Sea surface significant wave height inversion method based on X-band radar

Abstract

The invention provides a sea surface significant wave height inversion method based on an X-band radar, and the method comprises the steps: carrying out the local noise estimation through sliding window analysis and Gaussian weighted smoothing, obtaining a weighted local statistic, determining a false alarm probability through Bayesian optimization, and determining a dynamic threshold value through the combination of the false alarm probability and the weighted local statistic; constructing a Lagrange basis function and performing interpolation filling on the shadow region to obtain an image after interpolation filling; and performing two-dimensional Fourier transform on the image after interpolation filling to obtain a radar image frequency spectrum, calculating an energy spectrum by using the frequency spectrum, and performing filtering, removing high-frequency noise and retaining frequency components related to sea waves, thereby realizing estimation of the significant wave height. The method can effectively identify the shadow region of the X-band radar image and extract features, and improves the inversion precision and efficiency of the sea surface significant wave height.

Description

Technical Field

[0001] The present invention relates to the technical field of image inversion, and in particular, to a method for inverting the significant wave height of the sea surface. Background Art

[0002] The significant wave height of the sea surface is one of the core parameters for marine environmental monitoring, disaster warning, and marine engineering design. Traditional measurement methods mainly rely on buoys, wave buoys, and optical sensors. Although buoys and wave buoys can directly obtain wave height data, their deployment costs are high, maintenance is complex, and they are limited by physical locations, making it difficult to achieve large-scale continuous monitoring. Optical sensors are severely dependent on lighting conditions and cannot work effectively at night or in bad weather, greatly limiting their all-weather monitoring capabilities. In recent years, X-band radars have gradually become an important tool for sea surface wave height inversion due to their high resolution, all-weather working characteristics, and large-scale coverage advantages. However, existing methods based on X-band radars still have significant defects: firstly, the identification and processing of shadow areas are insufficient, resulting in serious signal interference and affecting the accuracy of wave height inversion; secondly, traditional threshold segmentation methods are mostly static or empirically set, making it difficult to adapt to the dynamic changes of the sea surface and prone to misjudgment or missed judgment of shadow areas; thirdly, the shadow area filling technology lacks adaptability to local texture features, resulting in interpolation results deviating from the true sea surface morphology and further introducing calculation errors.

[0003] The invention patent with the application number 202210304380.2 discloses a method for inverting the significant wave height based on X-band navigation radar images. After collecting the original navigation radar images, the analysis regions of spectral analysis technology and shadow statistics method are respectively selected, the root mean square wave steepness is obtained through edge detection, calculating the shadow ratio, etc., the sea wave spectrum is obtained by using spectral analysis technology in combination with a dispersion band-pass filter and a modulation transfer function, and the main wave number is extracted. Finally, the significant wave is obtained according to the root mean square wave steepness and the main wave number; the accuracy of wave height inversion by the shadow statistics method is improved. However, when using the shadow statistics method in this method, only edge detection and simple threshold processing are used to divide the shadow area, which may not be able to accurately identify the shadows in complex sea conditions, and the utilization of information in the shadow area is also insufficient. Summary of the Invention

[0004] Aiming at the technical problem of insufficient identification of shadow areas, the present invention proposes a method for inverting the significant wave height of the sea surface based on an X-band radar. By a series of operations such as sliding window analysis, Gaussian weighted smoothing, and Bayesian optimization to determine the false alarm probability to divide the shadow area, it can effectively identify the shadow area and improve the inversion accuracy and efficiency of the significant wave height of the sea surface.

[0005] In order to achieve the above object, the technical solution of the present invention is realized as follows:

[0006] A method for inverting the significant wave height of the sea surface based on an X-band radar, characterized by comprising the steps:

[0007] S1: Collect the original data of a single-frame sea surface image using an X-band radar, and perform convolution operations and

[0008] mean filtering and other preprocessing on the original data of the sea surface image to remove co-frequency interference noise;

[0009] S2: Obtain weighted local statistics by performing local noise estimation on the preprocessed sea surface image through sliding window analysis and Gaussian weighted smoothing, determine the false alarm probability through Bayesian optimization, determine the dynamic threshold by combining the false alarm probability with the weighted local statistics, and divide the shadow area according to the dynamic threshold;

[0010] S3: Select the neighborhood points of the shadow area, construct Lagrange basis functions and perform interpolation filling on the shadow area to obtain the interpolated and filled image;

[0011] S4: Perform two-dimensional Fourier transform on the interpolated and filled image to obtain the radar image spectrum, obtain the energy spectrum from the radar image spectrum, filter the energy spectrum, and then estimate the wave height.

