A single-channel sar moving ship three-dimensional reconstruction method based on implicit neural representation

Abstract

The application discloses a single-channel SAR moving ship three-dimensional reconstruction method based on implicit neural representation, first, through translation compensation and sub-aperture division processing, a focused two-dimensional image sequence is extracted from a single-channel SAR echo as a physical constraint of three-dimensional reconstruction re-projection, then an imaging geometry mapping is constructed to obtain a projection mapping relationship from a three-dimensional space to a two-dimensional imaging plane, a SAR imaging rendering model based on radar electromagnetic propagation is further constructed, a mapping relationship between a spatial position and target density and scattering intensity is fitted by using an implicit neural network, network weights are synchronously updated and ship motion parameters are estimated in a back propagation process through a re-projection supervision mechanism, an accurate projection plane is obtained, and a high-precision three-dimensional point cloud of the target is obtained by inversion. The method of the application does not need a complex multi-channel system, can effectively solve the problems of unknown projection matrix and image occlusion caused by non-cooperative motion, and realizes information dimension improvement from a single-channel two-dimensional sequence to a three-dimensional holographic image.

Description

Technical Field

[0001] This invention belongs to the field of interdisciplinary technology of radar maritime observation and artificial intelligence, specifically involving a single-channel SAR moving ship three-dimensional reconstruction method based on implicit neural representation (INR). Background Technology

[0002] Ships are the primary carriers of maritime transport, playing an irreplaceable role in supporting maritime activities, promoting economic development, and safeguarding national security. Ship target imaging is of paramount importance for ensuring maritime safety and stability. Synthetic Aperture Radar (SAR), with its all-weather, long-range, and high-resolution detection capabilities, occupies a key position in ship imaging. The autonomous motion characteristics of airborne SAR platforms enable active perspective changes in ship target imaging, avoiding passive reliance on target motion for controllable imaging performance while ensuring high-resolution imaging. In recent years, researchers have proposed various advanced imaging algorithms to acquire two-dimensional scattering and reflection images of ship targets. However, due to the rolling motion of ships on the sea surface, two-dimensional SAR ship images often exhibit distortion, limiting the presentation of ship information. Compared to two-dimensional SAR imaging, three-dimensional SAR reconstruction technology offers advantages such as intuitive spatial distribution of scattering points, accurate target size, and unique structure. This technology can provide more comprehensive and reliable structural information, showing broad application prospects in target recognition, structural damage diagnosis, and other fields.

[0003] Depending on the system configuration, current SAR ship target 3D reconstruction systems can be divided into multi-channel radar systems and single-channel radar systems. While multi-channel SAR-based ship 3D reconstruction methods can directly acquire 3D information from a specific perspective, these methods suffer from complex system structures, stringent configuration requirements, and high costs. Furthermore, they can only reconstruct the local structure of the target, making them less than optimal for ship 3D reconstruction. On the other hand, while single-channel SAR 3D reconstruction methods relax system constraints, they still face two major challenges in ship 3D reconstruction. First, single-channel SAR target 3D reconstruction methods primarily rely on keypoint matching, which is suitable for stationary targets or moving targets with negligible sway. However, for ship targets affected by waves, their imaging plane exhibits time-varying characteristics, changing drastically in high-wave conditions, leading to difficulties in keypoint matching and potentially causing 3D position calculation errors or even reconstruction failure. Moreover, the point clouds generated by such methods are typically sparse, making it difficult to accurately represent the ship target structure. Second, ship targets possess non-cooperative characteristics, meaning their motion parameters are unknown. Without establishing a projection relationship, the 3D coordinate inversion process between 3D space and the 2D imaging plane becomes extremely challenging. Therefore, none of the above methods can accurately reproduce the three-dimensional structure of a moving ship at a low cost. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for 3D reconstruction of moving ships using single-channel SAR based on implicit neural representation. By jointly estimating projection transformation, the method achieves target reconstruction, avoids reliance on key point matching in SAR stereo images, and solves the problems of unknown motion parameters and low reconstruction accuracy for non-cooperative ships, thus realizing 3D reconstruction of moving ships using single-channel SAR.

