Method and system for confidence calibration of super-resolution reconstructed image based on distribution matching

Abstract

This invention discloses a method and system for super-resolution reconstructed image confidence calibration based on distribution matching. The method includes: generating pixel-level reconstruction error maps of the super-resolution reconstructed image and the real high-resolution image; obtaining the error statistical distribution after normalization and constructing an inverse distribution; generating multiple sets of confidence maps corresponding to the half-integral interval widths according to a preset step size; extracting the confidence statistical distribution of each set; calculating the JS divergence and cosine similarity of the bi-distribution; determining the optimal half-integral interval width index corresponding to the two indices; and generating the final calibration confidence map based on the optimal half-integral interval width. This invention overcomes the limitations of the commonly used assumption of uniform distribution of super-resolution reconstruction confidence. By using distribution matching to achieve adaptive optimization of the half-integral interval width, it makes the confidence distribution strongly correlated with the actual reconstruction error, significantly improving the accuracy and reliability of confidence calibration. It is applicable to various biomedical super-resolution reconstruction imaging scenarios.

Description

Technical Field

[0001] This invention relates to the field of super-resolution imaging technology, and in particular to a method and system for confidence calibration of super-resolution reconstructed images based on distribution matching. Background Technology

[0002] Super-resolution reconstruction (SR) imaging technology, by overcoming the optical diffraction limit and enabling clear observation of minute structures, has become one of the core technologies in biomedical research, precision detection, and other fields. In the SR reconstruction process, the confidence map quantifies the reliability of pixel-level reconstruction, providing a crucial reference for subsequent analysis; its calibration accuracy directly affects the application effect of SR images. However, the rationality of the confidence calibration methods in existing SR reconstruction techniques still has room for improvement, hindering the further promotion of SR technology.

[0003] Current common methods for SR image confidence calibration assume that the confidence statistical distribution follows a uniform distribution on [0,1] and use kurtosis and skewness indices to filter the width of the half-integral interval. While this method can achieve a regularized confidence distribution, it ignores the intrinsic relationship between confidence and actual reconstruction error. In biomedical imaging, there is a significant difference in reconstruction error between the target structure region and the background noise region. The confidence distribution should ideally exhibit non-uniform characteristics; a uniform distribution is merely an idealized assumption. This leads to the calibrated confidence not accurately reflecting reconstruction reliability, resulting in physical limitations. Furthermore, existing methods do not introduce quantitative indicators to measure the degree of matching between the confidence distribution and the error distribution, lacking objective evaluation criteria for calibration effectiveness. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a distribution-matching-based super-resolution reconstructed image confidence calibration method and system that solves the technical problem of weak correlation between the uniform distribution assumption and the actual reconstruction error and limited calibration accuracy in existing SR reconstructed image confidence calibration methods.

[0005] Technical solution: The confidence calibration method for super-resolution reconstructed images based on distribution matching described in this invention is characterized by comprising the following steps:

[0006] (1) Obtain the super-resolution reconstructed image and the corresponding real high-definition image, calculate the pixel-level absolute reconstruction error between the two, and generate a reconstruction error map;

[0007] (2) The reconstructed error map is normalized to obtain a normalized error distribution, and an error inverse distribution is constructed based on the normalized error distribution;

[0008] (3) Set the search range and step size of the half-integral interval width, generate multiple sets of candidate half-integral interval width values ​​according to the step size, calculate the corresponding super-resolution reconstructed image confidence map based on the candidate half-integral interval width values, and extract the confidence statistical distribution of each set of confidence maps.

[0009] (4) Calculate the cosine similarity and JS divergence between the error inverse distribution and the confidence statistical distribution;

[0010] (5) The minimum value of the JS divergence corresponds to the first subscript, and the maximum value of the cosine similarity corresponds to the second subscript. The optimal subscript is obtained by taking the average of the first and second subscripts.

[0011] (6) Obtain the corresponding optimal half-integral interval width based on the optimal subscript, and calculate the final calibration confidence map based on the optimal half-integral interval width.

[0012] Further, in step (1), the formula for calculating the pixel-level absolute reconstruction error is:

[0013]

[0014] in, For pixels The absolute reconstruction error, To reconstruct images at the pixel level The intensity value at that location, For high-definition images at pixel The intensity value at that location.

[0015] Furthermore, in step (2), the formula for the maximum value normalization process is:

[0016]

[0017] in, Here, represents the normalized error value, and e represents the error matrix corresponding to the reconstructed error map. This represents the global maximum value of the error matrix.

