SAR (Synthetic Aperture Radar) water depth inversion method based on adaptive elliptic window function

Abstract

The invention discloses an SAR (Synthetic Aperture Radar) water depth inversion method based on a self-adaptive elliptic window function, which comprises the following steps of: realizing self-adaptive adjustment in the direction of an elliptic window, the proportion of a long axis to a short axis and the type of a window function by analyzing the energy distribution characteristics of a main peak of a two-dimensional frequency spectrum of an SAR sub-graph; therefore, the directivity expression of the spectrum main peak and the accuracy of wavelength extraction are remarkably improved. According to the method, the definition of the main peak of the frequency spectrum and the water depth inversion precision can be remarkably improved, and a more stable and accurate technical path is provided for SAR water depth inversion in a complex near-shore environment.

Description

Technical Field

[0001] This invention relates to a SAR depth inversion method based on an adaptive elliptic window function. Background Technology

[0002] High-precision shallow sea depth information is fundamental supporting data for marine development and governance, and is of great significance for port and waterway planning and maintenance, coastal disaster resilience assessment, and refined coastal zone management. Traditional single-beam or multi-beam acoustic bathymetry has advantages in point accuracy, but in large-scale, rapidly updated scenarios and complex nearshore terrain, it is difficult to meet the requirements of high spatiotemporal resolution and high update frequency due to cost, efficiency, and operational conditions. Optical remote sensing depth inversion methods can achieve effective inversion in clear waters, but they are highly dependent on water transparency and are easily affected by factors such as suspended matter, changes in seabed sediment, water disturbance, and clouds, limiting their applicability in turbid or variable sea conditions.

[0003] As swells propagate towards the shore, their wavelengths shorten due to shallowing and refraction. Based on the linear dispersion equation, swell wavelength information can be mapped to local water depth information. Synthetic Aperture Radar (SAR) possesses day / night, cloud-covered imaging capabilities and wide-swath revisit capabilities. Under moderate wind fields and imaging geometry conditions, it can provide information such as swell wavelength and wave direction, thus providing observational input for nearshore depth sounding. Current mainstream methods are mostly based on two-dimensional fast Fourier transform (2D FFT) to locate the main peak and extract the dominant wavelength from the SAR image spectrum, and then infer the water depth. However, the spectrum is susceptible to noise and edge effects, leading to unstable spectrum quality and ambiguous main peak location. Simultaneously, wave periods are difficult to obtain directly from images and are often replaced by fixed or empirical values, which can easily introduce systematic biases under different water depths and topographic conditions, thereby reducing inversion accuracy. These problems are particularly prominent in nearshore shallowing zones, fracture zones, and areas with significant swell-shore current interactions. Therefore, reducing spectral uncertainty, decreasing reliance on fixed period assumptions, and achieving robust estimation of wavelength and wave period are among the key challenges in current SAR depth inversion.

[0004] To suppress spectral leakage and improve the resolvability of the main peak, some studies apply weighted windows to SAR images during the spectrum calculation stage. This involves applying window functions with different weights at the receiver to balance spectral performance and improve spectral characteristics. Traditional window functions, such as rectangular windows and various cosine windows, are widely used in wave spectrum analysis. However, in scenarios with significant nearshore boundary effects and non-uniform wavefields, their ability to suppress leakage and sidelobes is limited. The main peak is still prone to diffusion and unstable positioning, leading to biases in depth inversion. Therefore, simply relying on fixed windows cannot guarantee spectral quality under complex conditions; it is necessary to introduce more adaptive window function designs and parameter adjustments.

[0005] On the other hand, to reduce reliance on the fixed-period assumption, it is necessary to accurately reflect nearshore dynamic processes in physical modeling. Influenced by nearshore surge-current interactions and the fracture zone, the mapping relationship between period and wavelength is no longer stable, thus inversion based on a fixed wave period is prone to systematic bias. Zhang et al.'s review shows that wave-current coupling can significantly alter wave velocity and propagation characteristics, thereby affecting wavelength extraction and depth sounding accuracy in SAR images. Ge et al.'s higher-order dispersion relation further points out that, especially at medium water depths, traditional linear dispersion relations are insufficient to accurately describe changes in wave propagation, thus limiting inversion accuracy. These physics-based improvements enhance the reliability of period and phase velocity estimation, but cannot replace quality control at the spectral end; and the adaptability of the fixed-period assumption remains insufficient under complex hydrodynamic conditions. Therefore, achieving robust wave period estimation under different water depths and complex topographic conditions remains one of the current research challenges. Summary of the Invention

[0006] The purpose of this invention is to propose an adaptive elliptical window function SAR water depth inversion method driven by peak-to-bandwidth ratio (PBR). This method dynamically adjusts the direction, major-minor axis ratio, and basis functions of the elliptical window based on spectral characteristics, thereby significantly enhancing the clarity of the main spectral peak and improving the accuracy and stability of wavelength extraction. By segmenting the initial inverted water depth, locally reestimating the wave period and correcting the dispersion relation accordingly, and then reverting the water depth again, the model's adaptability under different terrain and hydrodynamic conditions is enhanced, improving the physical consistency and spatial accuracy of the overall inversion results.

[0007] To achieve the above objectives, the solution of the present invention is:

[0008] A SAR depth inversion method based on an adaptive elliptic window function is proposed. The specific steps of this method are as follows:

[0009] Step 1: Acquire SAR images, prior water depth information, and measured water depth data, and perform unified projection, spatial registration, and vertical reference integration processing.

[0010] Step 2: The SAR image obtained in Step 1 is cropped by sliding at a set step size to form a sub-image sequence for spectral analysis;

[0011] Step 3: Perform Fast Fourier Transform (FFT) calculations on each sub-graph obtained in Step 2 to identify the main energy connected domains and characterize the main wave direction and spectral shape features.

[0012] Step 4: For each sub-graph obtained in Step 2, perform anisotropic elliptic windowing aligned with the corresponding main wave direction obtained in Step 3;

[0013] Step 5: Perform FFT calculation on the windowed image obtained in Step 4 to obtain the spectrum, and extract the position of the main wave peak and its corresponding wavelength and direction information from it. Use the linear dispersion relation to complete the water depth inversion.

[0014] Furthermore, in the step of performing anisotropic elliptical windowing aligned with the corresponding principal wave direction obtained in step 3, the step of obtaining the principal direction angle of the added elliptical window includes:

[0015] The centroid position and second-order center matrix of the main energy connected domain obtained in step 3 are calculated to quantify the distribution characteristics of the spectral energy in different directions.

[0016] By performing eigenvalue decomposition on the second-order central matrix, the direction of the eigenvector corresponding to its largest eigenvalue is extracted and used as the principal axis direction of the main peak of the spectrum, which is the principal direction angle of the elliptical window.

[0017] Furthermore, the steps for obtaining the major and minor axes of the added elliptical window include:

[0018] ,

[0019] ,

[0020] In the formula, a and b represent the major axis and minor axis, respectively; area represents the pixel area of ​​the main energy connected region; H and W represent the height and width of the corresponding subgraph, respectively; and e represents the eccentricity of the main peak of the spectrum.

[0021] Furthermore, the selection of the added elliptical window is based on the peak-to-bandwidth ratio (PBR):

[0022] When PBR < α, the Blackman window is selected as the basis function to construct an elliptical window;

[0023] When α≤PBR<β, the Hamming window is selected as the basis function to construct an elliptical window;

[0024] When PBR≥β, the Hanning window is used as the basis function to construct an elliptical window;

[0025] Where α and β are both preset PBR thresholds.