[0012] Furthermore, the method for obtaining weighted local statistics by performing local noise estimation through sliding window analysis and Gaussian weighted smoothing is as follows:

[0013] Define the size of the sliding window according to the specific required local analysis accuracy of the image; Initialize the position of the sliding window; Move the sliding window at a set step length and calculate the pixel gray value within each sliding window, and calculate the mean μ and variance σ of the background noise according to the pixel gray value within each sliding window 2 , until the sliding window covers the entire sea surface image;

[0014] Set the Gaussian weighting function according to the image resolution, determine the Gaussian weights according to the pixel distances, and perform weighted calculations on the mean and variance within the sliding window to obtain the weighted local statistics.

[0015] Furthermore, the weighted local statistics include weighted mean and weighted variance:

[0016] The weighted mean is:

[0017]

[0018] The weighted variance is:

[0019]

[0020] where, μ represents the mean of the background noise, σ 2represents the variance of the background noise, w represents the size of the sliding window, i and j are the initial coordinates of the upper left corner of the sliding window, k and l are the relative positions of the pixels within the window, and G(·) represents the Gaussian weighting function.

[0021] Further, the method for determining the false alarm probability through Bayesian optimization is as follows: Select two dynamic thresholds according to the distribution of the weighted mean and weighted variance, and calculate the initial first false alarm probability P FA and the initial second false alarm probability P' FA ;

[0022] With the minimization of the actual false alarm probability A(P FA ) corresponding to the false alarm probability as the objective, use the Gaussian process as a probability model to approximate the objective function. Based on the objective function, use the expected improvement function as the acquisition function to perform iterative calculations to select the next false alarm probability to be evaluated; Determine whether to converge according to the preset threshold; If the gap between the actual false alarm probability and the currently known minimum false alarm probability is less than the preset threshold, then output the optimal false alarm probability

[0023] Further, the objective function is:

[0024]

[0025] Among them, Δ 2 is the signal variance, and l is the length scale parameter;

[0026] The formula for the expected improvement is:

[0027] EI(P FA ) = (A(P FA ) - A best )Φ(Z) + Δ(P FA );

[0028]

[0029] Among them, EI(·) represents the expected improvement of the false alarm probability, A best is the currently known minimum false alarm probability, Φ and φ are the cumulative distribution function and probability density function of the standard normal distribution respectively; Δ(P FA ) = P FA - P' FA ;

[0030] In each iteration of the iterative calculation, the smaller of the first false alarm probability and the second false alarm probability in the previous iteration is used as the second false alarm probability, and the expected improvement of the false alarm probability is used as the first false alarm probability for iterative calculation.

[0031] Furthermore, the method for determining the dynamic threshold by combining the false alarm probability with the weighted local statistic is as follows:

[0032] Calculate the threshold sensitivity adjustment constant:

[0033]

[0034] Determine the dynamic threshold according to the weighted local statistic:

[0035]

[0036] where Φ -1 (·) is the inverse function of the standard normal distribution, and T i,j is the dynamic threshold corresponding to the selected sliding window.

[0037] Furthermore, the method for constructing the Lagrange basis function and interpolating and filling the shadow area is as follows: For each sliding window, select a set of neighborhood points around each shadow area, and construct the Lagrange basis function based on the neighborhood points; construct the interpolation calculation formula according to the Lagrange basis function and calculate the polynomial interpolation; apply the calculated interpolation to the shadow area to replace the original pixel values.

[0038]

[0039] where L i (x) and Mj(y) are the Lagrange basis functions in the x and y directions respectively, P(x, y) represents the interpolation, and f(x i , y j ) is the gray value of the neighborhood points.

