CN115932854A

CN115932854A - Ship wake SAR image detection method and device

Info

Publication number: CN115932854A
Application number: CN202211718716.6A
Authority: CN
Inventors: 石敏; 王雅芬; 王晶晶; 魏仪文; 郭立新; 李少猛; 王玉菊; 吕亚飞; 还迎春
Original assignee: Unit 91977 Of Pla
Current assignee: Unit 91977 Of Pla
Priority date: 2022-12-29
Filing date: 2022-12-29
Publication date: 2023-04-07

Abstract

The invention discloses a method and a device for detecting a ship wake SAR image, wherein the method comprises the following steps: acquiring Kelvin trail data information of a ship; the Kelvin wake data information of the ship comprises speed, sailing direction and ship parameters; processing Kelvin trail data information of the ship to obtain a trail geometric model; calculating a radar backscattering coefficient of the sea surface by using a double-scale method to obtain a scattering echo; the radar backscattering coefficient of the sea surface comprises a mirror image scattering coefficient and a Bragg scattering coefficient; processing the scattering echo by using a range-Doppler SAR imaging algorithm to obtain SAR imaging information of Kelvin trail data of the ship; and detecting the SAR imaging information of the Kelvin wake data by using a generalized maximum minimum concave sparse regularization method to obtain ship wake position information. The method can calculate Kelvin ship wake geometric models under different targets, different sea surface wind speeds, different sea surface wind directions and different ship speeds, and provides effective support for extracting ship information hidden in the wake.

Description

Ship wake SAR image detection method and device

Technical Field

The invention relates to the technical field of image detection of ship wake synthetic aperture radars, in particular to a method and a device for detecting an SAR image of a ship wake.

Background

The detection of the ship wake is very important for the accurate characterization of the sea surface state. The data provides key information for tracking the ship target and is also helpful for classifying the characteristics of the ship target generating the wake flow. Due to the difficulty and high cost of acquiring the actual measurement data of the trail SAR image of the ship target, the currently disclosed actual measurement SAR image data (such as COSMO-SkyMed in Italy, terrasAR-X in Germany and NovasAR in UK) are not clear about sea state and motion parameters of the target. Compared with actual measurement, the simulation method is adopted to simulate the geometric model of the ship wake and carry out SAR imaging simulation on the geometric model, and much attention is paid to the research on the image detection of the ship wake SAR.

Because the wake model of the ship target can be modeled as a linear structure, the corresponding detection method mostly adopts a linear feature extraction method, such as Hough transformation or Radon transformation, and the two methods form a peak value for a bright line in an SAR image in a transformation domain and a valley value for a dark line. Because the complexity of the Radon transform is low, the Radon transform is widely applied to the detection of the ship wake. However, a pure Radon transform may cause false detections due to bright pixels of the ship, and therefore, enhancing the pixel information of the Radon domain image may be considered.

Disclosure of Invention

The technical problem to be solved by the invention is to provide a method and a device for detecting the ship wake SAR image, which can solve the inverse problem by using a regularization criterion by reducing the problem of detecting the ship wake into the inverse problem. The method obtains Radon transformation of the image based on a GMC sparse regularization method, thereby enhancing the linear characteristics of the image in a Radon domain. The inverse problem is solved using bayesian inference and a point estimate of the unknown quantity is obtained using Maximum A Posteriori (MAP).

In order to solve the technical problem, a first aspect of the embodiment of the present invention discloses a method for detecting a ship wake SAR image, where the method includes:

s1, acquiring Kelvin trail data information of a ship; the Kelvin trail data information of the ship comprises speed, navigation direction and ship parameter information;

s2, processing Kelvin wake data information of the ship to obtain a wake geometric model;

s3, calculating a radar backscattering coefficient of the sea surface by using a double-scale method to obtain a scattering echo; the radar backscattering coefficient of the sea surface comprises a mirror image scattering coefficient and a Bragg scattering coefficient;

s4, processing the scattering echo by using a range Doppler SAR imaging algorithm to obtain ship SAR imaging information;

and S5, detecting the SAR imaging information of the Kelvin wake data by using a generalized maximum minimum concave sparse regularization method to obtain ship wake position information.

As an optional implementation manner, in the first aspect of the embodiment of the present invention, the processing the ship Kelvin wake data information to obtain a wake geometric model includes:

s21, processing the ship Kelvin wake data information to obtain ship Kelvin wake wave height information; kelvin wake wave height information of the ship

Comprises the following steps:

wherein x and y respectively represent coordinates of the wake on the x axis and the y axis, i is an imaginary unit, theta is an included angle between a free surface wave generated by the Kelvin wake of the ship and the x axis when the free surface wave propagates along the x axis, and k is an included angle between the free surface wave and the x axis _k sec ² θ (xcos θ + ysin θ) is the phase function, k _k sec ² Theta is the wave number of the wave component propagating along the included angle theta with the x-axis, sec represents the secant function, re represents the real part, a (theta) is the characteristic parameter of the ship, a (theta) is complex, for finite water depth,

h represents water depth; for an infinite water depth, i.e. (H → ∞), based on the water level>

U _s Representing the boat speed, g is the acceleration of gravity, and the subscript k represents the Kelvin wake;

s22, kelvin wake wave height information of the ship

Dividing the ship into a bow part and a stern part to obtain a wake geometric model;

the trail geometric model is as follows:

wherein C is viscosity coefficient, and the bow is

The stern is->

Wherein x and y respectively represent the coordinates of the wake on the x axis and the y axis, l is half ship length, d is side wall draft, b is half ship width, theta is the included angle between the free surface wave generated by the Kelvin wake of the ship and the x axis when the free surface wave propagates along the x axis, and h (x, y) = k _k sec ² θ(xcosθ+ysinθ)。

As an optional implementation manner, in the first aspect of the embodiment of the present invention, the method for calculating the characteristic parameter a (θ) of the ship includes:

wherein, H (k) _k Theta) is a Kochi function, theta is an angle between a free surface wave generated by a Kelvin wake of a ship and an x-axis when the free surface wave propagates along the x-axis, z represents the wave height of the wake, and S is _H Is the surface of the vessel, the water flow source intensity σ (x, y, z) can be expressed as:

where f (x, z) is the ship equation for the ship, and when the ship shape is simple parabolic, f (x, z) is:

wherein x is the offset position, z is the draft, b is half the craft width, l is half the craft length, and d is the sidewall draft.