[0026] Furthermore, the peak-to-bandwidth ratio (PBR) is defined as the ratio of the spectral peak energy to the global average energy:

[0027] ,

[0028] ,

[0029] ,

[0030] in, Main peak energy. As background energy, and These are the positive and negative frequency neighborhoods of the main peak, respectively. Represents frequency coordinates, where Ω is the effective domain of the spectrum. The power spectral density represents the spectrum. Indicates removal and The remaining region in the subsequent spectrum.

[0031] Furthermore, ,in, With the origin as the center and radius... small disk low-frequency exclusion zone

[0032] Furthermore, step 5, which involves extracting the position of the main wave peak and its corresponding wavelength and direction information, includes:

[0033] By utilizing the binary segmentation of the main wave peak energy position in the spectrogram and regional connectivity analysis, the main energy connected domain with the largest area is extracted, and its geometric centroid coordinates are calculated. ;

[0034] Extract the second largest peak from the remaining spectrum after removing the main peak, and calculate the set centroid coordinates of its corresponding region. ;

[0035] Calculate the wavelength corresponding to the main peak and wave direction angle :

[0036] ,

[0037] ,

[0038] In the formula, , M and N represent the length and width of the spectrum.

[0039] Furthermore, in step 5, the water depth is inverted using the linear dispersion relation, and the following inversion model is constructed:

[0040] ,

[0041] In the formula, Indicated by wavelength Sum of waves Let be the water depth function value of the independent variable, and g be the acceleration due to gravity.

[0042] Compared with the prior art, the significant advantage of this invention is that it analyzes SAR sub-data.Figure 2 The energy distribution characteristics of the spectral peak are adaptively adjusted in three aspects: elliptical window direction, major and minor axis ratio, and window function type. This significantly improves the accuracy of the directional expression of the spectral peak and wavelength extraction, thereby enhancing the clarity of the spectral peak and the accuracy of water depth inversion. Attached Figure Description

[0043] Figure 1 This is a schematic diagram showing the location of the research area on the east coast of Florida.

[0044] Figure 2 This is a schematic diagram showing the location of the research area on the west coast of Portugal.

[0045] Figure 3 This is a flowchart of the method of the present invention.

[0046] Figure 4 The following are typical two-dimensional spectrograms of SAR sub-images under unwindowed conditions: (a) is the spectrogram of sub-image 2-250, (b) is the spectrogram of sub-image 9-218, (c) is the spectrogram of sub-image 16-109, (d) is the spectrogram of sub-image 21-170, (e) is the spectrogram of sub-image 28-139, and (f) is the spectrogram of sub-image 35-128.

[0047] Figure 5 The images show SAR water depth inversion and error scatter plots based on unwindowed spectrum extraction. (a) is the water depth inversion map of the east coast of Florida, USA, and (b) is the error scatter plot of the corresponding inversion results.

[0048] Figure 6 The images show a comparison between the original SAR sub-image and the windowed image after applying a two-dimensional Hanning window. (a) is the original SAR sub-image, and (b) is the windowed image after applying a two-dimensional Hanning window.

[0049] Figure 7 The windowing effects and elliptical window distribution of different sub-images are visualized. Among them, (a) is the original image of sub-image 4-210, (b) is the image of sub-image 4-210 after adding elliptical windows, (c) is the original image of sub-image 13-96, (d) is the image of sub-image 13-96 after adding elliptical windows, (e) is the original image of sub-image 26-103, (f) is the image of sub-image 26-103 after adding elliptical windows, (g) is the original image of sub-image 37-81, and (h) is the image of sub-image 37-81 after adding elliptical windows.

[0050] Figure 8 A comparative analysis of the two-dimensional FFT spectrum before and after weighting with the elliptical Hanning window function is presented, where (a) is the two-dimensional FFT spectrum before weighting with the elliptical Hanning window function, and (b) is the two-dimensional FFT spectrum after weighting with the elliptical Hanning window function.

[0051] Figure 9 For weighted window function type to SAR sub Figure 2 The impact of the FFT spectrum is compared, where (a) is the spectrum obtained without using window function weighting, (b) is the spectrum obtained with Hanning window function weighting, (c) is the spectrum obtained with Hamming window function weighting, and (d) is the spectrum obtained with Blackman window function weighting.

[0052] Figure 10 The scatter plots and fitting curves of water depth inversion errors under two strategies, no windowing and adaptive windowing, are shown for comparison on the east coast of Florida. (a) is without windowing, and (b) is with adaptive windowing.

[0053] Figure 11 The scatter plots and fitting curves of water depth inversion errors under two strategies, namely no windowing and adaptive windowing, are shown for the west coast of Portugal. (a) is without windowing, and (b) is with adaptive windowing. Detailed Implementation

[0054] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0055] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0056] This embodiment selects two typical nearshore areas, the east coast of Florida and the west coast of Portugal, as comparative study areas. A two-dimensional fast Fourier spectrum is constructed using the Sentinel-1 GRDH (Ground Range Detected, High Resolution) product, and the initial wave period is estimated using GEBCO 2023 data. A 1 / 3 arcsecond resolution DEM published by the National Centers for Environmental Information (NCEI) is used as the reference water depth for the US study area, while Global Multi-Resolution Topography (GMRT) integrated topographic data is used as the reference water depth for the Portuguese study area. The inversion accuracy and stability of the proposed method under different shoreline conditions are systematically evaluated, providing strong theoretical support and methodological innovation for the application of SAR water depth inversion technology in complex nearshore areas.

[0057] I. Overview of the Study Area

[0058] like Figure 1 As shown, the first study area is located in the south-central part of the east coast of Florida, USA, mainly covering the nearshore zone and shallow offshore slopes near Brevard County and Indian River County, bordering the Atlantic Ocean. The coastline at this location is generally straight, and the seabed is a sandy, gently sloping area, exhibiting a typical continuous zone of coastline, shoals, and open sea.

[0059] The study area is located in a microtidal environment with mixed semi-diurnal tides and tidal ranges of approximately 0.6–1.5 m. Tidal current intensity is generally weak to moderate. Wave conditions are relatively stable, with wave climate jointly controlled by local wind waves and offshore swells, exhibiting significant seasonality and directionality. Nearshore hydrodynamics are dominated by long shore currents driven by oblique incidence waves. The fracture zone often develops sandbar-channel landforms and offshore current channels, amplifying small-scale spatiotemporal variations. The Florida Current and the western edge of the Gulf Stream on the outer continental shelf exert background modulation on regional water levels and offshore wavefields.

[0060] like Figure 2As shown, the second study area is located on the west coast of Portugal. Situated on the western side of the Iberian Peninsula, facing the North Atlantic, this region exhibits a generally north-south trending, zigzagging coastline with diverse features including straight sandy beaches, rocky headlands, and harbors, resulting in a complex coastline. The coastline is predominantly rocky with relatively steep slopes, exhibiting a clear transition between shallow and deep waters, and rapid depth changes at the headland edges. The region is characterized by semi-diurnal tides, classified as a mesotidal environment, with tidal ranges varying weakly with changes in coastline geometry and local channel conditions. Wave energy is high, with high-energy swells dominating the wave climate and exhibiting significant seasonality. Furthermore, rapid local slope changes further exacerbate the uneven distribution of the current field and wave direction within the fracture zone, thereby enhancing spectral anisotropy.

