine transform module is configured to: transform the obtained vector into a sparse vector representation through discrete cosine transform;

[0029] The transmission vector compression module is configured to: generate a Gaussian random matrix, perform a dimension-preserving semi-tensor product operation using a weighted all-ones vector to construct a measurement matrix; use the measurement matrix to sample the sparsified vector to obtain a compressed transmission vector;

[0030] The original image reconstruction module is configured to: send the Gaussian random matrix and the transmission vector to the receiving end, and the receiving end reconstructs and restores the original image based on the l1 norm optimization algorithm to complete the compressed sensing transmission.

[0031] The beneficial effects of the technical solution of the present invention are as follows:

[0032] 1) The compressed sensing method based on dimension-preserving semi-tensor product of the present invention improves the measurement matrix based on the dimension-preserving semi-tensor product. The measurement matrix construction method can reduce the size of the generated Gaussian random matrix, thereby saving memory, making the transmission process faster and saving bandwidth costs.

[0033] 2) The compressed sensing method based on dimension-preserving semi-tensor product of the present invention performs a reconstruction process through a measurement matrix, which can improve the quality of the reconstructed image, reduce the distortion of the image, and reduce the difference between the reconstructed image and the original image. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0035] Figure 1 1 is a flow chart of a compressed sensing method based on dimension-preserving semi-tensor product disclosed in Example 1 of the present invention;

[0036] Figure 2 These are the reconstructed images of the three original images in Example 1 of the present invention under the CS, STP-CS, and DK-STP-CS models. (a)(e)(i) are the original images, (b)(f)(j) are the reconstructed images under the CS model, (c)(g)(k) are the reconstructed images under the STP-CS model, and (d)(h)(l) are the reconstructed images under the DK-STP-CS model.

[0037] Figure 3 Figure 1 shows the results of 50 repeated experiments conducted in Example 1 of the present invention. (a), (b), and (c) respectively represent the reconstruction results of three original images. The blue curve represents the experimental results under traditional CS, the red curve represents the experimental results under STP-CS, and the yellow curve represents the experimental results under DK-STP-CS.

[0038] Figure 4 Figure 5 shows 50 repetitions of a noisy experiment in Example 1 of the present invention. (a), (b), and (c) respectively represent the reconstruction results of the three original images. The blue curve represents the experimental results under traditional CS, the red curve represents the experimental results under STP-CS, and the yellow curve represents the experimental results under DK-STP-CS.

[0039] Figure 5 These are curve diagrams of different measurement matrices mentioned in Example 1 of the present invention at different sampling rates, where (a), (b), and (c) represent changes in the peak signal-to-noise ratio of three different original images as the sampling rates gradually increase. DETAILED DESCRIPTION

[0040] It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0041] As introduced in the background technology, the purpose of the present invention is to overcome the shortcomings of the above-mentioned existing technologies and provide a compressed sensing method, system, medium and device based on the dimension-preserving half-tensor product, which improves the measurement matrix based on the dimension-preserving half-tensor product. The measurement matrix construction method can reduce the size of the generated Gaussian random matrix, thereby saving memory, making the transmission process faster and saving bandwidth costs.

[0042] Example 1

[0043] In a typical embodiment of the present invention, Figure 1 As shown, this embodiment discloses a compressed sensing method based on dimension-preserving semi-tensor product, including the following steps:

[0044] S100. Obtaining a vector representation of the original image;

[0045] S200. Converting the obtained vector into a sparse vector representation by discrete cosine transform;

[0046] S300. Generate a Gaussian random matrix and perform a dimension-preserving semi-tensor product operation on a weighted all-one vector to construct a measurement matrix; use the measurement matrix to sample the sparse vector to obtain a compressed transmission vector;

[0047] S400. Send the Gaussian random matrix and the transmission vector to the receiving end, which reconstructs and restores the original image based on the l1 norm optimization algorithm to complete the compressed sensing transmission.

[0048] The compressed sensing method based on dimension-preserving half-tensor product is introduced in detail below in conjunction with specific implementation methods.

[0049] S100. Obtain a vector representation of the original image.

[0050] In this embodiment, the transmission problem is solved to save bandwidth costs and increase transmission speed. The design aims to minimize the memory required for transmission while maintaining the quality of the reconstructed image. To this end, the original image in this embodiment is a grayscale image. If a color image is to be processed, only the RGB component matrices need to be processed separately.