As an optional implementation manner, in the first aspect of the embodiment of the present invention, the method for calculating the specular scattering coefficient includes:

calculating to obtain a mirror image scattering KA surface element scattering field E by using a mirror image scattering KA surface element scattering field calculation model _s (r)；

The calculation model of the mirror image scattering KA surface element scattering field is as follows: ,

wherein

Unit normal vector for bin>

The sea surface half-space wave impedance, R is the distance between the center of the surface element and the observation point, E and H are the total field on the surface boundary, and I (-) is the phase integral term on the surface element; />

And &>

Is a tangential field on the roughened surface>

Unit vector of scattered wave, mu ₀ Is the magnetic permeability in the medium, epsilon ₀ ω is the angular frequency for the dielectric constant.

As an optional implementation manner, in the first aspect of the embodiment of the present invention, the calculation method of the bragg scattering coefficient includes: using the formula:

ζ(ρ _c ,t)＝B(k _c )cos(k _c ·ρ _c -ω _c t)

calculating to obtain the geometrical profile zeta (rho) of Bragg scattering _c T), wherein k _c Wave number vector, ω, of Bragg capillary wave component _c Is a wave number k _c Corresponding spatial frequency, t represents time, B (k) _c ) Amplitude of capillary waves, p _c ＝(x _c ,y _c ) Indicates the position of each point on the patch, (x) _c ,y _c ) Is the coordinates of a point; using the formula:

z ^capi ＝f(ρ ₀ ,t)+ζ(ρ _c ,t)+Z _x x _c +Z _y y _c

capillary sine wave representation z calculated to obtain coordinates of any point on the face ^capi Where f (ρ) ₀ T) geometric profile of the undulation of the gravitational wave, p ₀ ＝(x _g ,y _g ) Representing the bin center, (x) _g ,y _g ) Wave number vector k of Bragg capillary wave component as plane element center point coordinate _c Direction and q _l Coincidence, q _l ＝(q _lx ,q _ly ,q _lz ) Is the Bragg scattering vector

Projection onto the inclined facet element, Z _x And Z _y Is a scale factor; using the formula:

calculating to obtain the amplitude B (k) of the capillary wave _c ) Wherein Δ S = Δ x _g Δy _g Is the size of the large and small bins, Δ x _g Is the sampling interval of the trail in the x direction, Δ y _g Is the sampling interval of the trail in the y-direction,

is a capillary spectrum.

As an optional implementation manner, in the first aspect of the embodiment of the present invention, the processing the scattering echo by using a range-doppler SAR imaging algorithm to obtain ship SAR imaging information includes:

s41, processing the scattering echo by using distance-to-FFT (fast Fourier transform) to obtain distance-to-frequency domain information of the scattering echo;

s42, processing the distance-direction frequency domain information of the scattered echo by using distance-direction matched filtering to obtain distance-direction compression information;

s43, processing the distance direction compressed information by utilizing distance direction IFFT conversion to obtain first distance direction compressed information;

s44, processing the first distance direction compressed information by using an orientation direction FFT to obtain orientation frequency domain information;

s45, performing range migration correction on the direction frequency domain information to obtain corrected direction frequency domain information;

and S46, carrying out azimuth IFFT on the corrected azimuth frequency domain information to obtain ship SAR imaging information.

As an optional implementation manner, in the first aspect of the embodiment of the present invention, the detecting the imaging information of the Kelvin wake data SAR by using the regularization method based on the generalized maximum concave-concave sparse mode to obtain the ship wake position information includes: using the formula:

p(X|Y)＝αP(Y|X)p(X)

obtaining posterior distribution P (X | Y) of an SAR image Y and an image X of a Radon domain, wherein P (Y | X) is likelihood distribution, P (X) is probability distribution of X, alpha is a regularization constant, and P (X) = alpha exp { -lambda ψ (X) };

setting a cost function F (X):

where λ is the scale parameter, ψ (t) is the MC penalty, C is the inverse Radon transform factor,

the relationship between the MC penalty and the Huber function s (t) is:

ψ(t)＝|t|-s(t)

obtaining the scaled MC penalty psi using a scalar b ≠ 0 _b (t)，

ψ _b (t)＝|t|-s _b (t)

Wherein s is _b (t) is the scaled Huber function; using the formula:

obtaining a generalized Huber function S _B (t), where B is the scaling matrix,

inf represents the largest lower bound in the aggregate, which is evaluated>

Representing an N-dimensional real number space, and t is a time variable; improved GMC penalty function psi _B (t) is:

ψ _B (t)＝||t|| ₁ -S _B (t)

wherein the content of the first and second substances,

λ ₁ is GMC prior scaling parameter, gamma is parameter for controlling non-convexity; using the formula:

p ₁ (X)＝αexp{-λ ₁ ψ _B (X)}＝αexp{-λ ₁ (||X|| ₁ -S _B (X))}

computing to obtain GMC sparse prior p ₁ (X); using the formula:

calculating to obtain a cost function F (X, upsilon); using the formula:

calculating to obtain maximum minimum optimization information

Optimizing the maximum minimum information using a forward-backward algorithm

And solving to obtain the ship trail position information.

As an optional implementation manner, in the first aspect of the embodiment of the present invention, the method further includes:

s61, acquiring SAR simulation image data information and SAR actual measurement image data information;

s62, carrying out scaling processing on the SAR simulation image data information and the SAR actual measurement image data information to obtain first SAR simulation image data information and first SAR actual measurement image data information which are the same in size;

s63, graying the first SAR simulation image data information and the first SAR actual measurement image data information to obtain grayscale SAR simulation image data information and grayscale SAR actual measurement image data information;

s64, respectively calculating the gray average value of the gray SAR simulation image data information and the gray average value of the gray SAR actual measurement image data information to obtain an SAR simulation image average value and an SAR actual measurement image average value;

s65, obtaining an SAR simulation image fingerprint sequence according to the gray SAR simulation image data information and the SAR simulation image average value;

the SAR simulation image fingerprint sequence comprises N elements, any one element is compared, the average value is larger than or equal to 1 and smaller than the average value and is marked as 0, and the SAR simulation image fingerprint sequence is obtained;

s66, comparing each gray value of the gray SAR actual measurement image data information with the average value of the SAR actual measurement image, recording the gray value as 1 when the gray value is larger than or equal to the average value, recording the gray value as 0 when the gray value is smaller than the average value, and obtaining the fingerprint sequence of the SAR actual measurement image;

s67, similarity calculation is carried out on the SAR simulation image fingerprint sequence and the SAR real-time image fingerprint sequence, and similarity values of the SAR simulation image and the SAR real-time image are obtained.