[0061] II. SAR Satellite Data

[0062] This embodiment utilizes C-band SAR imagery from the European Space Agency (ESA) Sentinel-1 A / B constellation. This constellation possesses day / night and cloud-covered imaging capabilities, along with a 250km wide swath revisit capability. It is highly sensitive to changes in sea surface roughness and can continuously acquire high-quality coastal imagery under various weather and lighting conditions. The GRDH amplitude imagery product in Interferometric Wide (IW) mode is used. This product is a multi-look processed amplitude imagery, with ground distance projection and radiometric correction completed, and resampled to a 10m × 10m ground pixel size. While maintaining high resolution, it also possesses wide swath coverage, making it suitable for spectral analysis and water depth inversion applications in regional-scale sea areas.

[0063] To ensure the effectiveness of 2D-FFT spectral analysis and dispersion inversion, this embodiment selected representative Sentinel-1 SAR images for each of the two study areas. The selected images needed to meet the following conditions: First, there were no strong convective processes during the image acquisition period; the ocean surface wave field was dominated by swells with relatively stable directions and long dominant wave periods; second, the images presented clear and continuous wave bands, facilitating the extraction of the dominant wave direction and wavelength; third, the SAR images covered mainly shallow to medium-shallow water (less than 100 meters deep); finally, the water flow disturbance in this area was relatively weak, with no significant coastal jet streams observed, to reduce the impact of water flow on wave propagation characteristics. The selected images are shown in Table 1.

[0064] Table 1. Basic information of the Sentinel-1 SAR images used in the research

[0065]

[0066] To support SAR image-driven shallow water depth inversion and to verify model accuracy, this embodiment introduces two types of auxiliary water depth data: one is prior water depth information, used to estimate the main wave period and construct the inversion model; the other is high-precision measured water depth data, used to evaluate the accuracy of the inversion results.

[0067] First, the GEBCO 2023 global seabed topography dataset was selected as the prior water depth input. This dataset, jointly provided by the International Hydrographic Organization (IHO) and the United Kingdom Hydrographic Office (UKHO), has a spatial resolution of 15 arcseconds and covers global ocean areas. Because GEBCO 2023 provides good continuity and availability of water depth information in nearshore shallow waters, it can provide initial water depth estimates for the SAR inversion model, thus supporting subsequent back-calculation of the dominant wave period based on dispersion relations.

[0068] Secondly, to verify the accuracy of the inverted water depth results, this embodiment uses DEM Global Mosaic (1 / 3 arc-second resolution) as the ground truth reference data. This data is provided by the U.S. National Center for Environmental Information and integrates multi-source measured water depth data with high-resolution topographic information. It has a spatial resolution of approximately 10m, high geometric consistency and sounding accuracy, and is particularly suitable for evaluating the accuracy of SAR water depth inversion at a regional scale.

[0069] Both types of auxiliary water depth data were subjected to unified projection and spatial registration to ensure consistency with the Sentinel-1 inversion results in terms of coordinate system and resolution, providing a solid reference basis for wave period calculation and error analysis.

[0070] To ensure that data from different sources are comparable and can be used for pixel-by-pixel pairing within the same reference frame, this embodiment implements unified spatial and vertical reference processing for Sentinel-1 imagery and two types of water depth data: First, the WGS84 projection zone corresponding to the study area is selected as the working coordinate system, and all gratings are reprojected onto this coordinate system; continuous variables are resampled using bilinear resampling, and discrete masks are resampled using nearest-neighbor resampling; then, the water depth data is rasterized to the same spatial resolution as Sentinel-1, and cropped based on the unified study area boundary to ensure that the grating size and the number of rows and columns are perfectly matched.

[0071] For spatial registration, nearshore geometric consistency is quickly verified using shoreline vectors and water body masks. SAR amplitude images are overlaid with shoreline buffers, and the median offset of the shoreline normal distance is calculated. When the median offset exceeds 0.5 pixels, rigid translation fine-tuning is performed until the residual offset is below a threshold. To avoid interference from non-oceanic scatterers, land and man-made structure masks are uniformly applied, and spectral estimation and sample pairing are performed only in open water. For the vertical reference, to avoid bias introduced by systematic differences in reference surfaces from different data sources, the mean sea level (MSL) is uniformly used as the target reference.

[0072] III. Overall Process of SAR Water Depth Inversion

[0073] To obtain robust water depth inversion results in complex nearshore environments, such as Figure 3 As shown, this embodiment constructs a spectral feature extraction and depth inversion workflow for SAR images. The core idea is to reliably extract the dominant wave elements in the spectral domain and improve the accuracy and stability of depth inversion using a spectral quality-aware strategy. First, the original Sentinel-1 image is slid-cropped at a fixed step size to form a sequence of sub-images for spectral analysis. Second, a two-dimensional fast Fourier spectrum is calculated on each sub-image to identify the main energy connected domain and characterize the dominant wave direction and spectral shape features. The relevant feature quantities and criteria are given in the next section of this chapter. Then, anisotropic elliptic windowing aligned with the dominant wave direction is performed, and the window type is adaptively selected by combining the quality metric of the peak-to-background energy ratio. Candidate windows include Hanning, Hamming, and Blackman. After windowing, the final spectral calculation is performed on the original sub-images to locate the dominant peak, obtain the dominant wavelength and wave direction, and use the linear dispersion relation to complete the depth inversion of the corresponding sub-image.

[0074] 1. Sub-window spectrum construction and main peak energy measurement

[0075] To establish a unified foundation for spectral analysis and a primary peak quality metric to support subsequent adaptive elliptic windowing with consistent orientation, this study first analyzes spectral leakage and sidelobe phenomena caused by image boundary effects, illustrating the impact of conventional frequency domain contamination on primary peak identification and wave parameter inversion. An isotropic window function weighting is then used as the standard processing strategy. Next, a two-dimensional Fast Fourier Transform (FFT) is applied to the windowed sub-windows to obtain the frequency position and principal energy direction of the dominant wave peak, providing an initial orientation for elliptic windowing. Finally, a Precision Boundary Ratio (PBR) index is defined to characterize the degree of primary peak energy concentration and background interference suppression capability. The aforementioned spectral information, primary peak characteristics, and PBR quality indicator will serve as inputs for subsequent anisotropic windowing and reliability fusion.

[0076] 1.1 Boundary Leakage Mechanism and Isotropic Windowing Suppression

[0077] In SAR spectral estimation based on two-dimensional fast Fourier transform (2D-FFT), the finite-size analysis domain is equivalent to the original SAR image. Apply rectangular cutoff This causes the frequency domain response to be affected by boundary conditions. Its observed spectrum is:

[0078] (1)

[0079] In the formula, It is a continuous spectrum. It is the two-dimensional Dirichlet kernel corresponding to the rectangular window. It is the raw spectrum, that is, the spectrum calculated without rectangular window truncation, representing the image. Continuous spectrum information; The original image With rectangular window function The frequency domain response after multiplication is obtained by directly truncating the image in the spatial domain, i.e., by multiplying with a rectangular window. The result is obtained by multiplying and then performing a Fourier transform. .

[0080] The aforementioned convolution operation causes the main peak energy to diffuse to adjacent frequencies, resulting in spectral leakage and sidelobe structures. This not only weakens the energy separation between the main peak and the background but also introduces a deviation in the main peak's position, thus affecting the stable identification of the dominant wavelength and propagation direction. To suppress this contamination, a common practice is to apply windowing to the image boundaries before the 2D-FFT transform to smooth abrupt boundary changes and improve the sidelobe structure of the frequency domain convolution kernel, thereby reducing the impact of spectral leakage on the main peak.