[0005] The technical solution adopted in this invention is: a method for three-dimensional reconstruction of moving ships based on implicit neural representation using single-channel SAR, the specific steps of which are as follows:

[0006] S1. Establish the spatial geometric configuration of the SAR platform and the moving ship target, and complete the parameter initialization;

[0007] To establish the spatial geometry of the SAR platform and moving ship targets, the global coordinate system is first set. by Let O be the origin of the coordinate system. , and The axes point east, north, and up, respectively. Then, a fixed coordinate system for the ship's hull is established. With center of mass With the origin as the origin, its The shaft is aligned with the ship's longitudinal axis. The axis is perpendicular to the vertical axis. Axis perpendicular to flat.

[0008] Then, using the ship's center of mass... Establish a local coordinate system with the origin as the origin. In terms of location and time At that time, the coordinate system coincides with the ship's fixed coordinate system, and the radar platform's position coordinates at time zero are... Flight speed is The initial coordinates of the center of mass of the moving target are The center frequency of the transmitted signal is The signal bandwidth is The pulse repetition frequency is PRF, and the electromagnetic wave velocity is .

[0009] S2. Based on step S1, establish a motion model of the ship target and complete the motion parameter settings;

[0010] The motion of a ship target consists of two parts: two-dimensional translation and three-dimensional rotation, as detailed below:

[0011] 1) The first part is the two-dimensional translation generated by the ship's own power. At that time, the ship's target center of mass was The position vector expression in the coordinate system is as follows:

[0012] (1);

[0013] in, This indicates the transpose operation. The coordinates are in the X-axis direction. Y-axis coordinate This is the Z-axis coordinate.

[0014] The two-dimensional translational velocity of the ship target The expression is as follows:

[0015] (2);

[0016] in, This represents the velocity component of the ship target along the X direction. This represents the velocity component of the ship target along the Y direction.

[0017] When setting up two-dimensional translational motion, the ship target is in Centroid position vector in coordinate system The expression is as follows:

[0018] (3);

[0019] 2) The second part is the three-dimensional rotation of the ship around the center of rotation under the action of external forces. This three-dimensional rotation is decomposed into roll, pitch, and yaw, which respectively represent the ship target in a fixed coordinate system. Middle winding axis, shaft and The rotational motion of the axis is approximated by a sine function. Then, with slow time... Variable roll, pitch and yaw angles The expression is as follows:

[0020] (4);

[0021] in, These correspond to the roll, pitch, and yaw angles, respectively. and These represent amplitude and period, respectively. Indicates the initial phase. The set of rotation parameters representing the azimuth and time is denoted as . .

[0022] S3. Based on step S2, construct the imaging geometry mapping and obtain the projection mapping relationship from three-dimensional space to two-dimensional imaging plane;

[0023] exist axis, shaft and Under the combined action of axes, the inherent rotation matrix of the ship target The expression is as follows:

[0024] (5);

[0025] in, , and They represent circumference respectively. axis, shaft and Axis rotation , and The rotation matrix of the angle is expressed as follows:

[0026] (6);

[0027] (7);

[0028] (8);

[0029] In the ship's fixed coordinate system In the middle, for the scattering point on the ship target , its in The position vector at time is denoted as After three-dimensional rotation, the scattering point In the local coordinate system Position vector in The expression is as follows:

[0030] (9);

[0031] in, Represents the scattering point Position component along the U-axis Represents the scattering point Position component on the V-axis Represents the scattering point Position component on the W-axis.

[0032] Then, by combining two-dimensional translation and three-dimensional rotation, the scattering point is obtained. In the global coordinate system of the ship target Position vector in The expression is as follows:

[0033] (10);

[0034] in, Indicates from the local coordinate system To the global coordinate system The rotation matrix.