The second aspect of the invention discloses a ship wake SAR image detection device, which comprises:

the data acquisition module is used for acquiring Kelvin trail data information of the ship; the Kelvin trail data information of the ship comprises speed, navigation direction and ship parameter information;

the wake geometric model construction module is used for processing Kelvin wake data information of the ship to obtain a wake geometric model;

the scattering echo calculation module is used for calculating a radar backscattering coefficient of the sea surface by using a double-scale method to obtain a scattering echo; the radar backscattering coefficient of the sea surface comprises a mirror image scattering coefficient and a Bragg scattering coefficient;

the SAR imaging information calculation module is used for processing the scattering echo by using a range-Doppler SAR imaging algorithm to obtain ship SAR imaging information;

and the ship wake detection module is used for detecting the SAR imaging information of the Kelvin wake data by using a generalized maximum minimum concave sparse regularization method to obtain ship wake position information.

As an optional implementation manner, in the second aspect of the embodiment of the present invention, the processing the ship Kelvin wake data information to obtain a wake geometric model includes:

Comprises the following steps:

h represents water depth; for infinite water depths, i.e., (H → ∞), ->

s22, kelvin wake wave height information of the ship

Dividing the ship into a bow part and a stern part to obtain a trail geometric model; the trail geometric model is as follows:

wherein C is the viscosity coefficient and the bow is

The stern is->

/>

wherein, H (k) _k Theta) is a Kochi function, theta is an angle between a free surface wave generated by a Kelvin wake of a ship and an x-axis when the free surface wave propagates along the x-axis, z represents the wave height of the wake, and S is _H Is the surface of a ship, the water flow source intensity σ (x, y, z) can be expressed as:

wherein x is the offset position, z is the draft, b is half the craft width, l is half the craft length, and d is the side wall draft.

As an optional implementation manner, in the second aspect of the embodiment of the present invention, the method for calculating the specular scattering coefficient includes:

calculating to obtain the mirror image scattering KA bin dispersion by using a mirror image scattering KA bin scattering field calculation modelRadiation field E _s (r)；

wherein

Is a unit normal vector of a bin>

The sea surface half-space wave impedance is shown, R is the distance between the center of the surface element and an observation point, E and H are total fields on the surface boundary, and I (-) is a phase integral term on the surface element; />

And &>

Is a tangential field on the roughened surface>

Unit vector of scattered wave, mu ₀ Is the permeability in the medium, epsilon ₀ Is the dielectric constant, ω is the angular frequency.

As an optional implementation manner, in the second aspect of the embodiment of the present invention, the calculation method of the bragg scattering coefficient uses a formula:

ζ(ρ _c ,t)＝B(k _c )cos(k _c ·ρ _c -ω _c t)

calculating to obtain the geometrical profile zeta (rho) of Bragg scattering _c T), wherein k _c Wave number vector, ω, of Bragg capillary wave component _c Is the wave number k _c Corresponding spatial frequency, t represents time, B (k) _c ) Is composed ofAmplitude of capillary waves, p _c ＝(x _c ,y _c ) Indicates the position of each point on the patch, (x) _c ,y _c ) Is the coordinates of a point; using the formula:

z ^capi ＝f(ρ ₀ ,t)+ζ(ρ _c ,t)+Z _x x _c +Z _y y _c

Projection onto an inclined facet element, Z _x And Z _y Is a scale factor; using the formula:

calculating to obtain the amplitude B (k) of the capillary wave _c ) Wherein Δ S = Δ x _g Δy _g Is the size of the large and small bins, Δ x _g Sampling interval, Δ y, of the trail in the x-direction _g Is the sampling interval of the trail in the y-direction,

is a capillary spectrum.

As an optional implementation manner, in a second aspect of the embodiment of the present invention, the processing the scattered echo by using a range-doppler SAR imaging algorithm to obtain ship SAR imaging information includes:

s41, the distance direction FFT is utilized to process the scattering echo, and the distance direction frequency domain information of the scattering echo is obtained;

s43, processing the distance direction compressed information by utilizing distance direction IFFT to obtain first distance direction compressed information;

As an optional implementation manner, in the second aspect of the embodiment of the present invention, the detecting the imaging information of the Kelvin wake data SAR by using a regularization method based on a generalized maximum minimum concave-sparse method to obtain ship wake position information includes using a formula:

p(X|Y)＝αP(Y|X)p(X)

obtaining posterior distribution P (X | Y) of an SAR image Y and an image X of a Radon domain, wherein P (Y | X) is likelihood distribution, P (X) is probability distribution of X, alpha is a regularization constant, and P (X) = alpha exp { -lambda ψ (X) }; set cost function F (X):

the relationship between the MC penalty and the Huber function s (t) is:

ψ(t)＝|t|-s(t)

obtaining the scaled MC penalty psi using a scalar b ≠ 0 _b (t)，

ψ _b (t)＝|t|-s _b (t)

Wherein s is _b (t) is the scaled Huber function; using the formula:

/>

obtaining a generalized Huber function S _B (t), where B is the scaling matrix,

inf represents the largest lower bound in the pool, based on>

ψ _B (t)＝||t|| ₁ -S _B (t)

wherein the content of the first and second substances,

p ₁ (X)＝αexp{-λ ₁ ψ _B (X)}＝αexp{-λ ₁ (||X|| ₁ -S _B (X))}

computing to obtain GMC sparse prior p ₁ (X); using the formula:

calculating to obtain a cost function F (X, upsilon); using the formula:

calculating to obtain maximum minimum optimization information

Optimizing the maximum minimum information using a forward-backward algorithm

And solving to obtain the ship trail position information.

As an optional implementation manner, in the second aspect of the embodiment of the present invention, the method further includes:

s67, similarity calculation is carried out on the SAR simulation image fingerprint sequence and the SAR real measurement image fingerprint sequence, and similarity values of the SAR simulation image and the SAR real measurement image are obtained.

The third aspect of the invention discloses another ship wake SAR image detection device, which comprises:

a memory storing executable program code;

a processor coupled with the memory;

the processor calls the executable program code stored in the memory to execute part or all of the steps of the ship wake SAR image detection method disclosed by the first aspect of the embodiment of the invention.

Compared with the prior art, the embodiment of the invention has the following beneficial effects:

the method utilizes a point disturbance theory to establish the Kelvin ship wake geometric model, and can calculate the Kelvin ship wake geometric model under different targets, different sea surface wind speeds, different sea surface wind directions and different ship speeds. Meanwhile, SAR imaging simulation calculation is carried out on the Kelvin ship wake model based on an RDA imaging algorithm, and the accuracy of an RDA algorithm simulation result is verified by utilizing a similarity calculation model of an SAR simulation image and an SAR real-time image. The method is characterized in that actual measurement data and simulation data of the Kelvin ship wake SAR image are detected by a GMC sparse regularization method respectively, and the detection result shows the effectiveness of the method, so that effective support is provided for extracting ship information hidden in the wake.

Drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the description below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.