[0081] Conventional windowing methods employ isotropic, separable two-dimensional windows. Its form is the product of rows and columns of one-dimensional windows:

[0082] , , (2)

[0083] In the formula, M is the number of rows of the window function, i.e., the vertical dimension of the window function. N is the number of columns of the window function, i.e., the horizontal dimension of the window function. and For a one-dimensional generalized cosine window, the functions are respectively applied to the first... row and number A column is defined as:

[0084] (3)

[0085] In the formula, M is the number of rows of the window function, that is, the dimension of the window function in the vertical direction. K is the upper limit of the summation, representing the number of weighted terms of the window function in the frequency domain.

[0086] The most commonly used window type is the Hanning window, whose one-dimensional weights in the horizontal and vertical axes are defined as follows:

[0087] (4)

[0088] (5)

[0089] The corresponding two-dimensional weighted window is obtained:

[0090] (6)

[0091] In the formula, For size × The two-dimensional window weight matrix.

[0092] Sub-image The image after windowing is as follows:

[0093] (7)

[0094] The Fourier transform result of the windowed sub-image is as follows:

[0095] (8)

[0096] In the formula, For the windowed frequency domain kernel, compared to the original... It exhibits significant advantages in sidelobe suppression. Through a windowing strategy, leakage energy around the main peak is effectively suppressed, thereby improving the spectral contrast and identifiability of the main peak.

[0097] 1.2 Two-dimensional FFT spectrum construction and dominant peak acquisition

[0098] After windowing the sub-image, in order to identify the periodic fluctuation features contained in the wave texture, the image needs to be mapped from the spatial domain to the frequency domain. In this embodiment, 2D-FFT is used to perform spectral domain transformation on the windowed sub-image, construct a spectrogram, and extract the dominant energy peak.

[0099] 2D-FFT is a core tool for analyzing the directional periodic structure of images, effectively revealing periodic texture patterns at various scales and directions. Let the windowed SAR sub-image be... Then its 2D-FFT transformed expression is:

[0100] (9)

[0101] In the formula, Represents frequency coordinates The spectral response at a given point is shown, with the image center representing low-frequency components and the edges corresponding to high-frequency information. To observe the structural features of the spectrogram, the transformation result is first frequency-shifted, and then the logarithm of its amplitude spectrum is taken to construct a more readable spectral image, namely the centered amplitude spectrum. :

[0102] (10)

[0103] In the formula, To prevent tiny constants with values ​​of zero.

[0104] The dominant wave peak appears as a bright spot with concentrated energy in the frequency spectrum, usually distributed in pairs on both sides of the frequency domain, reflecting the main propagation direction and wavelength information of the wave. If the ripples in the sub-image are clear, the spectral structure should have obvious dominant peak characteristics, and the position and orientation angle of the dominant peak can be used for subsequent wavelength inversion and directional modeling.

[0105] In this embodiment, the spectrogram is not only used for subsequent wavelength and wave direction extraction, but also serves as the basis for calculating spectral quality assessment indicators. The stability and accuracy of FFT processing not only determine the reliability of the spectral energy distribution, but also play a key supporting role in the overall water depth inversion process, affecting the overall reliability of subsequent wave parameter estimation and water depth extrapolation.

[0106] 1.3 Main Peak Distinguishing Index Based on Peak-to-Background Ratio (PBR)

[0107] In section 1.2, the spectrum was obtained from the windowed SAR sub-map using a two-dimensional fast Fourier transform, and the dominant spectral peaks were initially extracted. However, due to significant differences in wave characteristics across different regions, the dominant peaks in some sub-maps are not obvious or there is significant background interference, which may lead to unstable wavelength extraction. To further improve the identification of the dominant spectral peaks and the robustness of wavelength calculation, this embodiment introduces the Peak-to-Broadband Ratio (PBR) as a quantitative indicator of spectral clarity, and uses it to drive the adaptive selection of window type and parameters in subsequent chapters.

[0108] To avoid the nonlinear bias introduced by the logarithmic mapping, energy calculations are performed in the linear amplitude domain. Let the complex spectrum of the windowed 2D-FFT be denoted as... Take linear amplitude To eliminate the influence of DC / low-frequency substrate, the effective frequency domain is defined. ,in With the origin as the center and radius... The low-frequency exclusion zone of the small disk, It is the effective domain of the spectrum.

[0109] For the centered amplitude spectrum Initial inspection of the main peak was conducted to obtain the conjugate symmetrical peak positions. To accommodate the spatial distribution of the main peak in the spectrum, this embodiment constructs an elliptical neighborhood with a shape consistent with the second-order moment of the main peak's neighborhood. Specifically, this is achieved by adjusting the principal axis direction angle. Based on the scales of the primary and secondary axes, an elliptical region corresponding to the energy distribution of the main peak is defined. Expansion coefficient. By controlling the neighborhood size, we can obtain the neighborhoods of the two main peaks. and Based on this, the main peak energy is defined as follows:

[0110] (11)

[0111] And background energy:

[0112] (12)

[0113] Under the above energy definition, PBR is given as:

[0114] (13)

[0115] PBR directly reflects the degree of energy dominance of the main peak relative to the broadband background. The larger the value, the more concentrated the main peak is and the higher the separation from the background; a lower value indicates that the dominant frequency component is difficult to distinguish from the background, and may contain side lobes and noise, increasing the risk of variance and bias in subsequent wavelength calculations.

[0116] PBR provides a scale-insensitive and physically interpretable quantitative characterization of spectral clarity without introducing additional normalization processing. It can be used for both quality assessment and algorithm adaptive control, providing a fundamental guarantee for the stability and consistency of subsequent SAR water depth inversion.

[0117] 2. Spectrum-sensing driven anisotropic elliptic windowing

[0118] 2.1 Orientation constraints and adaptive geometric parameters of elliptical windows

[0119] Compared to an unweighted rectangular window, the weight of a two-dimensional cosine window function gradually decreases at the edges of the sub-image, effectively reducing the amplitude of spectral sidelobes and narrowing the leakage bandwidth, thereby mitigating energy diffusion and main peak interference caused by abrupt boundary changes. This windowing operation helps improve the prominence and identification accuracy of the spectral main peak and is a common method in SAR image spectral preprocessing. However, standard isotropic window functions still have certain limitations when dealing with the variable wave propagation characteristics in complex shallow sea areas. Under different wavefield conditions, the spectral main peak often exhibits significant directionality and irregular shape, making it difficult for a fixed-shape window function to simultaneously meet the requirements of suppressing leakage and highlighting the main peak.

[0120] To address this, this embodiment introduces an adaptive elliptical window on top of conventional windowing. By applying more concentrated weights along the principal axis and appropriately converging along the perpendicular principal axis, the window function shape better conforms to the energy distribution characteristics of a typical spectral peak. Compared to the isotropic standard cosine window, the elliptical window can enhance energy focusing in the principal direction while effectively suppressing energy leakage in non-principal axis directions, thereby increasing the prominence of the spectral peak and reducing sidelobe interference. This approach helps improve the accuracy of wavelength extraction and enhances the robustness of the overall method under different hydrodynamic and topographical conditions.

[0121] For a one-dimensional vector of length M, its Hanning window weight is shown in equation (3), with zero values ​​at both ends of the sequence and a maximum value of 1 at the center. To further extend this to the two-dimensional case and facilitate the unified processing of subsequent elliptical windows, the index i is mapped to the standard coordinate interval [-1, 1], and let... Further simplification yields Therefore, equation (4) can be rewritten as:

[0122] (14)

[0123] This is the mother window that constitutes a two-dimensional elliptical window.