[0051] When obtaining the vector expression of the original image, this embodiment first performs matrix processing on the original transmission image to obtain a grayscale matrix corresponding to the original transmission image, and performs matrix-vectorization on the grayscale matrix to obtain a vector expression.

[0052] Image matrixing is a fundamental step in digital image processing. It converts image data into a mathematical matrix, making subsequent analysis and processing more efficient and convenient. Each pixel value in the image is mapped to an element in a matrix, where the rows and columns correspond to the image's height and width, respectively. For example, a 3×3 grayscale image can be represented as a 3×3 matrix, where each element in the matrix represents the grayscale value of the corresponding pixel.

[0053] Assume that the size of the original image to be processed is m×n, and the corresponding grayscale matrix is A=(a ij )∈R m×n , where a ij is the element in row i and column j of the grayscale matrix, where 1 <i<m,1<j<n,R m×n is an m×n real matrix. The gray matrix A is processed in a column-wise manner, i.e., matrix vectorization. The result after vectorization is denoted as x, where x = (a 11 ,a 21 ,…,a m1 ,a 12 ,…,a m2 ,…,a 1n ,a 2n ,…,a mn ) T To simplify symbolic representation, the dimension of x is represented by n in this embodiment.

[0054] S200. Convert the obtained vector into a sparse vector representation through discrete cosine transform.

[0055] The discrete cosine transform (DCT) is a transform technique widely used in signal processing and image compression. Its primary function is to convert signal or image data from the time domain (or spatial domain) to the frequency domain, thereby achieving data sparsification. Based on the vector x obtained through S100 processing, a discrete cosine transform (DCT) is selected. Given a set of discrete cosine bases, x is expressed as x = Ψs, where s is the sparsified vector and Ψ represents a set of discrete cosine bases. The process of obtaining x from s is called the discrete inverse cosine transform (DICT), a set of mutually inverse transforms.

[0056] S300. Generate a Gaussian random matrix, perform a dimension-preserving semi-tensor product operation on a weighted all-one vector, and construct a measurement matrix; use the measurement matrix to sample the sparse vector to obtain a compressed transmission vector.

[0057] In this embodiment, a Gaussian random matrix Φ is generated, and the matrix size is Here n is the dimension value of x, and the weight value γ is a positive integer value that can be specified, usually 2. If γ is 1, the matrix size is m×n, which degenerates into the traditional compressed sensing process. Therefore, in this embodiment, γ cannot be 1. In this embodiment, the Gaussian random matrix Φ does not need to be extended to n columns, but rather to (γ is a positive integer not equal to 1), then the matrix size of the Gaussian random matrix Φ is In this way, memory is saved in the actual transmission process. In order to construct a measurement matrix that meets the conditions, this embodiment introduces a new operation called the dimension-preserving semi-tensor product operation. To express it, it is shown as follows:

[0058]

[0059] After generating the Gaussian random matrix Φ, use the weighted all-1 vector Perform dimension-preserving half-scale vector product operation to achieve dimension expansion and obtain the measurement matrix in, Represents the matrix Kronecker product. It plays the role of expanding the dimension of the Gaussian random matrix Φ. Here, it is necessary to determine the value of the weight γ, so that The weight value in , which is selected depending on the size of the vector signal.

[0060] After expanding the Gaussian random matrix Φ to obtain the measurement matrix, the sparse vector is sampled using the measurement matrix. The sampling process is to obtain the compressed transmission vector y by matrix multiplication, as follows:

[0061]

[0062] At this time, the dimension of the compressed transmission vector (represented by m) must be smaller than the dimension n of x, so that the compression goal can be achieved. At this time, the compression ratio (CR) is

[0063] S400. Send the Gaussian random matrix and the transmission vector to the receiving end, which reconstructs and restores the original image based on the l1 norm optimization algorithm to complete the compressed sensing transmission.

[0064] The generated Gaussian random matrix Φ and the sampling result (i.e. the compressed transmission vector) y are transmitted to the receiving end. During the transmission process, the memory size of the transmitted data should be reduced as much as possible to save bandwidth costs. Therefore, under the premise of ensuring that the image distortion is within a certain degree, the compression rate is Needs to be as small as possible.