FIG. 1 is a schematic flow chart of a method for detecting a ship wake SAR image according to an embodiment of the present invention;

FIG. 2 is a schematic diagram of trails produced by a missile destroyer at different boat speeds according to an embodiment of the invention;

FIG. 3 is a comparison of the actual measurement result and the simulation result of TerrasAR-X according to the present invention;

FIG. 4 is a calculation result of a similarity calculation model of the SAR simulation image and the SAR actual measurement image according to the present invention;

FIG. 5 is a comparison of the TerraSAR-X SAR actual measurement trail detection result and SAR simulation image detection result of the present invention;

FIG. 6 is a schematic structural diagram of an SAR image detection device for ship wake in an embodiment of the present invention;

fig. 7 is a schematic structural diagram of another ship wake SAR image detection apparatus according to an embodiment of the present invention.

Detailed Description

In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

The terms "first," "second," and the like in the description and claims of the present invention and in the above-described drawings are used for distinguishing between different objects and not necessarily for describing a particular sequential or chronological order. Furthermore, the terms "include" and "have," as well as any variations thereof, are intended to cover non-exclusive inclusions. For example, a process, method, apparatus, product, or apparatus that comprises a list of steps or elements is not limited to those listed but may alternatively include other steps or elements not listed or inherent to such process, method, product, or apparatus.

Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the invention. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. It is explicitly and implicitly understood by one skilled in the art that the embodiments described herein can be combined with other embodiments.

The invention discloses a ship wake SAR image detection method and a ship wake SAR image detection device, which can acquire ship Kelvin wake data information; the Kelvin trail data information of the ship comprises speed, sailing direction and ship parameters; processing Kelvin trail data information of the ship to obtain a trail geometric model; calculating a radar backscattering coefficient of the sea surface by using a double-scale method to obtain a scattering echo; radar backscattering coefficients of the sea surface comprise mirror image scattering coefficients and Bragg scattering coefficients; processing the scattering echo by using a range-Doppler SAR imaging algorithm to obtain SAR imaging information of Kelvin trail data of the ship; and detecting the SAR imaging information of the Kelvin wake data by using a generalized maximum minimum concave sparse regularization method to obtain ship wake position information. The method can calculate Kelvin ship wake geometric models under different targets, different sea surface wind speeds, different sea surface wind directions and different ship speeds, and provides effective support for extracting ship information hidden in the wake. The following are detailed below.

Example one

Referring to fig. 1, fig. 1 is a schematic flow chart of a method for detecting an SAR image of a ship wake disclosed in an embodiment of the present invention. The method for detecting the ship wake SAR image described in FIG. 1 can be applied to the aspects of ship target detection and identification, and the embodiment of the invention is not limited. As shown in fig. 1, the method for detecting a ship wake SAR image may include the following operations:

Optionally, the processing the ship Kelvin wake data information to obtain a wake geometric model includes:

Comprises the following steps:

wherein x and y respectively represent the coordinates of the wake on the x axis and the y axis, i is an imaginary number unit, theta is the included angle between the free surface wave generated by the Kelvin wake of the ship and the x axis when the free surface wave propagates along the x axis, and k is the included angle between the free surface wave and the x axis _k sec ² θ (xcos θ + ysin θ) is the phase function, k _k sec ² Theta is the wave number of the wave component propagating along the included angle theta with the x-axis, sec represents the secant function, re represents the real part, a (theta) is the characteristic parameter of the ship, a (theta) is complex, for finite water depth,

s22, kelvin wake wave height information of the ship

the trail geometric model is as follows:

wherein C is viscosity coefficient, and the bow is

The stern is->

Optionally, the method for calculating the characteristic parameter a (θ) of the ship comprises:

where f (x, z) is the ship equation for the ship, and when the shape of the ship is a simple parabolic shape, f (x, z) is:

Fig. 2 is a schematic diagram of trails generated by a certain missile destroyer at different ship speeds, wherein the size of the sea surface is 256m × 256m, the wind speed of the sea surface is 5m/s, the wind direction angle is 0 °, and other simulation parameters are that the ship length is 137.2m, the draught is 8.732m, the ship speed is 6m/s, the ship length is 137.2m, the draught is 8.732m and the ship speed is 10m/s in the drawing (b).

In the invention, a two-scale method (TSM) is utilized to solve the scattering echo of the ship wake. The double-scale rough sea surface model considers that small capillary waves are superposed on large-scale gravity waves, so that after the rough sea surface is divided into small inclined surface patches according to grids, each surface patch is considered to have roughness. Small-scale capillary waves are generally distributed on a large-scale sea surface, and in an actual sea surface, a series of small-scale sine wave components with continuous frequencies are superposed together to form capillary waves. The amount of calculation is undoubtedly prohibitive if modeled as a practical matter. In simulation calculation, the wave components which have the largest influence on the electromagnetic waves can be found out for calculation, other wave components which are not very important are abandoned, and the calculation efficiency is improved. When radar detects the sea surface, the capillary wave component which can cause the Bragg resonance of radar waves is undoubtedly the wave component which has the largest influence on scattering. Based on this, it can be considered that only one periodic cosine wave with a single frequency exists on the large scale wave, and the group of cosine waves can cause bragg scattering of incident electromagnetic waves and form resonance with the incident waves. The double-scale calculation method utilizes a formula:

ζ(ρ _c ,t)＝B(k _c )cos(k _c ·ρ _c -ω _c t)

calculating to obtain the geometrical profile zeta (rho) of Bragg scattering _c T), wherein k _c Wave number vector, ω, of Bragg capillary wave component _c Is the wave number k _c Corresponding spatial frequency, t represents time, B (k) _c ) Amplitude of capillary waves, p _c ＝(x _c ,y _c ) Indicates the position of each point on the patch, (x) _c ,y _c ) Is the coordinates of a point; using the formula:

z ^capi ＝f(ρ ₀ ,t)+ζ(ρ _c ,t)+Z _x x _c +Z _y y _c

capillary sine wave representation z calculated to obtain coordinates of any point on the face ^capi For convenience, the wake geometric model wave height z in the foregoing is denoted herein as f (ρ) ₀ T), i.e. f (ρ) ₀ T) geometric profile of the gravitational wave undulation of the sea surface containing the wake, ρ ₀ ＝(x _g ,y _g ) Representing the bin center, (x) _g ,y _g ) Wave number vector k of Bragg capillary wave component as plane element center point coordinate _c Direction and q _l Coincidence, q _l ＝(q _lx ,q _ly ,q _lz ) Is the Bragg scattering vector

Projection on oblique facet elements, q _lx ,q _ly ,q _lz Are each q _l Component in the x, y, z axis, k being the wave number of the electromagnetic wave, and->

Is an incident wave unit vector>

Unit vector of scattered wave; using the formula:

calculating to obtain the capillaryWave amplitude B (k) _c ) Wherein Δ S = Δ x _g Δy _g Is the size of the large-scale small bin, Δ x _g Is the sampling interval of the trail in the x direction, Δ y _g Is the sampling interval of the trail in the y-direction,

is a capillary spectrum.

