Compressed sensing driven terahertz tomography reconstruction method based on adaptive strategy

Abstract

The invention relates to the technical field of image reconstruction, in particular to a compressed sensing driven terahertz tomography reconstruction method based on an adaptive strategy. According to the technical scheme, the method comprises the following steps that a terahertz continuous wave imaging system is used for collecting intensity data P of a corresponding view angle at equal-interval sparse angles, and a sinogram of a sparse sampling view angle is obtained; performing data preprocessing on the intensity data to unify the data scale; relevant parameters of the algorithm are initialized, wherein the relevant parameters comprise step length and regularization parameters; through a core parameter dynamic adjustment mechanism, cooperative improvement of imaging quality, reconstruction efficiency and environmental adaptability is successfully realized, clearer and more accurate terahertz tomographic images can be obtained, reconstruction can be completed at a faster calculation speed, and the method is suitable for wider practical application scenes and has good application prospects. And the comprehensive performance is obviously superior to that of a traditional non-adaptive method.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of image reconstruction, and in particular to a compressed sensing driven terahertz tomography reconstruction method based on an adaptive strategy. BACKGROUND

[0002] Terahertz computed tomography, i.e., terahertz tomography technology, as a new non-destructive testing method, has shown significant application advantages and broad prospects in the fields of non-destructive testing, biomedical imaging, security screening, and material science, due to its unique non-ionizing property, excellent material penetration ability, and "fingerprint" spectral characteristics for a variety of substances.

[0003] The practical application of terahertz imaging technology still faces many technical bottlenecks. First, terahertz waves are easily affected by medium scattering and absorption during propagation, resulting in serious signal attenuation. Second, the noise of the terahertz detector itself further reduces the signal-to-noise ratio. More critically, to achieve high-precision reconstruction, the traditional tomography method needs to follow the Shannon-Nyquist sampling theorem to collect a large number (usually hundreds) of projection data within a 180-degree range, which not only leads to a long and inefficient data collection process, but also puts extremely high requirements on the stability of the imaging system and environmental control. The above factors together cause the core problems of low signal-to-noise ratio and sampling uncertainty in terahertz tomography, making it particularly difficult to achieve high-precision and high-reliability image reconstruction in an under-sampling scenario.

[0004] In order to overcome the above limitations, the theory of compressed sensing is introduced into terahertz tomography. This theory states that if a signal is sparse or compressible in a certain transform domain, it can be recovered from much less observation data than required by the Nyquist sampling theorem with high probability. In image reconstruction, total variation regularization is a commonly used sparse constraint method that can effectively preserve the edges and structure information of the image while suppressing noise and smoothing uniform regions. Combining TV regularization with the fast iterative shrinkage thresholding algorithm, an efficient reconstruction framework, FISTA-TV, is constructed, which is considered to achieve a good balance between optimization performance and imaging quality.

[0005] Existing traditional FISTA-TV-based methods still have inherent limitations. The core issue lies in their use of fixed regularization parameters and step sizes. This strategy fails to adapt to the dynamically changing noise characteristics of terahertz signals and the complex media differences among various test samples. Specifically, at high noise levels, fixed regularization parameters may lead to insufficient noise suppression or excessive smoothing of edge details; under undersampling conditions, fixed iteration step sizes can easily cause the algorithm to get trapped in local optima, resulting in slow convergence or even reconstruction failure. In other words, traditional fixed-parameter FISTA-TV algorithms struggle to achieve a dynamic balance between noise suppression and edge preservation, and there is an irreconcilable contradiction between computational efficiency and reconstruction accuracy, limiting their robustness and universality in complex real-world scenarios. Therefore, this application proposes a compressed sensing-driven terahertz tomography reconstruction method based on an adaptive strategy. Summary of the Invention

[0006] The purpose of this invention is to address the problem that existing FISTA-TV-based traditional methods typically employ fixed regularization parameters and step size strategies, which cannot adapt to the dynamically changing noise characteristics of terahertz signals and the complex medium differences of different test samples. This invention proposes a compressed sensing-driven terahertz tomography reconstruction method based on an adaptive strategy.