[0035] In the global coordinate system, both the SAR platform and the ship target are in motion; the total angular velocity of the system is... It consists of two parts: one part is the angular velocity generated by the relative translation between the SAR platform and the ship target. The other part is the angular velocity generated by the rotational motion of the ship target. The specific expression is as follows:

[0036] (11);

[0037] At the initial moment, the position vector of the SAR platform in the global coordinate system is defined as... The platform speed is... At any given time, the platform position is represented as... The equivalent line-of-sight and equivalent direction RLOS expression is as follows:

[0038] (12);

[0039] in, This represents the distance vector between the radar platform and the center point of the ship target.

[0040] The angular velocity generated by translation The expression is as follows:

[0041] (13);

[0042] in, Indicates the platform's translational velocity The component of RLOS perpendicular to the equivalent line-of-sight and equivalent direction. Indicates the ship's translational speed The component of RLOS perpendicular to the equivalent line of sight and equivalent direction.

[0043] In the local coordinate system, angular velocity The calculation expression is as follows:

[0044] (14);

[0045] in, This represents the angular velocity component along the U-axis. This represents the angular velocity component along the V-axis. This represents the angular velocity component along the W-axis.

[0046] In the global coordinate system, The calculation expression is as follows:

[0047] (15);

[0048] effective angular velocity This can be expressed as subtracting the projected component of the total angular velocity vector along the radar line-of-sight direction from the total angular velocity vector, as shown in the following expression:

[0049] (16);

[0050] in, This represents the angular velocity component parallel to the equivalent line-of-sight direction, RLOS. This represents the angular velocity component perpendicular to the equivalent line-of-sight direction RLOS.

[0051] In the local coordinate system, the basis vectors of the imaging coordinate system are expressed as follows:

[0052] (17);

[0053] in, , Represents the distance vector. Represents the orientation vector. This indicates that the scattering point is perpendicular to the imaging plane. The position expression in the imaging coordinate system is as follows:

[0054] (18);

[0055] in, Represents the scattering point Distance coordinates, Represents the scattering point The azimuth coordinates, Represents the scattering point The coordinates of the normal to the imaging plane. This represents the rotation matrix from the local coordinate system to the imaging coordinate system. This represents the global projection transformation from the local coordinate system to the imaging coordinate system.

[0056] Then set the point on the imaging plane The two-dimensional coordinate expression is as follows:

[0057] (19);

[0058] in, The projection matrix from the initial three-dimensional space to the two-dimensional imaging plane is represented by... It consists of the first two lines. and Establish geometric constraints for the projection mapping used for reprojection supervision.

[0059] S4. Based on step S3, construct a SAR imaging rendering model based on radar electromagnetic propagation;

[0060] By establishing a mapping relationship for scattering intensity, i.e., the contribution of a target point in space to the scattering intensity in the two-dimensional imaging result, and considering that the equivalent line-of-sight direction and the imaging projection direction are orthogonal during SAR imaging, the analytical representation of SAR imaging rendering is established by combining the SAR imaging mechanism and the electromagnetic propagation process as follows:

[0061] (20);

[0062] Among them, setting Indicates radar ray, This represents the sampling point on the two-dimensional imaging plane. This indicates a distance-oriented mesh partition, with the nearest boundary being... The far boundary is , Indicates the equivalent observation direction. Indicates the position along the IPP normal direction. This indicates a height-based mesh partitioning, with the near-boundary being... The far boundary is , Indicates the direction of accumulation. This represents the contribution of scattered energy. Indicates density. This represents the amplitude value of a pixel. It represents the cumulative transmittance along the equivalent line-of-sight direction. This represents the distance vector between the radar platform and the sampling point. Indicates the equivalent line of sight direction.

[0063] In the local coordinate system In this scenario, both the radar platform and the ship target are in motion; an initial time of 0 is chosen as the reference time for 3D reconstruction. The reconstructed scattering point locations are shown below. This is the initial position. Observation direction. The equivalent observation direction is expressed as follows:

[0064] (twenty one);

[0065] Similarly, cumulative direction The equivalent cumulative direction of writing is expressed as follows:

[0066] (twenty two);

[0067] Then combine and Equivalent azimuth direction The specific expression is as follows:

[0068] (twenty three);

[0069] Then along the height direction Distance and direction and direction Discretizing the imaging space yields the following discrete-form expression for the analytical representation of SAR imaging rendering:

[0070] (twenty four);

[0071] in, Represents the number of spatial sampling points, variable and These represent sampling points in the height and distance directions, respectively. Indicates the interval used for distance direction. Indicates the interval for height-direction sampling. Indicates density, This represents the contribution of scattered energy.