[0018] Furthermore, in step (3), the confidence map is distributed in the confidence interval using a pixel-mixed Laplace distribution. The integral within is obtained; where, For a confidence interval, Let be the mean of the super-resolution predictions for the q-th pixel. The half-length of the reliable interval.

[0019] Furthermore, the confidence plot is calculated using the following formula:

[0020]

[0021] in, For pixels The confidence level value within the width of the candidate half-integral interval. Let S be the mixture Laplace probability density function of the pixel, and let S represent a subset of all pixels.

[0022] Furthermore, in step (4), the formula for calculating the cosine similarity is:

[0023]

[0024] in, For a one-dimensional flattened sequence of confidence statistical distribution, The error distribution is a one-dimensional flattened sequence, where H×W is the image size. This represents the L2 norm.

[0025] Further, in step (4), the formula for calculating the JS divergence is:

[0026]

[0027] in, It is a mixed distribution of confidence level and error distribution; for The normalized probability distribution; for The normalized probability distribution, Let KL divergence be denoted as KL divergence.

[0028] Furthermore, the discrete form of the KL divergence is calculated using the following formula:

[0029]

[0030] in, , Let K be the probability of two distributions whose similarity needs to be measured in the i-th bin, and K be the number of bins for the distribution.

[0031] Further, in step (5), the formula for calculating the rounded average is:

[0032]

[0033] in, For the optimal index, Let the index be the first subscript corresponding to the minimum value of the JS divergence. This is the second index corresponding to the maximum cosine similarity, and round() is the rounding function.

[0034] A confidence calibration system for super-resolution reconstructed images based on distribution matching includes the following modules:

[0035] Error generation module: used to acquire super-resolution reconstructed images and high-resolution images, calculate pixel-level absolute reconstruction errors and generate reconstruction error maps;

[0036] Confidence map generation module: used to set the search range and step size of the half-integral interval width, generate multiple sets of candidate half-integral interval width values, and calculate the candidate confidence map corresponding to each set of half-integral interval widths;

[0037] Distribution construction module: used to extract the statistical distribution of the reconstruction error map and confidence map and perform normalization processing;

[0038] The index calculation and optimization module is used to calculate the JS divergence and cosine similarity between the error statistical distribution and the confidence statistical distribution of each group of candidates, and to determine the sequence index of the corresponding interval width based on the optimal value of the two indices.

[0039] Confidence calibration module: used to calculate the final calibration confidence map based on the optimal half-integral interval width.

[0040] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: 1. By achieving adaptive optimization of the half-integral interval width through dual-index distribution matching, the confidence distribution is strongly correlated with the actual reconstruction error, significantly improving the accuracy and reliability of confidence calibration; 2. The calibrated confidence map calculated using the optimal half-integral interval width has a distribution feature that highly matches the inverse distribution of the actual reconstruction error, which can accurately quantify the reconstruction reliability of each pixel and provide a reliable basis for subsequent SR image analysis; 3. The present invention can be directly adapted to various SR imaging devices and biological structure imaging needs, filling the market technology gap in confidence calibration. Attached Figure Description

[0041] Figure 1 The flowchart below shows the confidence calibration method and system for super-resolution reconstructed images based on distribution matching of this invention.

[0042] Figure 2 The figures shown are examples of super-resolution and high resolution of the present invention, where (a) is super-resolution and (b) is high resolution.

[0043] Figure 3 Here are examples of confidence levels for the absolute error and η=0.02 of the present invention, where (a) is the absolute error graph, (b) is the confidence level graph for η=0.02, and (c) is an example of a sequence of candidate confidence level graphs between η=0.02 and η=0.08.

[0044] Figure 4 This is a graph showing the relationship between the error distribution and the confidence level distribution under each η in this invention;

[0045] Figure 5This is a dual-index evaluation chart of error distribution and confidence distribution for this invention;

[0046] Figure 6 This is an example diagram illustrating the final calibration confidence level of this invention;

[0047] Figure 7 This is a framework diagram of the super-resolution reconstructed image confidence calibration system provided by the present invention. Detailed Implementation

[0048] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0049] like Figure 1 As shown, this invention provides a method for super-resolution reconstructed image confidence calibration based on distribution matching, comprising:

[0050] First, acquire the target image obtained through super-resolution reconstruction (SR). (H×W represents the image size), such as Figure 2 As shown in (a) above, and the corresponding real high-resolution (HR) image. ,like Figure 2 As shown in (b), ensure that the spatial alignment and size of the two images are consistent.

[0051] Calculate the pixel-level absolute reconstruction error and generate a reconstruction error map. For any pixel in the image... The formula for calculating its absolute reconstruction error is:

[0052]

[0053] in, For SR images at pixels The intensity value at that location, For HR images in pixels The intensity value at that location.