[0007] The technical solution of this invention: A terahertz tomography reconstruction method based on adaptive strategy and driven by compressed sensing, comprising the following steps:

[0008] S1. Use a terahertz continuous wave imaging system to collect intensity data P at equally spaced sparse angles corresponding to the viewpoint, and obtain the sine curve of the sparse sampling viewpoint.

[0009] S2, regarding the intensity data Perform data preprocessing to standardize data scale;

[0010] S3. Initialize the relevant parameters of the algorithm, including the step size. and regularization parameters ;

[0011] S4. Construct an objective function, which includes a weighted sum of unregularized residuals and TV regularization terms;

[0012] S5. Perform FISTA algorithm iteration, and use the FGP method to perform TV algorithm iteration in the FISTA algorithm iteration to optimize the reconstructed image;

[0013] S6. Based on the objective function value and the noise level of the reconstructed image, adaptively adjust the step size and regularization parameters;

[0014] S7. Determine whether the FISTA algorithm iteration has ended. If it has ended, output the reconstructed image; otherwise, return to step S5 to continue the iteration.

[0015] Optionally, the data preprocessing in step S2 includes:

[0016] S2-1. Dark field correction: Acquire dark field data. and the original projection data Subtract dark field data To obtain the corrected data ;

[0017] S2-2, Normalization processing of projection data. Normalization is performed to obtain ,in and These are the minimum and maximum values ​​of the projected data, respectively.

[0018] 3. The terahertz tomography reconstruction method based on adaptive strategy driven by compressed sensing according to claim 1, characterized in that the parameter initialization in step S3 includes:

[0019] Step length Initialize to Where A is the measurement matrix;

[0020] Regularization parameters Initialize to ,in The standard deviation of noise. For the measurement number, The number of pixels in the image. It is a constant.

[0021] Optionally, the objective function construction in step S4 includes:

[0022] S4-1 Calculate the unregularized residual ,in To reconstruct the image;

[0023] S4-2, Calculate the TV regularization term:

[0024]

[0025] in, For the row and column indices of the image pixels, To reconstruct the image In pixels along The partial derivative in the direction reflects the gradient of the image in the horizontal direction; To reconstruct the image In pixels the partial derivative along the direction, reflecting the gradient in the vertical direction of the image; the partial derivative along the direction, reflecting the gradient in the vertical direction of the image;

[0026] S4-3, combining the un-regularized residual and the TV regularization term, to obtain a target function wherein is a regularization parameter.

[0027] Optionally, the FISTA algorithm iteration in step S5 comprises:

[0028] S5-1, calculating the gradient of the un-regularized residual wherein is a projection matrix, is a transpose matrix of the projection matrix

[0029] S5-2, initializing a dual variable , and calculating the TV term:

[0030]

[0031] wherein, and respectively represent the values of the dual variable at pixels and , and respectively represent the values of the dual variable at pixels and ;

[0032] S5-3, constructing an intermediate image :

[0033]

[0034] wherein, is a reconstructed image, is the gradient of the un-regularized residual, is a regularization parameter, is the TV term of the dual variable ,

[0035] S5-4, calculating the gradient of the dual variable :

[0036]

[0037] wherein, is the gradient of the dual variable ,​​ for the dual variable , , and denote the pixel values of the intermediate image at pixels , and ;

[0038] S5-5, update the dual variable to , :

[0039]

[0040]

[0041] where , are auxiliary variables, and is a regularization parameter;

[0042] S5-6, update the momentum :

[0043]

[0044] where is the iteration number, and is the momentum value at the th iteration, and is the momentum value at the th iteration;

[0045] S5-7, update the auxiliary variables , :

[0046]

[0047] where and are the dual variables and updated at the th iteration, and are the dual variables and updated at the th iteration, and are the auxiliary variables and updated at the th iteration;

[0048] S5-8. Determine if the TV algorithm iteration has ended. If it has ended, output the reconstructed image. Otherwise, continue iterating.