[0124] set up Define a two-dimensional window function as the product of one-dimensional window functions:

[0125] (15)

[0126] It forms a two-dimensional rectangular window, with the maximum value at the center and the edge decaying to 0.

[0127] Further define the rotation transformation coordinates:

[0128] (16)

[0129] in The rotation angle is... For the long axis, It is the short axis.

[0130] Ultimately, the elliptical Hanning window can be defined as:

[0131] (17)

[0132] in, , .

[0133] In the specific implementation process, firstly, based on the spectrum obtained by the two-dimensional fast Fourier transform, the amplitude is logarithmically transformed, and the main spectral energy regions are identified through threshold segmentation and regional connectivity analysis. Subsequently, the centroid position and second-order central matrix of this main region are calculated to quantify the distribution characteristics of spectral energy in different directions. By eigenvalue decomposition of the second-order matrix, the eigenvector direction corresponding to its largest eigenvalue is extracted as the principal axis direction of the main spectral peak, thereby obtaining the rotation angle of the elliptical window, i.e., the principal direction angle.

[0134] Regarding the adaptive determination of the major and minor axis ratios, this embodiment designs dynamically adjustable major and minor axis lengths based on the normalized area and eccentricity of the main region. Specifically, the major axis ratio is determined by the change in the area of ​​the main region relative to the square root of the total image area, reflecting the spatial coverage of the spectral peak energy; while the minor axis ratio depends on the eccentricity of the main region. As the peak energy distribution along the main axis becomes more concentrated, the minor axis tends to contract, making the elliptical window more elongated. By constraining the range of the major and minor axis ratios, abnormal regions can be avoided from causing the window shape to become too extreme. This strategy ensures that the elliptical window's shape is highly consistent with the actual distribution height of the spectral peak, thereby significantly improving the identification of the spectral peak and the robustness of wavelength estimation.

[0135] (18)

[0136] Where area represents the pixel area of ​​the connected region of the main peak of the spectrum, and H and W are the height and width of the subgraph, respectively. This is the normalized proportion of the main peak region area across the entire image. The major axis proportion 'a' is further restricted to between 0.3 and 0.8 to avoid outliers that are too small or too large.

[0137] (19)

[0138] Here, e represents the eccentricity of the main peak of the spectrum; the closer to 1, the narrower and longer it is, and the closer to 0, the closer it is to a circle. The minor axis ratio α is also limited to between 0.1 and 0.8a to ensure that the elliptical shape is reasonable and physically acceptable.

[0139] It is worth noting that the weighting operation of the window function in this stage is not superimposed on the already weighted image, but is directly reapplied to the original unwindowed SAR sub-image to avoid spectral distortion or main peak energy attenuation caused by continuous windowing, thus ensuring the accuracy of the final FFT analysis. After completing the adaptive elliptical window weighting, the FFT operation is performed again to obtain the optimized spectrum, from which the position of the main peak and its corresponding wavelength and direction information are extracted. Compared with processing methods that rely solely on a single window function or a fixed window type, the dual adaptive strategy of window function type and geometric parameters driven by PBR proposed in this embodiment can dynamically match the window function shape and direction for different sub-image spectral characteristics, significantly improving the accuracy of spectral main peak identification and the overall stability of water depth inversion.

[0140] The adaptive elliptical window method proposed in this embodiment, which considers both directional consistency and anisotropy, determines the principal axis direction of the spectral peak and the energy distribution width along the principal and secondary axes by calculating the second-order matrix of the spectral amplitude distribution. It then dynamically sets the principal axis angle and the ratio of the major and minor axes of the elliptical window, enabling the window function shape to more accurately match the spatial distribution of the peak. This adaptive adjustment introduced at the geometric level not only enhances the energy focusing of the spectral peak in the principal direction but also effectively suppresses energy leakage in the vertical direction, thereby further improving the accuracy of wavelength extraction and the robustness of the overall method in complex nearshore hydrodynamic environments.

[0141] 2.2 Window type selection and window type adjustment rules based on PBR

[0142] In section 2.1, the weighting effect of the spectral main peak was optimized through directional constraints of the elliptical window and adaptive adjustment of geometric parameters. This method fully utilizes the geometric characteristics of the spectrogram, dynamically adjusting the shape of the window according to the spatial distribution of the main peak, thereby improving the sharpness of the main peak and the stability of wavelength estimation. However, although this method has high flexibility in handling different spectral configurations, it still cannot fully cope with complex scenarios with low signal-to-noise ratios or high background noise in the spectrum. To further improve the windowing effect, this embodiment further introduces PBR as a quantitative indicator of spectral sharpness and adaptively selects the most suitable window function type based on it.

[0143] The PBR value directly reflects the saliency of the spectral peak and quantifies the degree of background interference. A higher PBR value indicates a clear peak and weak background interference, while a lower PBR value indicates that the peak is difficult to distinguish in the spectrum and the background energy accounts for a larger proportion. Based on this spectral characteristic, this embodiment further proposes a PBR-based adaptive window selection strategy, which aims to dynamically select the most suitable window function type according to different spectral qualities, thereby maximizing the accuracy and stability of wavelength extraction.

[0144] When the PBR value is high, the main peak in the spectrum is usually very clear, and the background noise is relatively low, meaning that the dominant spectral component is well distinguished from the background frequency components. In this case, using the Hanning window as the weighting window is the most suitable choice. The Hanning window has a narrow main lobe, which can suppress side lobes while maintaining the sharpness of the main peak and good frequency resolution, thereby improving the accuracy of spectral analysis. Its advantage lies in providing accurate wavelength estimation in a clear spectrum because it effectively preserves the main characteristics of the spectrum, reduces spectral leakage, and avoids the broadening of the main peak. It is suitable for situations with a high signal-to-noise ratio and where the main peak energy dominates the spectrum.

[0145] When the PBR value is at a moderate level, the main peak of the spectrum is still identifiable, but the interference from side lobes increases, and background noise may also affect the prominence of the main peak. In this case, the Hamming window is a more ideal choice. The Hamming window can effectively attenuate side lobes while maintaining the energy of the main peak. Its main lobe is slightly wider than that of the Hanning window, but it performs better in attenuating side lobes, thus achieving a more balanced suppression effect in the spectrum. It can effectively suppress leakage while ensuring the clarity of the main peak and avoiding excessive expansion. This window function is suitable for spectra with moderate clarity, especially when the spectral quality is acceptable but there is some side lobe interference.

[0146] When the PBR value is low, the main peak in the spectrum is blurry or almost indistinguishable, background noise is strong, and the signal-to-noise ratio (SNR) is low. In this case, the Blackman window is a more suitable choice. The Blackman window has the strongest sidelobe suppression capability, effectively reducing leakage in the spectrum and significantly enhancing the energy contrast between the main peak and the background. Although the main lobe of the Blackman window is wide, its powerful sidelobe suppression function enhances the stability of the spectrum analysis, especially in low SNR situations, preventing background noise from interfering with the extraction of the main peak. This window function is suitable for situations with low SNR and where the main peak is difficult to distinguish, helping to improve the stability of the spectrum and thus obtaining a relatively reliable wavelength estimate even in noisy environments.