[0072] S5. Based on step S4, design the implicit neural network and extract the three-dimensional point cloud to complete the three-dimensional reconstruction of the single-channel SAR moving ship.

[0073] Scattering energy contribution Position of discrete points in space and radar observation direction Strong correlation, and density Only with position If they are related, their implicit expressions are as follows:

[0074] (25);

[0075] (26);

[0076] in, Representing spatial coordinates and observation direction Contribution of Scattered Energy The implicit mapping relationship, Representing spatial coordinates With density The implicit mapping relationship;

[0077] Fitting using implicit neural representation and The mapping relationship between them, and and The mapping relationship between them is used to construct an implicit neural network including a multilayer perceptron. The implicit neural network includes three cooperating modules: a motion parameter module, a neural representation module, and a joint optimization module.

[0078] The motion parameter module uses platform parameters and ship motion parameters to construct a projection matrix. The neural representation module is essentially an improved multilayer perceptron (MLP), whose input is spatial coordinates. and observation direction The output is the contribution of scattering energy. With density A joint optimization module with skip connections is used to establish the loss function. Based on the recorded gradient information, two Adam optimizers are used to synchronously update the MLP parameters in the neural representation module and the ship motion parameters in the motion parameter module.

[0079] The implicit neural network transforms the problem of estimating projection transformation into the problem of estimating ship motion parameters. It treats the ship's motion parameters as learnable variables and sets up two optimizers to jointly optimize the network weights and ship motion parameters, thereby obtaining the three-dimensional point cloud of the ship target and realizing the three-dimensional reconstruction of a moving ship using single-channel SAR.

[0080] Furthermore, in step S5, the joint optimization by the two optimizers is specifically as follows:

[0081] 1) Utilizing ship motion parameters ( A two-dimensional SAR image is generated, and based on the calibration results, the pixel coordinate system of the two-dimensional SAR image is converted into an imaging coordinate system with real physical scale.

[0082] 2) with the first The center of the SAR image is the origin. Spatially discrete sampling is performed along the propagation and accumulation directions. The projection transformation formula of equation (19) is used to transform the imaging coordinate system to the local coordinate system. In the middle, obtain the position coordinates and observation direction .

[0083] 3) The implicit neural network will and As input, obtain and The reprojection process of the two-dimensional SAR image is completed using the imaging rendering formula of equation (20).

[0084] 4) The joint optimization module uses mean squared error as the loss function in the implicit neural network training process to supervise the consistency between reprojected SAR images and other SAR images. The expression is as follows:

[0085] (27);

[0086] in, Indicates reprojected pixels. Indicates the number of pixels in the input image. Indicates the image height. This represents the image width. Furthermore, during backpropagation, the two optimizers synchronously update the network parameters and the ship motion parameters.

[0087] 5) Using the acquired long sequence of 2D images of the moving SAR ship target as input, initialize the ship motion parameters. Train the network according to the optimization criteria provided by the loss function. The optimizer synchronously updates the implicit neural network weight parameters and the ship motion parameters. After training, perform discrete sampling in the 3D space to obtain... and The output. Based on... The nonnegativity of the judgment space determines whether a point belongs to the reconstruction target. It is assumed that there are scattering points in space, and these points are preserved. The spatial network is traversed one by one to finally obtain the three-dimensional point cloud of the ship target.