[0049] in The reconstructed image is the output of the TV algorithm after iteration. For reconstructed images The nearest neighbor operator operation, For the updated auxiliary variables , The calculated TV term;

[0050] Optionally, the adaptive parameter adjustment in step S6 includes:

[0051] S6-1, Determining the Objective Function Value: If Then update the reconstructed image as follows: Otherwise, increase To shorten the step size and reset the reconstructed image to ;

[0052] S6-2. Noise Level Judgment: If Then increase the regularization parameter. ;like Then decrease The specific adjustment method is as follows: ,when

[0053] ,when ;

[0054] in, For the unregularized residual of the i-th iteration The norm (the magnitude of the quantization residual). Image pixel count With noise standard deviation The product of squares (reference threshold for noise capability). and For the first and The regularization parameter for the next iteration This is the adjustment factor for the regularization parameter. .

[0055] Optionally, the equally spaced sparse angles in step S1 are 1 / 20 of the total number of angles required for terahertz tomography reconstruction, where the total number of angles is 180.

[0056] Optionally, step S6-1 may also include updating the reconstructed image y using momentum t:

[0057] wherein, is the reconstructed image of the first iteration, and is the intermediate reconstructed image of the first and iteration;

[0058] Optionally, the TV algorithm iteration in step S5 employs the FGP method, and includes initialization and updating of dual variables and auxiliary variables to accelerate convergence and maintain image edge details.

[0059] Compared with the prior art, the present application includes at least one of the following beneficial technical effects:

[0060] The present application can intelligently balance the weights of the data fidelity term and the smoothing constraint term according to the residual and noise energy relationship in the reconstruction process by adaptively adjusting the regularization parameter λ, so that the algorithm can effectively suppress noise while maximizing the preservation of image edges and detail information. Experimental verification shows that the quality of the reconstructed image can be significantly improved.

[0061] The present application combines the fast convergence characteristics of the FISTA algorithm with the momentum acceleration strategy, and dynamically adjusts the iteration step size by real-time judgment of the objective function value, effectively avoiding the algorithm from falling into a local optimal solution and reducing invalid iterations, thereby greatly reducing the overall iteration number and significantly improving the calculation efficiency of image reconstruction.

[0062] The present application has the ability to perceive the noise level of the input signal in real time and can automatically adjust the core parameters accordingly, and has good robustness to different noise environments and complex sample media. Especially in poor imaging conditions with low signal-to-noise ratio, it can still maintain stable and high-quality reconstruction results, breaking the dependence of traditional algorithms on fixed prior conditions.

[0063] In summary, the present application successfully realizes the coordinated improvement of imaging quality, reconstruction efficiency and environmental adaptability through the core parameter dynamic adjustment mechanism. It not only can obtain clearer and more accurate terahertz tomographic images, but also can complete reconstruction at a faster calculation speed and be applicable to a wider range of practical application scenarios, and the comprehensive performance is significantly better than that of traditional non-adaptive methods. BRIEF DESCRIPTION OF DRAWINGS

[0064] Figure 1 is a flowchart of a compressed sensing driven terahertz tomographic imaging reconstruction method based on an adaptive strategy;

[0065] Figure 2 is a sample image in the embodiment of the present application;

[0066] Figure 3This is a slice projection image acquired by a terahertz continuous wave imaging system in an embodiment of the present invention;

[0067] Figure 4 This is a three-dimensional reconstruction image from an embodiment of the present invention. Detailed Implementation

[0068] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0069] Example

[0070] like Figure 1 As shown, the present invention proposes a compressed sensing-driven terahertz tomography reconstruction method based on an adaptive strategy, comprising the following steps:

[0071] (S1) See Figure 2 This is a schematic diagram of the sample to be tested. See [link / reference]. Figure 3 It acquires 180 slices of projection data corresponding to 1 / 20 of the required angle using a terahertz continuous wave imaging system. The resolution of each slice is 60×20 (number of detectors × projection angle).

[0072] (S2) Perform dark field correction and normalization preprocessing on each slice.

[0073] (S3) Initialize the reconstructed image For a 60×60 all-zero image, momentum 1, step size is The regularization parameter is The number of iterations is .