[0040] Furthermore, the method for performing two-dimensional Fourier transform on the interpolated and filled image to obtain the radar image spectrum is as follows:

[0041]

[0042] where M and N are the number of rows and columns of the image pixels respectively, I gray (i + k, j + l) is the pixel value of the pixel point, F(u, v) represents the frequency domain signal value at the coordinate (u, v) in the frequency domain, and u and v are the coordinate indices in the frequency domain.

[0043] The method for obtaining the energy spectrum from the radar image spectrum is as follows:

[0044] E(u, v) = |F(u, v)| 2

[0045] By filtering the energy spectrum, the purpose of filtering is to remove the low-frequency background and high-frequency noise and retain the frequency components related to the sea waves. Furthermore, the wave height is estimated.

[0046] The calculation formula for the significant wave height is as follows:

[0047] where C is an empirical constant factor.

[0048] The beneficial effects of the present invention are as follows:

[0049] By combining sliding window analysis with Gaussian weighted smoothing, local statistics are extracted, and the false alarm probability is dynamically determined using Bayesian optimization, significantly improving the adaptability and accuracy of shadow region recognition, and effectively overcoming the problem of insufficient adaptability of traditional static thresholds to complex sea conditions. Based on neighborhood points, Lagrange basis functions are constructed to perform high-precision interpolation filling on the shadow region, fully retaining the sea surface texture details and avoiding texture distortion caused by traditional interpolation methods. Finally, the inversion accuracy of the sea surface significant wave height is improved, which can provide better technical support and guarantee for ocean environmental monitoring and ship navigation safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the technology in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following-described drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0051] Figure 1 It is a flowchart of the method of the present invention.

[0052] Figure 2 In it, a is a single-frame X-band radar sea surface image collected; b and c are the mean map and variance map of a selected sliding window region respectively.

[0053] Figure 3 In it, a is a schematic diagram of the division of the shadow region and the non-shadow region; b is a schematic diagram of the shadow annotation filling result.

[0054] Figure 4 It is a two-dimensional frequency spectrum diagram corresponding to the frequency domain signal.

[0055] Figure 5 It is a wave height scatter diagram obtained at different timestamps in the embodiments of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0056] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

[0057] A method for retrieving the significant wave height of the sea surface based on an X-band radar, as Figure 1 shown, includes the following steps:

[0058] S1: Use the X-band radar to collect the original data of a single-frame sea surface image, and perform preprocessing such as convolution operation and mean filtering on the original data of the sea surface image to remove co-frequency interference noise.

[0059] Perform preliminary processing on the collected original data of the sea surface image, including improving the signal-to-noise ratio of the image through Gaussian denoising and correcting the time synchronization error to improve the usability of the data.

[0060] As Figure 2 shown in a of, it is a single-frame X-band radar sea surface image collected (data source: Liu Ningbo, Wang Guoqing, etc. Radar sea exploration test and target characteristic data acquisition - Radar Journal of the dual-polarization multi-sea-state scattering characteristic data set of marine targets, 2023, 12(2): 456-469. doi: 10.12000 / JR23029).

[0061] S2: Obtain the weighted local statistic by performing local noise estimation on the preprocessed sea surface image through sliding window analysis and Gaussian weighted smoothing, determine the false alarm probability through Bayesian optimization, determine the dynamic threshold by combining the false alarm probability with the weighted local statistic, and divide the shadow area according to the dynamic threshold.

[0062] Specifically, the method for obtaining the weighted local statistic by performing local noise estimation through sliding window analysis and Gaussian weighted smoothing is as follows:

[0063] Define the size w of the sliding window according to the specific required local analysis accuracy of the image (such as 3×3); initialize the position of the sliding window, that is, place the sliding window at the starting position in the upper left corner of the preprocessed sea surface image; move the sliding window at the set step size and calculate the pixel gray value within each sliding window, and calculate the mean and variance of the background noise according to the pixel gray value within each sliding window until the sliding window covers the entire sea surface image. As Figure 2 shown in b and c of, they are the mean map and variance map of a selected window area respectively.