[0147] By employing this PBR-based adaptive window selection strategy, this embodiment can dynamically adjust the windowing strategy according to different spectral characteristics and sharpness, as shown in Table 2. This method not only optimizes the accuracy of wavelength extraction but also enhances the robustness of spectral analysis, providing more stable spectral data support for subsequent depth inversion.

[0148] Table 2. Adaptive window adjustment strategy based on peak-to-bandwidth ratio (PBR)

[0149]

[0150] 3. Wavelength and Wave Direction Extraction

[0151] After completing the PBR-based adaptive elliptic windowing and spectral peak reconstruction, this embodiment presents a method for extracting the dominant wavelength and wave direction within the classic 2D spectral analysis framework. The position of the dominant wave peak reflects the dominant frequency component of the sea surface wave, and its offset relative to the spectral center can be used to calculate the actual physical wavelength. Specifically, firstly, using binary segmentation of the dominant peak energy position in the Fourier spectrum and region connectivity analysis, the dominant peak region with the largest area is extracted, and its geometric centroid coordinates are calculated. Subsequently, to enhance symmetry assessment and wave direction estimation, the second largest peak was extracted from the remaining spectrum after removing the main peak, and its centroid coordinates were calculated. The pixel spacing between the two main peaks is defined as the absolute value of the difference between the horizontal and vertical coordinates. Let the spectrum size be... × The spatial resolution of the subgraph is Then the spacing between the main peaks in the frequency domain can be converted into the actual physical wavelength. The calculation formula is as follows:

[0152] (20)

[0153] Furthermore, the wave propagation direction (wave angle) is calculated using the offset direction of the centroid of the main peak of the spectrum relative to the center of the spectrum:

[0154] (twenty one)

[0155] In the formula Wave direction angle, and The pixel spacing between the two main peaks.

[0156] 4. Linear wave dispersion relationship and water depth inversion model

[0157] In this embodiment, under the constraints of standard linear dispersion theory, the dominant wavelength field enhanced by PBR-elliptical window is mapped to pixel-level water depth estimation, forming a complete SAR water depth inversion chain.

[0158] In nearshore waters, because wave heights are typically small and wavelengths are much larger than their amplitudes, the nonlinear effects of wave motion can be largely ignored. Therefore, the propagation of waves on the surface of a homogeneous fluid layer can be simplified to a linear model, known as linear wave theory or Airy wave theory. Within this theoretical framework, the relationship between wave propagation and water depth can be described by a linear dispersion relation.

[0159] Within this theoretical framework, the wave frequency ω, wave number k (i.e., k = 2π / λ, where λ is the wavelength), and water depth h satisfy the following linear dispersion relation:

[0160] (twenty two)

[0161] in Angular frequency, For wave period; The acceleration due to gravity is taken as 9.8 m / s².

[0162] From this, the wave period can be derived. With wavelength , water depth Relationship between them:

[0163] (twenty three)

[0164] This expression shows that, for a known wavelength and water depth, the wave period can be uniquely determined.

[0165] After obtaining the wavelength and wave period, based on the dispersion relation in linear wave theory, an inversion model can be established to calculate the water depth using wave characteristic parameters:

[0166] (twenty four)

[0167] In actual calculations, this embodiment calculates the position of each pixel that meets the conditions. Applying the above formula, combined with its corresponding wavelength With wave period The inverted water depth value is calculated. To ensure that the mathematical domain of the inverse function holds, that is: This embodiment introduces a threshold judgment. If the value exceeds the defined domain, the pixel is regarded as an invalid point and is subsequently processed by interpolation.

[0168] 5. Experiment and Performance Evaluation

[0169] To evaluate the effectiveness of the proposed PBR-driven adaptive elliptical window method in nearshore SAR water depth inversion, this embodiment conducts comparative experiments on two typical coastal zones and constructs a unified comparison method and evaluation index. The east coast of Florida, representing a gently sloping sandy coastline transitioning from open ocean to the inland shelf with relatively regular wave climate, was selected as the main experimental area for method performance evaluation. The west coast of Portugal, with its complex seafloor topography and more variable wave conditions, was used to test the applicability and robustness of the method under different dynamic environments. Sentinel-1 GRDH imagery was used as input for both regions, and reference water depths were constructed by combining high-resolution topographic data, providing a basis for subsequent quantitative comparisons.

[0170] For the comparison schemes, the following strategies were designed: an unwindowed scheme, a scheme using a traditional isotropic window, and an adaptive window scheme that introduces the PBR index and elliptical geometric constraints. All schemes were used within the same framework for water depth inversion with the same subgraph size, step size, and periodic prior. The overall accuracy was evaluated using metrics such as mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²).

[0171] 5.1 Results of no window vs. traditional window addition

[0172] 5.1.1 Unwindowed spectral characteristics and water depth inversion error

[0173] To verify the practical role of spectral windowing in water depth inversion, this embodiment first uses an unwindowed SAR sub-image as input, directly performs a two-dimensional fast Fourier transform to extract the dominant wavelength, and combines it with the global average wave period to perform shallow water depth inversion as a benchmark scheme. This method does not optimize for spectral boundary leakage or energy distribution, and therefore can be used to reflect the basic performance of water depth inversion accuracy without spectral quality control.

[0174] Figure 4 Images (a) to (e) show the two-dimensional spectra of a typical SAR sub-image without windowing. It can be observed that the main peak of the spectrum is relatively dispersed, the energy distribution exhibits significant diffusion characteristics, and there is a large area of ​​energy "leakage" at the center of the spectrum. Furthermore, some spectra are accompanied by interference from multiple secondary energy clusters. Due to the lack of windowing, image edge effects are not suppressed, resulting in low contrast between the main peak and the background, difficulty in accurately locating the main frequency components, and a significant limitation on spectral resolution. These problems manifest in the spatial domain as discontinuities and local biases in wavelength extraction results, further affecting the reliability of subsequent depth inversion accuracy.

[0175] Based on this, the extracted wavelengths were combined with the global fixed period and substituted into the dispersion relation to complete the shallow water depth inversion of the study area, generating a water depth estimation map without windowing. Figure 5 (a) and (b) in the example). Subsequently, this embodiment uses a pixel-by-pixel matching method to compare and analyze the inverted water depth with the measured water depth data.

[0176] 5.1.2 Improvement Effect of Traditional Isotropic Windows

[0177] To evaluate the impact of spectral windowing on the accuracy of water depth inversion, this embodiment first employs a traditional window function for weighted processing. Compared to the unwindowed scheme, using a traditional window function can significantly reduce energy leakage and sidelobe interference in the spectrum, thereby improving the clarity of the spectrum and the accuracy of main peak identification to some extent.

[0178] like Figure 6 As shown in (a) and (b), applying a two-dimensional Hanning window to the original SAR sub-image before spectral analysis can smoothly weight the boundaries in the spatial domain, causing the intensity of edge pixels in the image to gradually decrease, thereby reducing energy leakage caused by boundary truncation and providing more stable frequency information for subsequent extraction of the main wavelength. Figure 6 As shown in (b), edge discontinuities are effectively suppressed after windowing, and the risk of spectrum leakage is reduced accordingly.

[0179] The Hanning window, a commonly used cosine-weighted window, can significantly suppress sidelobes and reduce leakage in the frequency domain, improving the contrast and discernibility between the main peak and the background. In this embodiment, after applying the Hanning window, the main peak localization is more stable, and the extraction accuracy of the dominant frequency component is correspondingly improved, thus providing a more reliable input for wavelength estimation.