After the expression form of the resonant capillary wave is determined, the amplitude and the wave number of the resonant capillary wave can be determined according to the incident radar parameters, the sea spectrum information and the inclination degree of the large-scale surface element. And deducing the scattering characteristics of each micro fluctuation inclined surface element according to the characteristics of the capillary waves, so as to obtain the scattering coefficient and the scattering field of a single large-scale subdivision surface element. The electromagnetic scattering of each micro-fluctuation tilting surface element can be solved according to a perturbation method, and the scattering coefficient of any tilting small surface element can be represented as follows:

where k is the wave number of incident electromagnetic waves, ε is the dielectric constant of the sea surface, F _pq The expression for the polarization factor will be given later. Where the subscripts p, q may both be denoted h or v, indicating h (horizontal) or v (vertical) polarization. Psi (q) _l ) Is the sea spectrum of surface capillary waves, q _l Is the scattering vector

Projection onto a tilted bin. The scattered field on a bin can be expressed as

Wherein R is ₀ The distance of the radar to the center of the sea surface.

For the scattering amplitude, expressed as:

the modulation effect of gravity wave on scattering field is reflected in scattering polarization factor F _pq The above equation is the polarization factor in global coordinates. Because the surface patch is inclined under the action of gravity waves, the conversion problem of local coordinates and global coordinates exists. In local coordinates, the local scattering amplitude bin is denoted as F _{pq_loc} I.e. by

F _{vh_loc} ＝[1-R _v (θ _{i_loc} )][1+R _h (θ _{s_loc} )]cosθ _{i_loc} sinφ _{s_loc}

F _{hv_loc} ＝[1+R _h (θ _{i_loc} )][1-R _v (θ _{s_loc} )]cosθ _{s_loc} sinφ _{s_loc}

F _{hh_loc} ＝[1+R _h (θ _{i_loc} )][1+R _h (θ _{s_loc} )]cosφ _{s_loc}

Wherein, theta _{i_loc} ，θ _{s_loc} ，φ _{i_loc} ，φ _{s_loc} The local incident angle, scattering angle, incident azimuth angle and scattering azimuth angle of the incident wave to the tilted patch are respectively. The value of which is not only related to the direction of the incident wave but also to the tilt angle of the bin. R _h And R _v Are reflection coefficients of different polarizations. After the local scattering amplitude is obtained, the local scattering amplitude is converted to a global scattering amplitude by the following equation.

Wherein

For the global horizontal and vertical polarization vectors, <' >>

The electromagnetic scattering of the tilted surface element capillary waves is as follows:

the integration in the above equation represents the integration of the capillary undulation over a small area, on which the phase modulation of the field by the capillary is reflected. In a global coordinate system, the integral term is expressed as:

wherein the normal direction is

The position vector of the micro-relief surface relative to the center point O' is r _c ＝(ρ _c ,ζ)＝r-r ₀ And r = (ρ, z), ρ = (x, y) is a coordinate of the central point of the microrelief bin in the global coordinate system. r is a radical of hydrogen ₀ For the vector of the position of the central point O' of the microrough surface element relative to the origin, i.e. r ₀ ＝(ρ ₀ ,η(ρ ₀ ,t))，ρ ₀ ＝(x _g ,y _g ). Write out rho _c ＝(x _c ,y _c )＝(x-x _g ,y-y _g ). After defining the microrelief on a surface element as periodic positive (cosine) sine waves, the microrelief height for each point on the surface element can be written as z = z ^capi ＝f(ρ ₀ ,t)+ζ(ρ _c ,t)+Z _x x _c +Z _y y _c Therefore, the following are:

it should be noted that the actual micro-fluctuation ζ (ρ, t) over the bin should be expressed as the fourier transform of the high frequency part of the sea surface power spectrum, i.e., { ρ, t) = { [ integral ] } W (p, q, t) exp (ipx + iqy) dpdq, with the actual ζ (ρ, t) being the superposition of a series of capillary waves of different frequencies. However, in the bragg hypothesis, only the capillary wave component that causes the bragg resonance is described, which is equivalent to a first order approximation of the above integration.

By means of the Euler formula, the cosine function form of the capillary fluctuation is written in exponential form, i.e.

The exponential part is expanded with a special function:

the exponential part is a tension wave phase modulation part, and high-order harmonics are required because the phase part is sensitive to modulation. When n =0 in the above formula, the phase portion is 1, i.e., the first order perturbation is obtained. B (k) _c ) Amplitude of capillary wave, Δ S is area of bin, n _z Is the z-component normal to the oblique surface element, I ₀ (k _c ) Can be expressed as

It should be noted that, the single-frequency cosine waves causing the bragg resonance on the sea surface are divided into two types according to the propagation direction, one type is propagated along the radar irradiation direction, and the other type is propagated in the direction opposite to the radar visual direction, and both types of contributions must be included in the scattering calculation step. Thus, the scattering amplitude of a small bin is written as the following expression

Wherein

And &>

Bragg wave component, bragg wave number vector->

Can be expressed as:

wherein λ is _c Capillary wavelength, λ, to induce Bragg resonance _c ＝2π/(q|sinθ _q )，θ _q Is q and bin normal vector

The included angle of (a). The scattering field on each inclined sea surface sheet can be obtained as follows:

the total field of the entire sea surface can be expressed as the sum of the scattered fields over the bins, i.e.

Wherein M is the number of surface elements subdivided in the sea surface in the x direction, and M = L _x The/delta x and N are the number of surface elements of the sea surface divided in the y direction, and M = L _y /Δy。

The echo signal received by the radar is firstly demodulated to the baseband, and then the demodulated radar echo equation can be expressed as:

s ₀ (τ,η)＝Eω _r [τ-2R(η)/c]ω _a (η-η _c )×exp{-i4πf ₀ R(η)/c}exp{iπK _r (τ-2R(η)/c) ² }

where E is the complex scattering constant of the bin containing the wake of the sea, i.e. as above

τ denotes the distance time, η denotes the near azimuth time, η _c Representing beam centre offset time, ω _r (τ) represents the distance envelope, ω _a (η) represents the azimuthal envelope, f ₀ Representing the radar center frequency, K _r Denotes the distance chirp frequency, R (η) denotes the instantaneous slope, and i is an imaginary unit. The method for calculating the mirror image scattering coefficient comprises the following steps:

calculating to obtain a mirror image scattering KA surface element scattering field E _s (r) wherein