[0064] Mean:

[0065]

[0066] Among them, Γ is the number of pixels within the sliding window, and I gray (i + k, j + l) is the gray value of the pixel within each sliding window; i and j are the initial coordinates of the upper left corner of the sliding window, and k and l are the relative positions of the pixel within the window.

[0067] Variance:

[0068]

[0069] Further, a Gaussian weighting function is set according to the image resolution, the Gaussian weights are determined according to the pixel distance, and the mean and variance within the sliding window are weighted and calculated to obtain weighted local statistics:

[0070] The Gaussian weighting function is:

[0071]

[0072] where G(i + k, j + l) is the Gaussian weight of the pixel at the position (i + k, j + l). η is the standard deviation of the Gaussian distribution, which is used to control the distribution range of the weights.

[0073] Further, the Gaussian weights are applied to the mean and variance of each sliding window to obtain weighted local statistics, namely weighted mean and weighted variance:

[0074] Weighted mean:

[0075]

[0076] Weighted variance:

[0077]

[0078] Sliding window analysis divides the image into multiple small windows, and the mean and variance of the pixel gray values are calculated within each window to estimate the local noise. Gaussian weighted smoothing weights the pixels within the window according to the Gaussian function, highlighting the role of the central pixel, and obtaining weighted local statistics that can better reflect the local characteristics.

[0079] Further, the method for determining the false alarm probability by Bayesian optimization is:

[0080] Two dynamic thresholds are selected according to the distribution of the weighted mean and weighted variance (for example, selecting the mean or median of the weighted mean and weighted variance as the threshold), and the initial first false alarm probability P FA and the initial second false alarm probability P' FA .

[0081] Taking the minimization of the actual false alarm probability A(P FA ) corresponding to the false alarm probability P FA as the objective, a Gaussian process is used as a probability model to approximate the objective function A(P FA ):

[0082]

[0083] Among them, Δ 2 is the signal variance, and l is the length scale parameter.

[0084] Based on the objective function, the expected improvement EI is used as the acquisition function to perform iterative calculations to select the next P value to be evaluated. FA During each iteration of the iterative calculation, the smaller of the first false alarm probability and the second false alarm probability in the previous iteration is used as the second false alarm probability, and the expected improvement of the false alarm probability is used as the first false alarm probability for iterative calculation.

[0085] The formula for the expected improvement (EI) is:

[0086] EI(P FA ) = (A(P FA ) - A best )Φ(Z) + Δ(P FA )φ(Z);

[0087]

[0088] Among them, EI(·) represents the expected improvement of the false alarm probability, A best is the currently known minimum false alarm probability, Φ and φ are the cumulative distribution function and probability density function of the standard normal distribution respectively, and Δ(P FA ) = P FA - P′ FA .

[0089] Judge whether the model converges according to the preset threshold, that is, the gap between the newly evaluated actual false alarm rate A(P FA ) and the current optimal value f best is less than the preset threshold. After iteration, Bayesian optimization outputs the optimal false alarm probability to minimize the false alarm probability.

[0090] Furthermore, the method for determining the dynamic threshold by combining the false alarm probability with the weighted local statistic is: calculate the threshold sensitivity adjustment constant:

[0091]

[0092] Among them, Φ -1 (·) is the inverse function of the standard normal distribution.

[0093] Furthermore, determine the dynamic threshold according to the weighted local statistic:

[0094]

[0095] Among them, T i，j is the dynamic threshold corresponding to the selected sliding window.

[0096] Shadow area division based on dynamic threshold:

[0097] For each sliding window, compare each pixel within the sliding window with the dynamic threshold. If a pixel is less than the dynamic threshold, this pixel belongs to the shadow area; otherwise, this pixel is a non-shadow area. As Figure 3 shown, a is a schematic diagram of the division between the shadow area and the non-shadow area; this scheme greatly improves the accuracy of shadow area recognition. Calculate the dynamic threshold by combining the false alarm probability and the weighted local statistic, and this threshold can adaptively change according to the local features of the image. Divide the image pixels into shadow areas and non-shadow areas based on the dynamic threshold, and accurately identify the parts affected by shadows. Traditional fixed threshold methods are difficult to adapt to the complex situations in different regions of the image, while the dynamic threshold can be adjusted according to local noise and signal features, effectively avoiding misjudgment. For example, in a sea surface image, the wave patterns and lighting conditions in different regions are different, and the dynamic threshold can better adapt to these changes and accurately divide the shadow area, providing an accurate basis for subsequent processing of the shadow area.