[0180] 5.1.3 Limitations of Traditional Isotropic Windows

[0181] While isotropic cosine windows can significantly suppress leakage and sidelobes caused by finite analysis domains, their frequency response is direction-independent and separable, aligned with the image coordinate axes. When the main peak is obliquely stretched or elliptically eccentric in the spectrum, an inherent mismatch exists between the window shape and the spectral shape. Uniform smoothing along non-principal axis directions can amplify the main lobe, dilute the peak value, and induce a slight shift in the peak centroid, leading to a decrease in the resolution of dominant wavelengths and directions. In complex nearshore scenarios, such as low signal-to-noise ratio, small sub-images, strong shoreline gradients, intersecting sea states, or multi-peak interference, this direction-independent smoothing amplifies the fixed trade-off between leakage suppression and resolution preservation. If smoothing is increased to suppress sidelobes, the main lobe becomes too wide, making it difficult to distinguish adjacent frequencies and directional components; if smoothing is tightened to maintain resolution, residual sidelobes and background energy can easily overwhelm the main peak.

[0182] Since the window shape and intensity remain unchanged across different sub-graphs, traditional isotropic windows cannot adaptively adjust to spectral quality and directionality. The aforementioned trade-offs are unlikely to be optimal simultaneously under different sea states and topographic conditions, thus limiting the extent of improvement. This mechanistic constraint explains its performance in two types of regions: while there is an improvement in consistency compared to the unwindowed scheme, error convergence and stability are still insufficient in sub-regions with significant main peak eccentricity or multi-peak interference, suggesting the need to introduce an adaptive strategy that can sense spectral quality and match directional geometry.

[0183] 5.2. Water depth inversion results of PBR-driven adaptive elliptical window in the Florida region

[0184] To further improve the wavelength extraction accuracy and stability of SAR sub-images under different spectral characteristics, this embodiment constructs an adaptive elliptical window weighting scheme based on the quality of the spectral main peak, in addition to introducing the main peak energy ratio index. This scheme not only dynamically selects the direction and major and minor axis ratios according to the clarity of the spectral main peak and background contrast of different sub-images, but also achieves dual adaptive optimization at both the window function type and geometric parameter levels.

[0185] Figure 7 Figures (a) to (h) show four examples of sub-images randomly selected from the study area, comparing the image performance before and after applying the elliptical Hanning window. Figures (a), (c), (e), and (g) are the original sub-images, while (b), (d), (f), and (h) are the weighted results. The red dashed line indicates the extent of the applied elliptical Hanning window, visually demonstrating the spatial distribution and coverage of the window function.

[0186] Figure 8 Figures (a) and (b) show the SAR sub-scores under unwindowed and SAR sub-scores with and without a two-dimensional elliptical Hanning window. Figure 2 A comparison of the spectral graphs reveals that without windowing, the spectrum exhibits significant random noise and energy leakage, the main peak structure is unclear, and the sidelobe energy is strong. However, after incorporating the Hanning window, the spectrum displays a more pronounced centrally symmetrical main peak structure, significantly improved energy concentration, effective suppression of sidelobe interference, and a more uniform background. Windowing significantly improves the recognizability and stability of the main peak, providing a higher-quality frequency information foundation for subsequent extraction of the main wave direction and wavelength.

[0187] The Precision Wavelength Regulator (PBR) is defined as the ratio of the spectral peak energy to the global average energy, effectively characterizing the prominence and energy concentration of the spectral peak. Experiments show that when the PBR value is low, the spectral peak typically exhibits blurred diffusion and significant energy leakage; while a high PBR value indicates a clear and concentrated spectral peak, which is beneficial for accurate extraction of the dominant wavelength. Based on this characteristic, this embodiment designs the following adaptive elliptical window selection and adjustment rules:

[0188] When PBR < 2.5, it indicates that the main peak of the spectrum is blurred and the energy is dispersed. A Blackman window is selected as the basis function, and a relatively narrow elliptical window is constructed to enhance the focus in the main direction and minimize sidelobe leakage. When 2.5 ≤ PBR < 4.0, it indicates that the spectral quality is moderate. A Hamming window is selected, and the elliptical shape is adjusted appropriately according to the signal eccentricity to highlight the main peak while also considering out-of-band suppression. When PBR ≥ 4.0, it indicates that the energy of the main peak of the spectrum is highly concentrated. A Hamming window is used, and an approximately circular window is generated to maintain high resolution and avoid spectral information loss due to overweighting. This strategy can achieve fully automatic window function type identification and adaptive adjustment of elliptical geometric parameters in batch SAR sub-image processing without manual intervention.

[0189] Figure 9 Figures (a) to (d) show the two-dimensional FFT spectra of typical SAR submaps before and after applying adaptive elliptical window weighting under different PBR values. Compared with the unwindowed processing, the adaptive elliptical window scheme significantly improves the suppression of spectral edge leakage and the enhancement of energy concentration in the main direction, and can significantly improve the morphological clarity and directionality of the spectral peak. It is worth noting that blindly using the Blackman window and excessively elongated elliptical shape in high-quality spectra may shrink the effective spectral information area, leading to peak divergence and resolution reduction, which is detrimental to the accurate extraction of wavelength and wave direction. This result further verifies the important significance of the dual adaptive strategy of PBR-driven window function type and elliptical geometric parameters in spectral quality control proposed in this embodiment, which helps to ensure the accuracy and robustness of water depth inversion results under different wavefield conditions.

[0190] To systematically evaluate the application effect of the PBR-driven adaptive elliptical window strategy in SAR image depth inversion, the inversion accuracy of the "no windowing" and "adaptive windowing" processing methods was compared and analyzed. Figure 10 As shown in (a) and (b), the scatter distribution of water depth error and its fitting curves under different schemes of "no windowing" and "adaptive windowing" are presented respectively.

[0191] In the experimental area on the east coast of Florida, the mean absolute error (MAE) of the unwindowed scheme was 2.48 m, the root mean square error (RMSE) was 3.45 m, and the coefficient of determination (R²) was 0.959. Although the overall fit was high, the error points were scattered, with significant local deviations, indicating that without spectral weighting, the main peak energy was susceptible to edge leakage and background noise interference, affecting the stability of wavelength extraction. In contrast, after adopting the PBR-driven adaptive elliptical window weighting scheme, the MAE and RMSE decreased to 2.12 m and 2.85 m, respectively. The overall distribution of error points was significantly tightened, and extreme discrete values ​​were significantly reduced, effectively improving the clarity of the spectral main peak and the extraction stability. Although the R² value decreased slightly to 0.942, the overall fit trend remained good, showing that the method has strong adaptability and robustness in complex wavefields.

[0192] The comparative analysis above shows that by introducing adaptive adjustment of the elliptical window shape based on the selection of the window function type, the directional expression and energy focusing degree of SAR spectral features can be effectively improved, thereby enhancing the accuracy of dominant wavelength extraction and water depth inversion. This fully verifies the practical application value and promotion potential of the dual adaptive strategy of window function type and elliptical geometric parameters driven by PBR in complex nearshore environments.