[0074] in, It is a measurement matrix. It is the noise standard deviation. It is a measurement number. It refers to image pixels.

[0075] (S4) Unregularized residuals The weighted sum of the TV regularization term is used as the objective function.

[0076] (S5), starting FISTA algorithm iteration, in which FISTA algorithm iteration adopts FGP method to perform TV algorithm iteration, and in each iteration, the objective function value of the reconstructed image and the noise level of the reconstructed image are calculated.

[0077] (S6), modulating the step size and the regularization parameter according to the value of the objective function and the noise level of the reconstructed image, and realizing self-adaptation.

[0078] (S7), judging whether the FISTA algorithm iteration is completed, if yes, outputting the reconstructed image, otherwise, entering the next iteration until the iteration is completed.

[0079] Referring to Figure 1 , in step (S2), the data preprocessing includes the following steps:

[0080] (S2-1), dark field correction: collecting dark field data and original projection data , that is .

[0081] (S2-2), performing normalization processing on the projection data :

[0082]

[0083] Wherein and are the minimum value and the maximum value of the projection data respectively;

[0084] Referring to Figure 1 , in step (S4), the objective function construction includes the following steps:

[0085] (S4-1), calculating the un-regularized residual:

[0086]

[0087] Wherein is the reconstructed image;

[0088] (S4-2), calculating the TV regularization term:

[0089]

[0090] Wherein, is the row and column index of the image pixel, is the reconstructed image at the pixel in the direction of , the partial derivative (reflecting the horizontal gradient of the image) of the reconstructed image at the pixel in the direction of , the partial derivative (reflecting the vertical gradient of the image) of the reconstructed image derivative of the direction (reflecting the gradient in the vertical direction of the image);

[0091] (S4-3) Combining the un-regularized residual and the TV regularization term, the target function is obtained:

[0092]

[0093] wherein is a regularization parameter;

[0094] Referring to Figure 1 , in step (S5), the FISTA-TV algorithm iteration comprises the following steps:

[0095] (S5-1), the gradient of the un-regularized residual is calculated, and the gradient information is introduced:

[0096]

[0097] wherein, is a projection matrix, is a projection matrix is a transpose matrix of the projection matrix;

[0098] (S5-2), the dual variable is initialized, and the TV term generated by is calculated:

[0099]

[0100] wherein, and respectively represent the values of the dual variable at pixels and , and respectively represent the values of the dual variable at pixels and ;

[0101] (S5-3), the gradient calculation intermediate image is constructed:

[0102]

[0103] wherein, is a reconstructed image, is the gradient of the un-regularized residual, is a regularization parameter, is the TV term of the dual variable , ; and

[0104] (S5-4) Calculate the dual variables gradient:

[0105]

[0106] in, dual variables gradient, dual variables gradient, , and These represent the intermediate images respectively. In pixels , and Pixel value at;

[0107] (S5-4) Initialize auxiliary variables , Update the dual variable to , :

[0108]

[0109]

[0110] in, , As an auxiliary variable, For regularization parameters;

[0111] (S5-4) Update Momentum :

[0112]

[0113] in, For the number of iterations, For the first The momentum value of the next iteration. For the first The momentum value of the next iteration;

[0114] (S5-4) Update auxiliary variables , :

[0115]

[0116] in, and The first Iteratively updated dual variables and , and The first iteratively updated dual variable and , and are the first iteratively updated auxiliary variable and ;

[0117] (S5-4), determine whether the TV algorithm iteration is finished, if the iteration is finished, output the reconstructed image as , otherwise enter the next iteration until the iteration is completed.

[0118] wherein is the reconstructed image output after the TV algorithm iteration, is the proximal operator operation on the reconstructed image , is the updated auxiliary variable , TV term calculated by

[0119] Further, step (S5) can be summarized as the following algorithm:

[0120] Algorithm: FGP-TV

[0121] Input:; initialize reconstruction parameters: dual variable , auxiliary variable , ; For

[0122] , execute the following steps; Calculate the TV term generated by

[0123] , to obtain the intermediate image Calculate the dual variable

[0124] gradient: ,

[0125] Update the dual variable: ,

[0126] Update the auxiliary variable: ,

[0127] End for

[0128] Output the reconstructed image: .