Is a unit normal vector of a bin>

The sea surface half-space wave impedance, R is the distance between the bin center and the observation point, E and H are the total field on the surface boundary, I (·) = E ^-jq·r′ Is the phase integral term over the bin; />

And &>

A tangential field on the rough surface; using the formula:

obtaining a basic reference coordinate system; decomposing an incident wave into a horizontal component and a vertical component to obtain:

using the formula:

calculating to obtain a tangential horizontal polarization field; wherein

Unit vector which is the direction of the reflection field>

Is a horizontally polarized field of the reflected electric field, is present>

A horizontally polarized field that is a reflected magnetic field; using the formula:

calculating to obtain a tangential vertical polarization field; wherein

Is the unit vector of the transmission direction, R _VV Is the vertically polarized fresnel reflection coefficient; using the formula:

calculating to obtain a total tangential electromagnetic field; using the formula:

obtaining the image scattering coefficient E ^s (r)。

Optionally, processing the scattering echo by using a range-doppler SAR imaging algorithm to obtain ship SAR imaging information, including:

the distance-wise matched filter function is:

wherein T is the pulse width, f _τ Representing the offset frequency, rect is a rectangular window function, K _r Is a constant.

Distance direction compression output s _rc (τ, η) is:

s _rc (τ,η)＝IFFT _τ {S ₀ (f _τ ,η)H(f _τ )}＝Ep _r [τ-2R(η)/c]ω _a (η-η _c )exp{-i4πf ₀ R(η)/c}

wherein S is ₀ (f _τ Eta) is s ₀ Distance Fourier transform of (tau, eta), p _r (τ) is a window function W _τ (f _τ ) The inverse fourier transform of (d). For rectangular windows, p _r (τ) is the sinc function, p for the sharpening window _r (τ) is a sinc function with lower side lobes, η is a frequency variable, τ is a time variable, c is a constant, where f ₀ For the Doppler frequency, omega, of the echo signal _a As a function of the azimuth window, E is the echo intensity, η _c Is the center frequency.

At low squint angles, the beam points approximately in the zero doppler direction. If the aperture is not very large, the distance equation can be approximated as a parabola, i.e.

R ₀ Is a corresponding distance, V _r For velocity, a distance compressed signal s can be obtained by combining the above distance equation and the distance compressed output information _rc (τ, η) is:

from the second exponential term, the azimuth direction has a chirp characteristic, η _c For the beam center crossing time, the frequency is adjusted to

λ is a constant and i is an imaginary unit.

s44, processing the first distance direction compressed information by using the direction FFT to obtain direction frequency domain information;

the data is transformed to the range-doppler domain by the azimuthal FFT, which only needs to consider the second exponential term since the first exponential term of the range-compressed signal is constant. By using the principle of stationary phase (POSP), the time-frequency relation in the direction of the azimuth is obtained

f _η ＝-K _a η

Eta = -f _η /K _a Substituting a distance direction compression signal equation, wherein the azimuth frequency domain information after azimuth direction FFT is as follows:

wherein, W _a (f _a -f _ηc ) For azimuth antenna pattern omega _a (η-η _c ) In the frequency domain, f _ηc Is the doppler center frequency. From the distance equation and the time-frequency relation in the azimuth direction, R in the distance envelope can be obtained _rd (f _η ) Namely:

the RCM to be corrected is:

the distance migration correction is realized based on the interpolation of the sinc function. The sinc kernel is truncated and weighted by a sharpening window. After RCMC interpolation, the signal becomes:

and S46, carrying out azimuth IFFT on the corrected azimuth frequency domain information to obtain ship SAR imaging information. The azimuth matched filter function is:

for azimuthal compression, s is ₂ (τ,f _η ) Multiplication by an azimuth matched filter function, i.e.

/>

Wherein p is _a Is the magnitude of the azimuth impulse response, is a sinc function.

FIG. 3 is a comparison of the actual measurement result and the simulation result of TerrasAR-X of the present invention. As shown in FIG. 3, the radar platform TerrraSAR-X operates in the X-band (9.650 GHz). The present invention intercepts the ship wake portion in the "TSX _ 20191128tv 052044.652 v cu c414 u o093 u d v r v u sm003 v ssc" number data as shown in fig. 3 (c), and its corresponding measured terrain position coordinates are shown in fig. 3 (a) and 3 (b). When simulating the trail SAR image, the wind speed and the ship speed are respectively set to be 3m/s and 26m/s, and the simulation result of the method is shown in figure 3 (d). And observing according to the comparison result that the SAR imaging simulation result of the ship wake is basically the same as the actually measured SAR image characteristic.

Optionally, detecting the imaging information of the Kelvin wake data SAR by using a generalized maximum minimum concave sparse regularization method to obtain ship wake position information, where the method includes using a formula:

p(X|Y)＝αP(Y|X)p(X)

obtaining posterior distribution P (X | Y) of an SAR image Y and an image X in a Radon domain, wherein P (Y | X) is likelihood distribution, P (X) is probability distribution of X, alpha is a regularization constant, and P (X) = alpha exp { -lambda ψ (X) };

set cost function F (X):

the relationship between the MC penalty and the Huber function s (t) is: ψ (t) = | t | -s (t)

Obtaining the scaled MC penalty psi using a scalar b ≠ 0 _b (t)，ψ _b (t)＝|t|-s _b (t) wherein, s _b (t) is the scaled Huber function; using the formula:

obtaining a generalized Huber function S _B (t), where B is a scaling matrix,

inf represents the largest lower bound in the pool, based on>

ψ _B (t)＝||t|| ₁ -S _B (t)

wherein the content of the first and second substances,

p ₁ (X)＝αexp{-λ ₁ ψ _B (X)}＝αexp{-λ ₁ (X ₁ -S _B (X))}

computing to obtain GMC sparse prior p ₁ (X); using the formula:

calculating to obtain a cost function F (X, upsilon); using the formula:

calculating to obtain maximum minimum optimization information

Optimizing the maximum minimum information using a forward-backward algorithm

And solving to obtain the ship trail position information. The pseudo code for the forward-backward algorithm is:

input:λ＞0,0.5≤γ≤0.9

output:Radon image X

set:0＜μ＜1.9andi＝0

do

ω ⁽ⁱ⁾ ＝X ⁽ⁱ⁾ -μC ^T (C(X ⁽ⁱ⁾ +γ(υ ⁽ⁱ⁾ -X ⁽ⁱ⁾ ))-Y)

u ⁽ⁱ⁾ ＝υ ⁽ⁱ⁾ -μγC ^T C(υ ⁽ⁱ⁾ -X ⁽ⁱ⁾ )

X ⁽ⁱ⁾ ＝soft(ω ⁽ⁱ⁾ ,μλ)

υ ⁽ⁱ⁾ ＝soft(u ⁽ⁱ⁾ ,μλ)

i++

whileε ⁽ⁱ⁾ ＞10 ^-3 or i＜MaxIter

maxter is the number of loop iterations,

where soft (-) represents the optimization problem soft threshold function.