[0088] The beneficial effects of this invention are as follows: First, the method of this invention extracts a focused two-dimensional image sequence from the single-channel SAR echo through translational compensation and sub-aperture segmentation, serving as the physical constraint for three-dimensional reconstruction reprojection. Then, a differentiable projection transformation relationship is established, fusing ship roll, pitch, and yaw motion models, constructing a geometric bridge between the three-dimensional physical space and the two-dimensional imaging plane. Next, combined with electromagnetic propagation mechanisms, a forward rendering model conforming to SAR imaging characteristics is established, and an implicit neural network is used to fit the mapping relationship between spatial position and target density and scattering intensity. Finally, since the projection plane of ship imaging is transient and unknown, a joint optimization architecture is designed. Through a reprojection supervision mechanism, network weights are updated synchronously during backpropagation, and ship motion parameters are estimated to obtain an accurate projection plane and inversely obtain a high-precision three-dimensional point cloud of the target. This method utilizes the multi-angle information naturally provided by the ship's three-dimensional oscillation to learn key parameters of the imaging rendering process and simultaneously estimate the ship's three-dimensional motion parameters. It effectively solves the challenge of the transient and unknown projection plane over time when observing non-cooperative ship targets on the sea surface using a single channel, achieving dense three-dimensional reconstruction of ship targets. The method of this invention does not require a complex multi-channel system, and can effectively solve the problems of unknown projection matrix and image occlusion caused by non-cooperative motion, thereby achieving an improvement in information dimension from single-channel two-dimensional sequence to three-dimensional holographic image. Attached Figure Description

[0089] Figure 1 This is a flowchart of a single-channel SAR moving ship 3D reconstruction method based on implicit neural representation according to the present invention.

[0090] Figure 2 This is a schematic diagram of the spatial geometric configuration of the SAR platform and the moving ship target in an embodiment of the present invention.

[0091] Figure 3 This is a schematic diagram of SAR imaging projection mapping in an embodiment of the present invention.

[0092] Figure 4 This is a diagram of the three-dimensional reconstruction implicit neural network architecture in an embodiment of the present invention.

[0093] Figure 5 This is a schematic diagram of reprojection-supervised training in an embodiment of the present invention.

[0094] Figure 6 This is a schematic diagram of the sub-aperture sequential image in an embodiment of the present invention.

[0095] Figure 7 This is a schematic diagram of the three-dimensional reconstruction result of the ship target in an embodiment of the present invention. Detailed Implementation

[0096] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0097] like Figure 1 The flowchart of a single-channel SAR moving ship 3D reconstruction method based on implicit neural representation of the present invention is shown below. The specific steps are as follows:

[0098] S1. Establish the spatial geometric configuration of the SAR platform and the moving ship target, and complete the parameter initialization;

[0099] The spatial geometry of the SAR platform and the moving ship target used in this embodiment is as follows: Figure 2 As shown, the global coordinate system by Let O be the origin of the coordinate system. , and The axes point east, north, and up, respectively. Then, a fixed coordinate system for the ship's hull is established. With center of mass With the origin as the origin, its The shaft is aligned with the ship's longitudinal axis. The axis is perpendicular to the vertical axis. Axis perpendicular to flat.

[0100] Then, using the ship's center of mass... Establish a local coordinate system with the origin as the origin. In terms of location and time At that time, the coordinate system coincides with the ship's fixed coordinate system, and the system parameters used are shown in Table 1.

[0101] Table 1

[0102]

[0103] The position coordinates of the radar platform at time zero are: Flight speed is The initial coordinates of the center of mass of the moving target are The center frequency of the transmitted signal It is 9.6GHz, with a signal bandwidth The frequency is 200MHz, the pulse repetition frequency (PRF) is 800Hz, and the electromagnetic wave velocity is... for m / s.

[0104] S2. Based on step S1, establish a motion model of the ship target and complete the motion parameter settings;

[0105] The motion of a ship target consists of two parts: two-dimensional translation and three-dimensional rotation, as detailed below:

[0106] 1) The first part is the two-dimensional translation generated by the ship's own power. At that time, the ship's target center of mass was The position vector expression in the coordinate system is as follows:

[0107] (1);

[0108] in, This indicates the transpose operation. The coordinates are in the X-axis direction. Y-axis coordinate This is the Z-axis coordinate.

[0109] The two-dimensional translational velocity of the ship target The expression is as follows:

[0110] (2);

[0111] in, This represents the velocity component of the ship target along the X direction. This represents the velocity component of the ship target along the Y direction.