[0054] The reconstructed error map is normalized to eliminate dimensional differences, mapping the error values ​​to the [0,1] interval. The formula for the normalized error values ​​is as follows:

[0055]

[0056] Where e is the error matrix corresponding to the reconstructed error map. This represents the global maximum value of the error matrix.

[0057] Then, the search range and step size of the half-integral interval width η are set. The search range of η is set to [0.001, 0.1], and the step size is set to 0.001, generating a total of M candidate values. (k=1,2,...,M), corresponding confidence plot ,like Figure 3 (a) in the figure shows the absolute error. Figure 3 (b) shows the confidence level when η = 0.02. Figure 3 (c) shows an example of a confidence graph sequence to be matched between η=0.02 and η=0.08.

[0058] Confidence maps are calculated based on the candidate η values ​​for each group, and the pixel blending Laplacian distribution is then used to determine the confidence interval. The integral within the range is obtained, and the calculation formula is:

[0059] ]

[0060] in, For pixels The confidence value for candidate η, where, For a confidence interval, Let be the mean of the super-resolution predictions for the q-th pixel. The confidence interval half-length is used to control the clinical tolerance range of confidence assessment. Let S be the mixture Laplace probability density function of the pixel, and let S represent a subset of all pixels.

[0061] like Figure 4 The relationship between the error distribution and the confidence distribution at each η is shown. Among them, the confidence distribution with η = 0.06 is most similar to the error distribution, that is, the distribution characteristics of the confidence value at this time can best reflect the distribution law of the actual reconstruction error.

[0062] Secondly, cosine similarity is used to measure the consistency of the trend between the backward distribution of errors and the statistical distribution of confidence scores. The calculation formula is as follows:

[0063]

[0064] in, For a one-dimensional flattened sequence of confidence statistical distribution, The error distribution is a one-dimensional flattened sequence, where H×W is the image size. Let L2 be the norm, and cosine similarity ranges from [−1, 1]. The closer the value is to 1, the stronger the consistency of the trends between the two distributions.

[0065] JS divergence is a symmetric improvement based on KL divergence, quantifying the morphological differences between two probability distributions. The calculation formula is as follows:

[0066]

[0067] in, It is a mixed distribution of confidence level and error distribution; for The normalized probability distribution; for The normalized probability distribution, Let KL divergence be denoted as KL divergence.

[0068] The discrete form of the KL divergence is calculated using the following formula:

[0069]

[0070] in, , Let K be the probability of two distributions whose similarity needs to be measured in the i-th bin, and K be the number of bins for the distribution, with a value of 50.

[0071] Finally, the optimal index for both indices is determined: traverse all candidate η values ​​corresponding to the JS divergence and cosine similarity, and select the minimum JS divergence value as the first index. And the maximum cosine similarity, corresponding to the second subscript. .

[0072] The optimal index is obtained by merging the two subscripts using the rounding average formula. The calculation formula is as follows:

[0073]

[0074] in, The optimal index is given by `round()`, which is the rounding function.

[0075] Based on the optimal index Extract the corresponding η value from the candidate η set as the optimal half-integral interval width η.

[0076] like Figure 5 This paper presents a dual-index evaluation of the error distribution and confidence distribution. The cosine similarity is maximized when η is 0.06, and the JS divergence is minimized. This allows us to determine the optimal distribution corresponding to the point with the highest distribution matching degree. The value is 0.06.

[0077] like Figure 6 An example graph showing the final calibration confidence level is presented, showing the substitution of the optimal η into the confidence level calculation formula. The confidence values ​​of each pixel in the SR reconstructed image are recalculated to generate a final calibration confidence map. The distribution characteristics of this confidence map are highly consistent with the inverse distribution of the actual reconstruction error, which can accurately quantify the reconstruction reliability of each pixel and provide a reliable basis for subsequent SR image analysis.

[0078] This invention also provides a confidence calibration system for super-resolution reconstructed images based on distribution matching, the system framework of which is as follows: Figure 7 As shown, it includes the following modules:

[0079] Error generation module: used to acquire super-resolution reconstructed images and high-resolution images, calculate pixel-level absolute reconstruction errors and generate reconstruction error maps;

[0080] Confidence map generation module: used to set the search range and step size of the half-integral interval width, generate multiple sets of candidate half-integral interval width values, and calculate the candidate confidence map corresponding to each set of half-integral interval widths;

[0081] Distribution construction module: used to extract the statistical distribution of the reconstruction error map and confidence map and perform normalization processing;

[0082] The index calculation and optimization module is used to calculate the JS divergence and cosine similarity between the error statistical distribution and the confidence statistical distribution of each group of candidates, and to determine the sequence index of the corresponding interval width based on the optimal value of the two indices.