[0129] Referring to Figure 1In step (S6), parameter adjustment includes the following steps:

[0130] (S6-1) Determining the objective function value: If Then update the reconstructed image as follows: Conversely, increase To shorten the step size Reset the reconstructed image to .

[0131] (S6-2) Noise Level Judgment: If Then increase ,like Then decrease ,Right now:

[0132]

[0133] in, For the unregularized residual of the i-th iteration The norm (the magnitude of the quantization residual). Image pixel count With noise standard deviation The product of squares (reference threshold for noise capability). and For the first and The regularization parameter for the next iteration This is the adjustment factor for the regularization parameter. .

[0134] See Figure 4 All the reconstructed slices are then overlaid in three dimensions to obtain the final three-dimensional reconstructed image.

[0135] This invention systematically addresses the inherent limitations of fixed parameter systems in traditional reconstruction methods by introducing an adaptive mechanism to dynamically adjust regularization parameters and iteration step size. The principle behind this method is based on real-time monitoring of the objective function value and noise level during reconstruction, automatically balancing the weight relationship between data fidelity and image smoothness. Its direct effect is that the algorithm can intelligently adjust the constraint strength according to the current reconstruction state, preserving edge and detail structures while suppressing noise, thus achieving better reconstructed image quality. During iterative optimization, this invention combines the fast convergence characteristics of the FISTA algorithm with adaptive step size control. The principle is to dynamically adjust the iteration step size by judging the convergence of the objective function value and reset the iteration state when necessary. This mechanism effectively avoids the algorithm continuously searching in undesirable directions, preventing it from getting trapped in local optima. The practical effect is a significant reduction in invalid iterations, improved overall convergence speed, and thus increased computational efficiency while maintaining reconstruction accuracy.

[0136] It is worth mentioning that the adaptive strategy of the present application enables it to cope with different imaging conditions and noise environments. The principle is to perceive the noise level of the input data in real time, and automatically adjust the regularization parameter according to the relationship between the residual and the noise energy. This enables the algorithm to automatically adjust the strength of its smoothing constraint when facing projection data with different signal-to-noise ratios. The direct effect is to enhance the adaptability of the reconstruction system to complex samples and changing imaging environments, and to improve the robustness and reliability of the method in practical application.

[0137] The above specific embodiments are only several optional embodiments of the present application, and based on the technical solutions of the present application and the related inspirations of the above embodiments, those skilled in the art can make various alternative improvements and combinations on the above specific embodiments.

Claims

1. A method for terahertz tomography reconstruction based on adaptive policy driven compressive sensing, characterized in that, The method comprises the following steps: S1, using a terahertz continuous wave imaging system to collect intensity data P of corresponding view angles at equidistant sparse angles to obtain a sinogram of sparse sampling view angles; S2, on the intensity data Data preprocessing is performed to unify the data scale; S3, initialize the related parameters of the algorithm, including step size and regularization parameters ; S4, constructing a target function, wherein the target function comprises a weighted sum of an un-regularized residual and a TV regularization term; S5, performing FISTA algorithm iteration and using an FGP method to perform TV algorithm iteration in the FISTA algorithm iteration to optimize a reconstructed image; S6, adaptively adjusting a step size and a regularization parameter based on a target function value and a noise level of the reconstructed image; S7, judging whether the FISTA algorithm iteration is ended, if yes, outputting the reconstructed image, otherwise, returning to step S5 to continue iteration.

2. The compressive sensing driven terahertz tomography reconstruction method based on adaptive strategy according to claim 1, characterized in that, The data preprocessing in step S2 comprises: S2-1, dark field correction, collect dark field data and subtract the dark field data from the raw projection data to obtain corrected data ;​ S2-2, normalizing the projection data are the minimum and maximum values of the projection data, respectively.​​​ 3. The compressive sensing driven terahertz tomography reconstruction method based on adaptive strategy according to claim 1, characterized in that, The parameter initialization in step S3 comprises: Step size initialized to where A is a measurement matrix; regularization parameter initialized to where is the noise standard deviation, is the number of measurements, is the number of image pixels, is a constant.