Alternatively, the ship wake position information may be calculated using the following method.

After SAR trail image input, firstly, determining the size of a sliding window with fixed size according to the size of a ship targetAnd determining the false alarm rate P _fa Then calculating the intensity value x of the current pixel according to the intensity of each pixel in the window and the intensity similarity of each pixel intensity and the central pixel of the window _i And by a kernel density function f _h (x) The obtained spatial value x _i And passing the intensity value x _i And the spatial value x _s Calculating to obtain a comprehensive value x _c . After traversing the entire image with a sliding window, the composite value x _c And detecting the image. The threshold is calculated using the entire image or a large portion of the image as the only background. And judging that the integrated value in all pixels in the image is higher than the threshold value as a target, otherwise, judging as a background. The size of the window is less than half the width of the boat. The nuclear density calculation formula is as follows:

wherein x ₁ ，x ₂ ，…，x _n Are the pixels in the sliding window other than the central pixel. n is the number of pixels in the sliding window except the center pixel. h represents the width of the kernel function. k is a function satisfying the following equation

I.e. the kernel function. A gaussian function is selected as the kernel function.

Thus, the kernel density function can be expressed as

Setting h to 1, then the kernel density function f _h (x) Is a standard gaussian distribution function.

After the kernel density of a pixel is calculated, the kernel density function is mapped to [0,1 ] by linear transformation]Thereby obtaining a spatial value x _s 。

Spatial value x _s Compared with the kernel density, the method is more stable, and the spatial characteristics of the pixel points are better represented. And meanwhile, the calculation is more convenient.

Composite value x _c Is an intensity value x _i And the spatial value x _s Product of (1)

x _combined ＝x _intensity ×x _spatial

In order to reduce the interference of abnormal conditions on the target detection, the comprehensive value x is calculated _c Taking the average value of the comprehensive values in the small window, namely:

from the composite value x _c The calculation formula shows that the comprehensive value x _c Intensity dependent value x _i And the spatial value x _s Due to the restriction of two factors, when the current pixel belongs to the normal sea background, the spatial value is large, the intensity value is small, and the comprehensive value is small.

Designing a distribution model for the background, i.e. specifying the probability density function f of the image _pdf (x) According to a given false alarm rate P _fa And a probability density function f _pdf (x) The threshold T can be calculated by:

the method for detecting the ship wake SAR image further comprises a similarity calculation model of the SAR simulation image and the SAR actual measurement image;

the similarity calculation model calculation step comprises:

And comparing the SAR simulation image fingerprint sequence with the SAR real-time image fingerprint sequence, and then calculating the Hamming distance (exclusive OR operation, different bits are 1) of the two fingerprints, thereby obtaining the similarity value of the SAR simulation image and the SAR real-time image.

FIG. 4 is a calculation result of a similarity calculation model of the SAR simulation image and the SAR actual measurement image, and the similarity of the SAR simulation image and the SAR actual measurement image reaches 95.3125%. FIG. 5 is a comparison of the results of the terraSAR-X SAR actual measurement trail detection and SAR simulation image detection, and the simulation parameters in FIG. 5 (b) are ship length 137.2m, ship width 16.617m, draft 8.732m, ship speed 18m/s and sea surface size 256m; then, calculating the scattering echo of the trail model by using a double-scale method; then, performing SAR imaging simulation on the trail model by using an RD algorithm; and finally, detecting the SAR image of the trail by using the method disclosed by the invention, wherein the obtained detection result is consistent with the actual result.

Therefore, the Kelvin ship wake geometric model is established by using the point disturbance theory, and the Kelvin ship wake geometric model under different targets, different sea surface wind speeds, different sea surface wind directions and different ship speeds can be calculated. Meanwhile, SAR imaging simulation calculation is carried out on the Kelvin ship trail model based on an RDA imaging algorithm, and the accuracy of an RDA algorithm simulation result is verified by utilizing a similarity calculation model of an SAR simulation image and an SAR real-time image. The method is characterized in that actual measurement data and simulation data of the Kelvin ship wake SAR image are detected by a GMC sparse regularization method respectively, and the detection result shows the effectiveness of the method, so that effective support is provided for extracting ship information hidden in the wake.

Example two

Referring to fig. 6, fig. 6 is a schematic structural diagram of a ship wake SAR image detection apparatus according to an embodiment of the present invention. The ship wake SAR image detection apparatus described in fig. 6 may be applied to aspects such as ship target detection and identification, and the embodiment of the present invention is not limited. As shown in fig. 6, the ship wake SAR image detection apparatus may include the following operations:

s301, a data acquisition module is used for acquiring Kelvin trail data information of the ship; the Kelvin trail data information of the ship comprises speed, navigation direction and ship parameter information;

s302, a wake geometric model construction module is used for processing Kelvin wake data information of the ship to obtain a wake geometric model;

s303, a scattered echo calculation module is used for calculating a radar backscattering coefficient of the sea surface by using a double-scale method to obtain a scattered echo; the radar backscattering coefficient of the sea surface comprises a mirror image scattering coefficient and a Bragg scattering coefficient;

s304, an SAR imaging information calculation module is used for processing the scattering echo by using a range-Doppler SAR imaging algorithm to obtain ship SAR imaging information;

and S305, a ship wake detection module for detecting the SAR imaging information of the Kelvin wake data by using a generalized maximum minimum concave sparse regularization method to obtain ship wake position information.

EXAMPLE III

Referring to fig. 7, fig. 7 is a schematic structural diagram of another ship wake SAR image detection apparatus disclosed in the embodiment of the present invention. The ship wake SAR image detection apparatus described in fig. 7 may be applied to aspects such as ship target detection and identification, and the embodiment of the present invention is not limited. As shown in fig. 7, the ship wake SAR image detection apparatus may include the following operations:

a memory 401 storing executable program code;

a processor 402 coupled to a memory 401;

the processor 402 calls the executable program code stored in the memory 401 for executing the steps in the ship wake SAR image detection method described in the first embodiment.

The above-described embodiments of the apparatus are only illustrative, and the modules described as separate parts may or may not be physically separate, and the parts displayed as modules may or may not be physical modules, may be located in one place, or may be distributed on a plurality of network modules. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.