[0112] When setting up two-dimensional translational motion, the ship target is in Centroid position vector in coordinate system The expression is as follows:

[0113] (3);

[0114] 2) The second part is the three-dimensional rotation of the ship around its center of rotation under the action of external forces such as waves. This three-dimensional rotation is decomposed into roll, pitch, and yaw, which represent the ship target in a fixed coordinate system. Middle winding axis, shaft and The rotational motion of the axis is approximated by a sine function. Then, with slow time... Variable roll, pitch and yaw angles The expression is as follows:

[0115] (4);

[0116] in, These correspond to the roll, pitch, and yaw angles, respectively. and These represent amplitude and period, respectively. Indicates the initial phase. The set of rotation parameters representing the azimuth and time is denoted as . Sea state parameters are shown in Table 2.

[0117] Table 2

[0118]

[0119] S3. Based on step S2, construct the imaging geometry mapping and obtain the projection mapping relationship from three-dimensional space to two-dimensional imaging plane;

[0120] exist axis, shaft and Under the combined action of axes, the inherent rotation matrix of the ship target The expression is as follows:

[0121] (5);

[0122] in, , and They represent circumference respectively. axis, shaft and Axis rotation , and The rotation matrix of the angle is expressed as follows:

[0123] (6);

[0124] (7);

[0125] (8);

[0126] In the ship's fixed coordinate system In the middle, for the scattering point on the ship target , its in The position vector at time is denoted as After three-dimensional rotation, the scattering point In the local coordinate system Position vector in The expression is as follows:

[0127] (9);

[0128] in, Represents the scattering point Position component along the U-axis Represents the scattering point Position component on the V-axis Represents the scattering point Position component on the W-axis.

[0129] Then, by combining two-dimensional translation and three-dimensional rotation, the scattering point is obtained. In the global coordinate system of the ship target Position vector in The expression is as follows:

[0130] (10);

[0131] in, Indicates from the local coordinate system To the global coordinate system The rotation matrix.

[0132] This establishes the position of the target point in three-dimensional space as a function of slow time. The changing relationship, but in order to obtain The mapping relationship from three-dimensional space to the two-dimensional imaging plane needs further analysis in conjunction with platform motion parameters. In the global coordinate system, both the SAR platform and the ship target are in motion, and the total angular velocity of the system... It consists of two parts: one part is the angular velocity generated by the relative translation between the SAR platform and the ship target. The other part is the angular velocity generated by the rotational motion of the ship target. The specific expression is as follows:

[0133] (11);

[0134] At the initial moment, the position vector of the SAR platform in the global coordinate system is defined as... The platform speed is... At any given time, the platform position is represented as... The equivalent line-of-sight and equivalent direction RLOS expression is as follows:

[0135] (12);

[0136] in, This represents the distance vector between the radar platform and the center point of the ship target.

[0137] The angular velocity generated by translation The expression is as follows:

[0138] (13);

[0139] in, Indicates the platform's translational velocity The component of RLOS perpendicular to the equivalent line-of-sight and equivalent direction. Indicates the ship's translational speed The component of RLOS perpendicular to the equivalent line of sight and equivalent direction.

[0140] In the local coordinate system, angular velocity The calculation expression is as follows:

[0141] (14);

[0142] in, This represents the angular velocity component along the U-axis. This represents the angular velocity component along the V-axis. This represents the angular velocity component along the W-axis.

[0143] In the global coordinate system, The calculation expression is as follows:

[0144] (15);

[0145] Furthermore, the rotation vector parallel to the line of sight does not contribute to imaging, thus the effective angular velocity... This can be expressed as subtracting the projected component of the total angular velocity vector along the radar line-of-sight direction from the total angular velocity vector, as shown in the following expression:

[0146] (16);

[0147] in, This represents the angular velocity component parallel to the equivalent line-of-sight direction, RLOS. This represents the angular velocity component perpendicular to the equivalent line-of-sight direction RLOS.