[0193] 5.3 Comparison of water depth inversion performance between the two test areas

[0194] Wave conditions off the west coast of Portugal are more complex than those off the east coast of Florida, with greater variations in water depth and significantly different wave propagation characteristics. Experimental results show that the MAE and RMSE for water depth inversion under the unwindowed scheme are 4.13m and 5.15m, respectively, with a coefficient of determination of [missing information]. The coefficient of determination (COD) is 0.668, indicating a significantly lower fit than in the Florida region, with a more dispersed error distribution. This is closely related to the more complex wave conditions and more variable spectral characteristics in this region. To further optimize the spectral processing, this embodiment introduces adaptive elliptical window weighting in this region. The results show that, through this improvement, MAE and RMSE are reduced to 3.20m and 3.98m, respectively, and the coefficient of determination is [missing value]. The error rate was significantly improved to 0.878, the error point distribution became more concentrated, and local deviations were significantly suppressed. For example... Figure 11 The results (a) and (b) in the figure further verify the universality and potential for generalization of the adaptive elliptical window strategy under diverse wavefield conditions, indicating that the strategy can effectively adapt to the spectral characteristics of different regions and significantly improve the accuracy and stability of water depth inversion.

[0195] By comparing experimental results from the east coast of Florida and the west coast of Portugal, it can be seen that despite significant environmental differences between the two regions, the proposed method demonstrates a marked improvement in water depth inversion accuracy in both locations. This result indicates that the method proposed in this embodiment possesses strong generalization ability and robustness, adapting to different geographical regions and complex hydrodynamic conditions, and exhibits good cross-regional applicability. This generalization and robustness lay a solid foundation for the widespread application of this method in practical applications.

[0196] The experimental results described above verify the cross-regional generalization and robustness of the proposed method. It achieved excellent inversion results not only on the east coast of Florida but also demonstrated significant improvement on the west coast of Portugal. These verifications show that the method in this embodiment can maintain high water depth inversion accuracy under different wave conditions and topographic features, proving its wide applicability.

[0197] This invention addresses the need for improved accuracy in SAR depth retrieval in nearshore shallow water areas by proposing an adaptive elliptical window weighting strategy and systematically constructing an improved SAR wavelength extraction and depth retrieval workflow. This method not only dynamically selects the optimal window function basis function type based on the PBR value but also adaptively adjusts the principal axis direction and major-minor axis ratio of the elliptical window by considering the spatial distribution characteristics of the spectral peak energy, thus achieving dual adaptive optimization in both window function type and geometric shape. Experimental results show that:

[0198] (1) The PBR-driven adaptive elliptical window mechanism significantly improves the energy concentration and directional expression of the main peak of the spectrum, and enhances the accuracy and robustness of wavelength extraction, especially in sub-figures with blurred spectrum or low signal-to-noise ratio.

[0199] (2) Compared with the unwindowed and fixed elliptical window processing methods, the adaptive elliptical window method achieved better inversion accuracy in two typical study areas, the east coast of Florida and the west coast of Portugal. The MAE and RMSE were reduced by about 15%, the R² was significantly improved, and the error points were more compactly distributed.

[0200] (3) This method has good automated processing capabilities and strong generalization adaptability, providing a feasible technical path for its application in subsequent SAR sounding research in multiple time phases and regions.

[0201] The present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program that can run on the processor, and when the program is executed on the processor, it implements the steps in the SAR depth inversion method based on the adaptive elliptical window function as described above.

[0202] The present invention also provides a storage medium storing a computer program, which, when executed by a processor, implements the steps in the SAR depth inversion method based on the adaptive elliptical window function as described above.

[0203] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the modules described above can be referred to the corresponding process in the aforementioned method implementation, and will not be repeated here.

[0204] The modules described as separate components may or may not be physically separate. Similarly, the components shown as modules may or may not be physical modules; they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0205] Furthermore, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module. The integrated module can be implemented in hardware or in a combination of hardware and software functional modules.

[0206] The integrated modules implemented as software functional modules described above can be stored in a computer-readable storage medium. These software functional modules, stored in a storage medium, include several instructions to cause a computer system (which may be a personal computer, server, or network system, etc.) or processor to execute some steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0207] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A SAR depth inversion method based on an adaptive elliptic window function, characterized in that, The specific steps of this method are as follows: Step 1: Acquire SAR images, prior water depth information, and measured water depth data, and perform unified projection, spatial registration, and vertical reference integration processing. Step 2: The SAR image obtained in Step 1 is cropped by sliding at a set step size to form a sub-image sequence for spectral analysis; Step 3: Perform Fast Fourier Transform (FFT) calculations on each sub-graph obtained in Step 2 to identify the main energy connected domains and characterize the main wave direction and spectral shape features. Step 4: For each sub-graph obtained in Step 2, perform anisotropic elliptic windowing aligned with the corresponding main wave direction obtained in Step 3; Step 5: Perform FFT calculation on the windowed image obtained in Step 4 to obtain the spectrum, and extract the position of the main wave peak and its corresponding wavelength and direction information from it. Use the linear dispersion relation to complete the water depth inversion.

2. The method according to claim 1, characterized in that, In the anisotropic elliptical windowing process aligned with the corresponding main wave direction obtained in step 3, the main direction angle of the added elliptical window is obtained as follows: The centroid position and second-order center matrix of the main energy connected domain obtained in step 3 are calculated to quantify the distribution characteristics of the spectral energy in different directions. By performing eigenvalue decomposition on the second-order central matrix, the direction of the eigenvector corresponding to its largest eigenvalue is extracted and used as the principal axis direction of the main peak of the spectrum, which is the principal direction angle of the elliptical window.

3. The method according to claim 2, characterized in that, The steps for obtaining the major and minor axes of the added elliptical window include: ， ， In the formula, a and b represent the major axis and minor axis, respectively; area represents the pixel area of ​​the main energy connected region; H and W represent the height and width of the corresponding subgraph, respectively; and e represents the eccentricity of the main peak of the spectrum.

4. The method according to claim 1, characterized in that, The selection of the added elliptical window is based on the peak-to-bandwidth ratio (PBR): When PBR < α, the Blackman window is selected as the basis function to construct an elliptical window; When α≤PBR<β, the Hamming window is selected as the basis function to construct an elliptical window; When PBR≥β, the Hanning window is used as the basis function to construct an elliptical window; Where α and β are both preset PBR thresholds.

5. The method according to claim 4, characterized in that, The peak-to-bandwidth ratio (PBR) is defined as the ratio of the spectral peak energy to the global average energy. ， ， ， in, Main peak energy. As background energy, and These are the positive and negative frequency neighborhoods of the main peak, respectively. Represents frequency coordinates, where Ω is the effective domain of the spectrum. The power spectral density represents the spectrum. Indicates removal and The remaining region in the subsequent spectrum.

6. The method according to claim 5, characterized in that, ,in, With the origin as the center and radius... The low-frequency exclusion zone of the small disc.

7. The method according to claim 1, characterized in that, Step 5, which involves extracting the position of the main wave peak and its corresponding wavelength and direction information, includes: By utilizing the binary segmentation of the main wave peak energy position in the spectrogram and regional connectivity analysis, the main energy connected domain with the largest area is extracted, and its geometric centroid coordinates are calculated. ; Extract the second largest peak from the remaining spectrum after removing the main peak, and calculate the set centroid coordinates of its corresponding region. ; Calculate the wavelength corresponding to the main peak and wave direction angle : ， ， In the formula, , M and N represent the length and width of the spectrum.

8. The method according to claim 7, characterized in that, In step 5, the water depth inversion is performed using the linear dispersion relation, and the following inversion model is constructed: ， In the formula, Indicated by wavelength Sum of waves period Let be the water depth function value of the independent variable, and g be the acceleration due to gravity.

9. A computer-readable storage medium storing a computer program thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the SAR depth inversion method based on the adaptive elliptic window function as described above.

10. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor is used to execute the computer program to implement the steps of the SAR depth inversion method based on the adaptive elliptic window function as described above.

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