[0083] Confidence calibration module: used to calculate the final calibration confidence map based on the optimal half-integral interval width.

Claims

1. A distribution matching based super-resolution reconstruction image confidence calibration method, characterized in that, Includes the following steps: (1) Obtain the super-resolution reconstructed image and the corresponding real high-definition image, calculate the pixel-level absolute reconstruction error between the two, and generate a reconstruction error map; (2) The reconstructed error map is normalized to obtain a normalized error distribution, and an error inverse distribution is constructed based on the normalized error distribution; (3) Set the search range and step size of the half-integral interval width, generate multiple sets of candidate half-integral interval width values ​​according to the step size, calculate the corresponding super-resolution reconstructed image confidence map based on the candidate half-integral interval width values, and extract the confidence statistical distribution of each set of confidence maps. (4) Calculate the cosine similarity and JS divergence between the error inverse distribution and the confidence statistical distribution; (5) The minimum value of the JS divergence corresponds to the first subscript, and the maximum value of the cosine similarity corresponds to the second subscript. The optimal subscript is obtained by taking the average of the first and second subscripts. (6) Obtain the corresponding optimal half-integral interval width based on the optimal subscript, and calculate the final calibration confidence map based on the optimal half-integral interval width.

2. The super-resolution reconstructed image confidence calibration method of claim 1, wherein, In step (1), the formula for calculating the pixel-level absolute reconstruction error is: in, For pixels The absolute reconstruction error, To reconstruct images at the pixel level The intensity value at that location, For high-definition images at pixel The intensity value at that location.

3. The method for super-resolution reconstructed image confidence calibration according to claim 1, characterized in that, In step (2), the formula for the maximum value normalization process is: in, Here, represents the normalized error value, and e represents the error matrix corresponding to the reconstructed error map. This represents the global maximum value of the error matrix.

4. The method for super-resolution reconstructed image confidence calibration according to claim 1, characterized in that, In step (3), the confidence map is distributed in the confidence interval using a pixel-mixed Laplacian distribution. The integral within is obtained; where, For a confidence interval, Let be the mean of the super-resolution predictions for the q-th pixel. The half-length of the reliable interval.

5. The method for calibrating the confidence level of super-resolution reconstructed images according to claim 4, characterized in that, The confidence plot is calculated using the following formula: in, For pixels The confidence level value within the width of the candidate half-integral interval. Let S be the mixture Laplace probability density function of the pixel, and let S represent a subset of all pixels.

6. The method for calibrating the confidence level of super-resolution reconstructed images according to claim 1, characterized in that, In step (4), the formula for calculating the cosine similarity is: in, For a one-dimensional flattened sequence of confidence statistical distribution, The error distribution is a one-dimensional flattened sequence, where H×W is the image size. This represents the L2 norm.

7. The method for super-resolution reconstructed image confidence calibration according to claim 1, characterized in that, In step (4), the formula for calculating the JS divergence is: in, It is a mixed distribution of confidence level and error distribution; for The normalized probability distribution; for The normalized probability distribution, Let KL divergence be denoted as KL divergence.

8. The method for calibrating the confidence level of super-resolution reconstructed images according to claim 7, characterized in that, The discrete form of the KL divergence is calculated using the following formula: in, , Let K be the probability of two distributions whose similarity needs to be measured in the i-th bin, and K be the number of bins for the distribution.

9. The method for calibrating the confidence level of super-resolution reconstructed images according to claim 1, characterized in that, In step (5), the formula for calculating the rounded average is: in, For the optimal index, Let the index be the first subscript corresponding to the minimum value of the JS divergence. This is the second index corresponding to the maximum cosine similarity, and round() is the rounding function.

10. A confidence calibration system for super-resolution reconstructed images based on distribution matching, characterized in that, Includes the following modules: Error generation module: used to acquire super-resolution reconstructed images and high-resolution images, calculate pixel-level absolute reconstruction errors and generate reconstruction error maps; Confidence map generation module: used to set the search range and step size of the half-integral interval width, generate multiple sets of candidate half-integral interval width values, and calculate the candidate confidence map corresponding to each set of half-integral interval widths; Distribution construction module: used to extract the statistical distribution of the reconstruction error map and confidence map and perform normalization processing; The index calculation and optimization module is used to calculate the JS divergence and cosine similarity between the error statistical distribution and the confidence statistical distribution of each group of candidates, and to determine the sequence index of the corresponding interval width based on the optimal value of the two indices. Confidence calibration module: used to calculate the final calibration confidence map based on the optimal half-integral interval width.

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