[0065] The receiver uses the received Gaussian random matrix Φ and the compressed transmission vector y to perform reconstruction operations, mainly to solve an l0 norm problem:

[0066]

[0067] This problem is NP-Hard, so in this embodiment we choose to solve its convex relaxation form, namely the l1 norm problem:

[0068]

[0069] The purpose of recovery here is to ensure that the non-sparse part of the vector is reconstructed as accurately as possible to reduce the loss of information in the image, so that the recovered sparse vector can be obtained. Then the column-wise vector of the image information can be used to recover the sparse vector The recovered vector representation is calculated by using the discrete cosine basis Ψ What is obtained at this time Is the vector information, the recovered vector representation Perform the inverse process of matrix vectorization, convert it into image format, complete the reconstruction process, and obtain the restored original image, thus completing the compressed sensing transmission of the image.

[0070] The algorithm flow of this embodiment is applied to specific image processing and compared with existing methods in terms of memory and image quality. In this embodiment, the reconstruction effects of the images are compared to see if they are similar. On the one hand, the visual effect is compared, and on the other hand, the Peak Signal-to-Noise Ratio (PSNR) is used to measure the signal quality. Especially in the field of image and video compression, it is used to evaluate the difference between the reconstructed signal (such as the compressed image) and the original signal. The higher the PSNR value, the better the quality of the reconstructed signal. Three different images are selected for simulation, and the reconstructed image results are compared. Figure 2 The image information of three original images reconstructed under the CS, STP-CS, and DK-STP-CS models is shown.

[0071] from Figure 2 It can be seen from the images that DK-STP-CS has a certain improvement in image quality compared to CS and STP-CS, and some details on the picture are relatively well preserved. In the experiment, since the Gaussian random matrix is randomly generated, it leads to strong randomness. Therefore, 50 repeated experiments were conducted in this embodiment to compare the PSNR mean and verify the visual improvement from the data level. The experimental results are as follows: Figure 3 Here x represents the number of experiments, and y represents the peak signal-to-noise ratio (PSNR value).

[0072] Depend on Figure 3 It can be seen that the DK-STP-CS curve has a significant improvement compared to the CS and STP-CS curves, which is consistent with what is seen visually. Table 1 shows the average PSNR values of various models for 50 repeated experiments.

[0073]

[0074] Table 1

[0075] Table 1 shows that the DK-STP-CS mean values are the maximum values among the three images, verifying the effectiveness of the method of this embodiment in image compression and transmission. The figure also reveals that different original images exhibit different peak signal-to-noise ratios, which depend on the image's properties, such as edge information and grayscale distribution. Overall, the DK-STP-CS method can better reconstruct the original image at the same compression rate.

[0076] Next, add Gaussian noise with an expected value of 0 and a variance of 0.01 to the image to simulate the noise effect on the image during transmission and perform the compressed sensing process. Repeat the experiment 50 times to draw the relevant curve, as shown in the following example: Figure 4 shown.

[0077] Table 2 gives Figure 4 The PSNR average of the experimental results in the middle curve shows that, under the influence of noise, DK-STP-CS still performs better than the other two methods. This demonstrates that DK-STP-CS in this embodiment is highly robust to noise.

[0078]

[0079] Table 2

[0080] The choice of measurement matrix is also a problem that needs to be decided in practical applications. For different measurement matrices, the relationship between the sampling rate and the curve is drawn to facilitate the selection of the measurement matrix under different sampling rates. The experimental results are drawn as follows Figure 5 Here x represents the compression ratio and y represents the peak signal-to-noise ratio. Figure 5 As can be seen from the above, under most sampling rates, the effects of the Bernoulli matrix and the Gaussian random matrix are similar, while the Toeplitz matrix is basically worse than the other two measurement matrices, so generally Bernoulli or Gaussian random matrix can be selected.

[0081] Example 2

[0082] In a typical implementation of the present invention, this embodiment discloses a compressed sensing system based on dimension-preserving semi-tensor product, including:

[0083] The original image processing module is configured to: obtain a vector representation of the original image;

[0084] The discrete cosine transform module is configured to: transform the obtained vector into a sparse vector representation through discrete cosine transform;

[0085] The transmission vector compression module is configured to: generate a Gaussian random matrix, perform a dimension-preserving semi-tensor product operation using a weighted all-ones vector to construct a measurement matrix; use the measurement matrix to sample the sparse vector to obtain a compressed transmission vector;

[0086] The original image reconstruction module is configured to send the Gaussian random matrix and the transmission vector to the receiving end, and the receiving end reconstructs and restores the original image based on the l1 norm optimization algorithm to complete the compressed sensing transmission.