[0098] S3: Select the neighborhood points of the shadow area, construct the Lagrange basis function and perform interpolation filling on the shadow area to obtain the image after interpolation filling.

[0099] Construct the interpolation calculation formula according to the Lagrange basis function and calculate the polynomial interpolation:

[0100]

[0101] L i (x) and M j (y) are the Lagrange basis functions in the x and y directions respectively, and f(x i , y j ) is the gray value of the neighborhood points.

[0102] Apply the calculated interpolation P(x, y) to the shadow area to replace the original pixel values; enhance the texture details of the shadow area through interpolation, thereby adjusting the contrast of the image. As Figure 3 shown, b is a schematic diagram of the shadow annotation filling result. Restore the image information of the shadow area and enhance the texture details of the image. Through interpolation filling, the image content originally lost due to shadows is supplemented, improving the readability and analyzability of the image. For example, when analyzing the wave texture in a sea surface image, the image after interpolation filling can provide more complete texture information, which helps to study the characteristics of waves more accurately.

[0103] S4: Perform a two-dimensional Fourier transform on the interpolated and filled image to obtain the radar image spectrum. Obtain the energy spectrum from the radar image spectrum, filter the energy spectrum, and then estimate the wave height. Specifically, the method for performing a two-dimensional Fourier transform on the interpolated and filled image to obtain the radar image spectrum is as follows:

[0104]

[0105] where M and N are the number of rows and columns of the image pixels respectively, and I gray (i + k, j + l) is the gray value of the pixel point. F(u, v) represents the value of the original frequency domain signal at the coordinate (u, v) in the frequency domain, and u and v are the coordinate indices in the frequency domain.

[0106] Specifically, the method for obtaining the energy spectrum from the radar image spectrum:

[0107] E(u, ν) = |F(u, v)| 2

[0108] The estimation formula for the wave height H is:

[0109]

[0110] where C is an empirical constant factor (taking the value of 2.2 in this method).

[0111] The wave height scatter plot obtained by the present invention at different timestamps is as Figure 5 shown.

[0112] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A sea surface significant wave height inversion method based on X-band radar, characterized in that: Includes steps: S1: Use X-band radar to collect single-frame sea surface image raw data, and perform convolution operation and mean filtering on the sea surface image raw data to remove the same-frequency interference noise; S2: local noise estimation of the pre-processed sea surface image is performed through sliding window analysis and Gaussian weighted smoothing to obtain weighted local statistics, false alarm probability is determined through Bayesian optimization, dynamic threshold is determined by combining false alarm probability with weighted local statistics, and shadow area is divided according to the dynamic threshold; S3: Selecting neighborhood points of the shadow area, constructing a Lagrangian basis function and performing interpolation filling on the shadow area to obtain an interpolated and filled image; S4: Perform two-dimensional Fourier transform on the interpolated and filled image to obtain a radar image spectrum, obtain an energy spectrum from the radar image spectrum, filter the energy spectrum, and then estimate the wave height.

2. The sea surface significant wave height inversion method based on X-band radar according to claim 1 is characterized in that: The method for obtaining weighted local statistics by performing local noise estimation through sliding window analysis and Gaussian weighted smoothing is: Define the size of the sliding window according to the specific required local image analysis accuracy; initialize the sliding window position; move the sliding window according to the set step size and calculate the pixel grayscale value in each sliding window, and calculate the mean μ and variance σ of the background noise based on the pixel grayscale value in each sliding window 2 , until the sliding window covers the entire sea surface image; The Gaussian weighting function is set according to the image resolution, the Gaussian weight is determined according to the pixel distance, and the mean and variance in the sliding window are weighted to obtain the weighted local statistics.