[0148] Conventional echo preprocessing algorithms can already compensate for the translational motion components of the ship target relative to the radar. Therefore, in the local coordinate system, the basis vector expression of the imaging coordinate system is as follows:

[0149] (17);

[0150] in, , Represents the distance vector. Represents the orientation vector. This indicates that the scattering point is perpendicular to the imaging plane. The position expression in the imaging coordinate system is as follows:

[0151] (18);

[0152] in, Represents the scattering point Distance coordinates, Represents the scattering point The azimuth coordinates, Represents the scattering point The coordinates of the normal to the imaging plane. This represents the rotation matrix from the local coordinate system to the imaging coordinate system. This represents the global projection transformation from the local coordinate system to the imaging coordinate system, which forms a bridge between the three-dimensional physical world and the SAR imaging space. A schematic diagram of the SAR imaging mapping from three-dimensional space to the two-dimensional imaging plane is shown in Figure 3.

[0153] Because two-dimensional SAR images lack height information, points on the imaging plane The two-dimensional coordinate expression is as follows:

[0154] (19);

[0155] in, The projection matrix from the initial three-dimensional space to the two-dimensional imaging plane is represented by... It consists of the first two lines. and Establish geometric constraints for the projection mapping used for reprojection supervision.

[0156] S4. Based on step S3, construct a SAR imaging rendering model based on radar electromagnetic propagation;

[0157] Projection transformations can only establish mapping relationships in geometric space. To achieve reprojection supervision, a mapping relationship for scattering intensity also needs to be established, i.e., the contribution of the scattering intensity of a target point in space to the 2D imaging result. Furthermore, during SAR imaging, the equivalent line-of-sight direction is orthogonal to the imaging projection direction, such as... Figure 3 As shown. Therefore, combining the SAR imaging mechanism and electromagnetic propagation process, the analytical representation of SAR imaging rendering is established as follows:

[0158] (20);

[0159] Among them, setting Indicates radar ray, This represents the sampling point on the two-dimensional imaging plane. This indicates a distance-oriented mesh partition, with the nearest boundary being... The far boundary is , Indicates the equivalent observation direction. Indicates the position along the IPP normal direction. This indicates the height-oriented mesh division (image plane normal), with the near boundary being... The far boundary is , Indicates the direction of accumulation. This represents the contribution of scattered energy. Indicates density. This represents the amplitude value of a pixel. It represents the cumulative transmittance along the equivalent line-of-sight direction. This represents the distance vector between the radar platform and the sampling point. Indicates the equivalent line of sight direction.

[0160] In the local coordinate system In this scenario, both the radar platform and the ship target are in motion. To achieve 3D reconstruction of the ship target, a reference time needs to be selected. Without loss of generality, an initial time of 0 is chosen as the reference time for 3D reconstruction. The reconstructed scattering point location... This is the initial position. Observation direction. The equivalent observation direction is expressed as follows:

[0161] (twenty one);

[0162] Similarly, cumulative direction The equivalent cumulative direction of writing is expressed as follows:

[0163] (twenty two);

[0164] Then combine and Equivalent azimuth direction The specific expression is as follows:

[0165] (twenty three);

[0166] Then along the height direction Distance and direction and direction Discretizing the imaging space yields the following discrete-form expression for the analytical representation of SAR imaging rendering:

[0167] (twenty four);

[0168] in, Represents the number of spatial sampling points, variable and These represent sampling points in the height and distance directions, respectively. Indicates the interval used for distance direction. Indicates the interval for height-direction sampling. Indicates density, This represents the contribution of scattered energy.

[0169] Of particular note is the position in the distance direction. The pixel amplitude at that location is only related to the previous pixel in the distance direction. It relates to one spatial point, but not to subsequent spatial points. Due to the occlusion effect, The point after the position was The location obstructs the view and will not affect it. Imaging of location points. The forward rendering process makes reprojection supervision possible.

[0170] S5. Based on step S4, design the implicit neural network and extract the three-dimensional point cloud to complete the three-dimensional reconstruction of the single-channel SAR moving ship.