[0087] Example 3

[0088] In a typical embodiment of the present invention, this embodiment provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the steps of the compressed sensing method based on the dimension-preserving semi-tensor product described in Example 1 are implemented, including:

[0089] Get the vector representation of the original image;

[0090] The obtained vector is converted into a sparse vector representation through discrete cosine transform;

[0091] Generate a Gaussian random matrix and perform a dimension-preserving semi-tensor product operation on a weighted all-one vector to construct a measurement matrix. Use the measurement matrix to sample the sparse vector to obtain a compressed transmission vector.

[0092] The Gaussian random matrix and transmission vector are sent to the receiving end, which reconstructs and restores the original image based on the l1 norm optimization algorithm to complete the compressed sensing transmission.

[0093] Example 4

[0094] In a typical embodiment of the present invention, this embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the compressed sensing method based on the dimension-preserving semi-tensor product described in Example 1 are implemented. The steps include:

[0095] Get the vector representation of the original image;

[0096] The obtained vector is converted into a sparse vector representation through discrete cosine transform;

[0097] Generate a Gaussian random matrix and perform a dimension-preserving semi-tensor product operation on a weighted all-one vector to construct a measurement matrix. Use the measurement matrix to sample the sparse vector to obtain a compressed transmission vector.

[0098] The Gaussian random matrix and transmission vector are sent to the receiving end, which reconstructs and restores the original image based on the l1 norm optimization algorithm to complete the compressed sensing transmission.

[0099] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A compressed sensing method based on dimension-preserving semi-tensor product, characterized in that: include: Get the vector representation of the original image; The obtained vector is converted into a sparse vector representation through discrete cosine transform; Generate a Gaussian random matrix and perform a dimension-preserving semi-tensor product operation on a weighted all-one vector to construct a measurement matrix. Use the measurement matrix to sample the sparse vector to obtain a compressed transmission vector. The Gaussian random matrix and the transmission vector are sent to the receiving end, and the receiving end reconstructs and restores the original image based on the l1 norm optimization algorithm to complete the compressed sensing transmission.

2. The compressed sensing method based on dimension-preserving semi-tensor product according to claim 1, wherein: The obtaining of the vector expression of the original image is specifically as follows: performing matrix processing on the original transmission image to obtain a grayscale matrix corresponding to the original transmission image, and performing matrix-vectorization on the grayscale matrix to obtain a vector expression.

3. The compressed sensing method based on dimension-preserving semi-tensor product according to claim 1, wherein: The discrete cosine transform is specifically as follows: using a discrete cosine basis Ψ to transform the obtained vector x into a sparse vector representation: x=Ψs, where s is the sparse vector.

4. The compressed sensing method based on dimension-preserving semi-tensor product according to claim 3, wherein: The construction of the measurement matrix is as follows: Generate a Gaussian random matrix Φ, use the weighted all-1 vector Perform dimension-preserving half-sheet vector product operation to obtain the measurement matrix in, Represents the matrix Kronecker product, and the weight value γ is a specified positive integer value, usually 2.

5. The compressed sensing method based on dimension-preserving semi-tensor product according to claim 4, characterized in that: The compressed transmission vector is:

6. The compressed sensing method based on dimension-preserving semi-tensor product according to claim 1, wherein: The receiving end uses the Gaussian random matrix Φ and the compressed transmission vector y to perform reconstruction operations by solving: Get the recovered sparse vector Using the recovered sparse vector The recovered vector representation is calculated by using the discrete cosine basis Ψ 7. The compressed sensing method based on dimension-preserving semi-tensor product according to claim 6, characterized in that: The recovered vector representation Perform the inverse process of matrix vectorization, convert it into image format, complete the reconstruction process, and obtain the restored original image.

8. A compressed sensing system based on dimension-preserving semi-tensor product, characterized in that: include: The original image processing module is configured to: obtain a vector representation of the original image; The discrete cosine transform module is configured to: transform the obtained vector into a sparse vector representation through discrete cosine transform; The transmission vector compression module is configured to: generate a Gaussian random matrix, perform a dimension-preserving semi-tensor product operation using a weighted all-ones vector to construct a measurement matrix; use the measurement matrix to sample the sparsified vector to obtain a compressed transmission vector; The original image reconstruction module is configured to: send the Gaussian random matrix and the transmission vector to the receiving end, and the receiving end reconstructs and restores the original image based on the l1 norm optimization algorithm to complete the compressed sensing transmission.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the compressed sensing method based on dimension-preserving half-tensor product as described in any one of claims 1 to 7 are implemented.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the compressed sensing method based on dimension-preserving semi-tensor product are implemented as described in any one of claims 1 to 7.

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