3. The sea surface significant wave height inversion method based on X-band radar according to claim 2 is characterized in that: The weighted local statistics include weighted mean and weighted variance: The weighted mean is: The weighted variance is: Among them, μ represents the mean of background noise, σ 2 represents the variance of the background noise, w represents the sliding window size, i and j are the initial coordinates of the upper left corner of the sliding window, k and l are the relative positions of the pixels in the window, and G(·) represents the Gaussian weighting function.

4. The sea surface significant wave height inversion method based on X-band radar according to claim 3 is characterized in that: The method for determining the false alarm probability by Bayesian optimization is as follows: selecting two dynamic thresholds according to the distribution of the weighted mean and the weighted variance, and calculating the initial first false alarm probability P according to the dynamic threshold calculation formula and the threshold sensitivity adjustment constant calculation formula. FA and the initial second false alarm probability P′ FA ; The actual false alarm probability A(P FA ) is minimized as the goal, and the Gaussian process is used as the probability model to approximate the objective function. Based on the objective function, the expected improvement function is used as the acquisition function to iteratively calculate and select the next false alarm probability to be evaluated; whether it converges is determined according to the preset threshold; if the difference between the actual false alarm probability and the currently known minimum false alarm probability is less than the preset threshold, the optimal false alarm probability is output 5. The sea surface significant wave height inversion method based on X-band radar according to claim 4 is characterized in that: The objective function is: Among them, Δ 2 is the signal variance, l is the length scale parameter; The expected improvement formula is: EI(P FA )=(A(P FA )-THE best )Φ(Z)+Δ(P FA )φ(Z); Where EI(·) represents the expected improvement in false alarm probability, A best is the currently known minimum false alarm probability, Φ and φ are the cumulative distribution function and probability density function of the standard normal distribution respectively; Δ(P FA )=P FA -P′ FA ; In each iteration process of the iterative calculation, the smaller value of the first false alarm probability and the second false alarm probability in the previous iterative calculation is the second false alarm probability, and the iterative calculation is performed with the expected improvement amount of the false alarm probability as the first false alarm probability.

6. The sea surface significant wave height inversion method based on X-band radar according to claim 4 or 5, characterized in that: The method for determining the dynamic threshold by combining the false alarm probability with the weighted local statistics is: Calculate the threshold sensitivity adjustment constant: Determine dynamic thresholds based on weighted local statistics: Among them, Φ -1 (·) is the inverse function of the standard normal distribution, T i,j is the dynamic threshold corresponding to the selected sliding window.

7. The sea surface significant wave height inversion method based on X-band radar according to any one of claims 1 to 5, characterized in that: The method for constructing a Lagrangian basis function and performing interpolation filling on the shadow area is as follows: for each sliding window, a group of neighborhood points are selected around each shadow area, and a Lagrangian basis function is constructed based on the neighborhood points; an interpolation calculation formula is constructed according to the Lagrangian basis function and a polynomial interpolation is calculated; and the calculated interpolation is applied to the shadow area to replace the original pixel value.

8. The sea surface significant wave height inversion method based on X-band radar according to claim 7, characterized in that: L i (x) and M j (y) are the Lagrangian basis functions in the x and y directions respectively, P(x, y) represents the interpolation, and f(x i ,y j ) is the gray value of the neighborhood point.

9. The sea surface significant wave height inversion method based on X-band radar according to claim 8, characterized in that: The method of performing two-dimensional Fourier transform on the interpolated and filled image to obtain the radar image spectrum is: Where M and N are the number of rows and columns of image pixels, respectively. gray (i+k, j+l) is the pixel value of the pixel point, F(u,υ) represents the original frequency domain signal value at the coordinate (u,υ) in the frequency domain, and u and υ are the coordinate indexes in the frequency domain.

10. The sea surface significant wave height inversion method based on X-band radar according to claim 9, characterized in that: The method for obtaining the energy spectrum from the radar image spectrum is: E(u,υ)=|F(u,υ)| 2 The calculation formula of the effective wave height is: Where C is the empirical constant factor.

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