Through the above detailed description of the embodiments, those skilled in the art will clearly understand that the embodiments may be implemented by software plus a necessary general hardware platform, and may also be implemented by hardware. Based on such understanding, the above technical solutions may be embodied in the form of a software product, which may be stored in a computer-readable storage medium, wherein the storage medium includes a Read-Only Memory (ROM), a Random Access Memory (RAM), a Programmable Read-Only Memory (PROM), an Erasable Programmable Read-Only Memory (EPROM), a One-time Programmable Read-Only Memory (OTPROM), an Electrically Erasable Programmable Read-Only Memory (EEPROM), a Compact Disc-Read-Only Memory (CD-ROM) or other Memory capable of storing data, a magnetic tape, or any other computer-readable medium capable of storing data.

Finally, it should be noted that: the method and the device for detecting the ship wake SAR image disclosed by the embodiment of the invention are only the preferred embodiment of the invention, and are only used for explaining the technical scheme of the invention, but not limiting the technical scheme; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those skilled in the art; the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A ship wake SAR image detection method is characterized by comprising the following steps:

s1, acquiring Kelvin trail data information of a ship; the Kelvin wake data information of the ship comprises speed, sailing direction and ship parameter information;

2. The method for detecting the ship wake SAR image according to claim 1, wherein the processing the ship Kelvin wake data information to obtain a wake geometric model comprises:

Comprises the following steps:

h represents water depth; for infinite water depth, i.e. (H → ∞),

s22, kelvin wake wave height information of the ship

Dividing the ship into a bow part and a stern part to obtain a trail geometric model;

the trail geometric model is as follows:

wherein C is the viscosity coefficient and the bow is

The stern is->

3. The method for detecting the ship wake SAR image according to claim 2, characterized in that the method for calculating the characteristic parameter A (theta) of the ship is as follows:

/>

wherein the content of the first and second substances,

wherein x is the offset position, z is the draft, b is half the beam, l is half the beam, and d is the sidewall draft.

4. The ship wake SAR image detection method according to claim 1, characterized in that the calculation method of the mirror scattering coefficient is:

wherein

Is a unit normal vector of a bin>

And &>

Is a tangential field on the roughened surface>

Unit vector of scattered wave, mu ₀ Is the permeability in the medium, epsilon ₀ ω is the angular frequency for the dielectric constant.

5. The method for detecting the ship wake SAR image according to claim 1, characterized in that the calculation method of the Bragg scattering coefficient is as follows:

using the formula:

ζ(ρ _c ,t)＝B(k _c )cos(k _c ·ρ _c -ω _c t)

calculating to obtain the geometrical profile zeta (rho) of Bragg scattering _c T), wherein k _c Wave number vector, ω, of Bragg capillary wave component _c Is the wave number k _c Corresponding spatial frequency, t represents time, B (k) _c ) Amplitude of capillary waves, p _c ＝(x _c ,y _c ) Indicates the position of each point on the patch, (x) _c ,y _c ) Is the coordinates of a point;

using the formula:

z ^capi ＝f(ρ ₀ ,t)+ζ(ρ _c ,t)+Z _x x _c +Z _y y _c

Projection onto the inclined facet element, Z _x And Z _y Is a scale factor;

using the formula:

calculating to obtain the amplitude B (k) of the capillary wave _c ) Wherein Δ S = Δ x _g Δy _g Is the size of the large-scale small bin, Δ x _g Is the sampling interval of the trail in the x direction, Δ y _g Is the sampling interval of the trail in the y-direction,

is a capillary spectrum.

6. The method for detecting the ship wake SAR image according to claim 1, wherein the processing the scattering echo by using a range-Doppler SAR imaging algorithm to obtain the ship SAR imaging information comprises:

s42, processing the distance direction frequency domain information of the scattered echoes by using distance direction matched filtering to obtain distance direction compression information;

s45, performing range migration correction on the azimuth frequency domain information to obtain corrected azimuth frequency domain information;

7. The method for detecting the ship wake SAR image according to claim 1, wherein the detecting the imaging information of the Kelvin wake data SAR based on the generalized maximum minimum concave-sparse regularization method to obtain the ship wake position information comprises:

using the formula:

p(X|Y)＝αP(Y|X)p(X)

setting a cost function F (X):

the relationship between the MC penalty and the Huber function s (t) is:

ψ(t)＝|t|-s(t)

obtaining the scaled MC penalty psi using a scalar b ≠ 0 _b (t)，

ψ _b (t)＝|t|-s _b (t)

Wherein s is _b (t) is the scaled Huber function;

using the formula:

obtaining a generalized Huber function S _B (t), where B is a scaling matrix,

inf represents the largest lower bound in the set,

representing an N-dimensional real number space, and t is a time variable;

improved GMC penalty function psi _B (t) is:

ψ _B (t)＝||t|| ₁ -S _B (t)

wherein the content of the first and second substances,

λ ₁ is GMC prior scaling parameter, gamma is parameter for controlling non-convexity;

using the formula:

p ₁ (X)＝αexp{-λ ₁ ψ _B (X)}＝αexp{-λ ₁ (||X|| ₁ -S _B (X))}

computing to obtain GMC sparse prior p ₁ (X)；

Using the formula:

calculating to obtain a cost function F (X, upsilon);

using the formula:

calculating to obtain maximum minimum optimization information

Optimizing information for the maximum and minimum using a forward-backward algorithm

And solving to obtain the ship trail position information.

8. The ship wake SAR image detection method according to claim 1, characterized in that the method further comprises:

s62, carrying out scaling processing on the SAR simulation image data information and the SAR actual measurement image data information to obtain first SAR simulation image data information and first SAR actual measurement image data information with the same size;

s66, comparing each gray value of the gray SAR actual measurement image data information with the average value of the SAR actual measurement image, and recording the gray value of each gray value of the gray SAR actual measurement image data information as 1 when the gray value is greater than or equal to the average value and recording the gray value of each gray value of the SAR actual measurement image data information as 0 when the gray value is less than the average value to obtain a fingerprint sequence of the SAR actual measurement image;

9. A ship wake SAR image detection device, characterized in that, the device includes:

the wake geometric model building module is used for processing Kelvin wake data information of the ship and warship to obtain a wake geometric model;

the scattered echo calculation module is used for calculating the radar backscattering coefficient of the sea surface by using a double-scale method to obtain a scattered echo; the radar backscattering coefficient of the sea surface comprises a mirror image scattering coefficient and a Bragg scattering coefficient;

and the ship wake detection module is used for detecting the SAR imaging information of the Kelvin wake data by utilizing a generalized maximum minimum concave sparse regularization method to obtain ship wake position information.

10. A ship wake SAR image detection device, characterized in that, the device includes:

a memory storing executable program code;

a processor coupled with the memory;

the processor calls the executable program code stored in the memory to execute the ship wake SAR image detection method according to any one of claims 1-8.