4. The compressive sensing driven terahertz tomography reconstruction method based on adaptive strategy according to claim 3, characterized in that, The target function construction in step S4 comprises: S4-1, compute unregularized residual wherein is the reconstructed image; S4-2, calculating the TV regularization term: ； in, For the row and column indices of the image pixels, To reconstruct the image In pixels along The partial derivative in the direction reflects the gradient of the image in the horizontal direction. To reconstruct the image In pixels along The partial derivative in the direction reflects the gradient in the vertical direction of the image; S4-3, combine the un-regularized residual and the TV regularization term, get the objective function wherein is a regularization parameter.

5. The compressive sensing driven terahertz tomography reconstruction method based on adaptive strategy according to claim 1, characterized in that, The FISTA algorithm iteration in step S5 comprises: S5-1, computing the gradient of the unregularized residual where is a projection matrix, is a projection matrix is the transpose matrix of S5-2, initializing dual variables p and q and calculating the TV term: ； wherein and respectively represent the dual variables at the pixel and values at the pixel and respectively represent the dual variables at the pixel and values at the pixel S5-3, constructing an intermediate image : ； wherein, is the reconstructed image, is the gradient of the unregularized residual, is the regularization parameter, is the dual variable , TV term; S5-4, computing dual variables Gradient: ； wherein is the gradient of the dual variable , is the gradient of the dual variable , , and denote the pixel values of the intermediate image at pixels , and , respectively. S5-5, updating the dual variable to , : ， ， wherein , is an auxiliary variable, is a regularization parameter; S5-6, update momentum : ； wherein, is the iteration number, is the momentum value for the th iteration, is the momentum value for the th iteration; S5-7, update auxiliary variables 、 : ； wherein and are the first iteratively updated dual variables and , and are the second iteratively updated dual variables and , and are the third iteratively updated auxiliary variables and ; S5-8, judge whether the TV algorithm iteration is ended, if yes, output the reconstructed image , otherwise, continue iteration; wherein is the reconstructed image output by the TV algorithm iteration, is a neighboring operator applied to the reconstructed image , is the updated auxiliary variable , TV term computed.

6. The compressive sensing driven terahertz tomography reconstruction method based on adaptive strategy according to claim 1, characterized in that, The adaptive parameter adjustment in step S6 comprises: S6-1, target function value judgment: if , update the reconstructed image as ; otherwise, increase to shorten the step , and reset the reconstructed image as ; S6-2, noise level judgment: if , increase the regularization parameter ; if , decrease ; the specific adjustment method is: , when , When ; wherein is the norm of the regularized residual of the i-th iteration quantifies the amplitude of the residual; is the number of image pixels is the product of the number of image pixels and the square of the noise standard deviation is the reference threshold for the noise capacity; and is the regularization parameter of the i-th and iteration, is the adjustment factor for the regularization parameter, .

7. The compressive sensing driven terahertz tomography reconstruction method based on adaptive strategy according to claim 1, characterized in that, The equidistant sparse angles in step S1 are 1 / 20 of the total number of angles required for terahertz tomographic reconstruction, wherein the total number of angles is 180.

8. The compressive sensing driven terahertz tomography reconstruction method based on adaptive strategy according to claim 6, characterized in that, The step S6-1 also includes updating the reconstructed image y by the momentum t: , wherein is the reconstructed image of the first iteration, is the reconstructed image of the second iteration, and is the intermediate reconstructed image of the first iteration. and is the intermediate reconstructed image of the second iteration.

9. The compressive sensing driven terahertz tomography reconstruction method based on adaptive strategy according to claim 1, characterized in that, The TV algorithm iteration in step S5 uses the FGP method and comprises initialization and updating of dual variables and auxiliary variables to accelerate convergence and maintain image edge details.

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