[0171] In reality, the attenuation process of electromagnetic propagation is extremely complex and difficult to model accurately. and The mapping relationship between them. Scattered energy contribution. Position of discrete points in space and radar observation direction Strong correlation, and density Only with position If they are related, their implicit expressions are as follows:

[0172] (25);

[0173] (26);

[0174] in, Representing spatial coordinates and observation direction Contribution of Scattered Energy The implicit mapping relationship, Representing spatial coordinates With density The implicit mapping relationship;

[0175] In the propagation of electromagnetic waves in space, and It is a complex process, difficult to model accurately, and establishing explicit expressions is extremely challenging. Fitting using implicit neural representations is the solution. and The mapping relationship between them, and and The mapping relationship between them is used to construct an implicit neural network including a multilayer perceptron. For example... Figure 4 As shown, the implicit neural network comprises three cooperating modules: a motion parameter module, a neural representation module, and a joint optimization module. Except for the final output layer, the output dimension of each layer is 128, with intermediate layers using... As an activation function. In the output part of the network, pass The function is normalized, while Then through Ensure its non-negativity. It is worth noting that, in addition to the network weights to be optimized, the projection transformation throughout the reprojection supervision process is also unknown due to the ship's motion.

[0176] The motion parameter module (blue area) constructs a projection matrix using platform parameters and ship motion parameters. (Among them, the ship's motion parameters are the parameters to be estimated, and these parameters together determine the projection matrix.) This is used to map three-dimensional spatial points to coordinates under a specific observation viewpoint; the neural representation module (orange area) is an improved multilayer perceptron (MLP), whose input is spatial coordinates. and observation direction The output is the contribution of scattering energy. With density A joint optimization module (purple area) with skip connections is used to establish the loss function. Based on the recorded gradient information, two Adam optimizers are used to synchronously update the MLP parameters in the neural representation module and the ship motion parameters in the motion parameter module.

[0177] The projection transformation is obtained using ship motion parameters and platform parameters. Since the platform parameters are known, the implicit neural network described in this embodiment transforms the problem of estimating the projection transformation into the problem of estimating ship motion parameters. The ship's motion parameters are treated as learnable variables, and two optimizers are set up to jointly optimize the network weights and ship motion parameters, obtaining the 3D point cloud of the ship target and realizing the 3D reconstruction of a moving ship using single-channel SAR. A schematic diagram of the reprojection supervision is shown below. Figure 5 As shown.

[0178] In this embodiment, the joint optimization by the two optimizers in step S5 is as follows:

[0179] 1) Utilizing ship motion parameters ( A two-dimensional SAR image is generated, and the pixel coordinate system of the two-dimensional SAR image is converted into an imaging coordinate system with real physical scale according to the calibration results. The input two-dimensional image is shown in Figure 6.

[0180] 2) with the first The center of the SAR image is the origin. Spatially discrete sampling is performed along the propagation and accumulation directions. The projection transformation formula of equation (19) is used to transform the imaging coordinate system to the local coordinate system. In the middle, obtain the position coordinates and observation direction .

[0181] 3) The implicit neural network will and As input, obtain and The reprojection process of the two-dimensional SAR image is completed using the imaging rendering formula of equation (20).

[0182] 4) The joint optimization module uses mean squared error as the loss function in the implicit neural network training process to supervise the consistency between reprojected SAR images and other SAR images. The expression is as follows:

[0183] (27);

[0184] in, Indicates reprojected pixels. Indicates the number of pixels in the input image. Indicates the image height. This represents the image width. The entire reprojection process is differentiable, so the gradient of each node can be calculated throughout the process. During backpropagation, the two optimizers synchronously update the network parameters and the ship motion parameters.

[0185] 5) Using the acquired long sequence of 2D images of the moving SAR ship target as input, initialize the ship motion parameters. Train the network according to the optimization criteria provided by the loss function. The optimizer synchronously updates the implicit neural network weight parameters and the ship motion parameters. After training, perform discrete sampling in the 3D space to obtain... and The output. Based on... The nonnegativity of the judgment space determines whether a point belongs to the reconstruction target. It is assumed that scattering points exist in space and these points are preserved. The spatial network is then traversed one by one to finally obtain the three-dimensional point cloud of the ship target. The reconstructed three-dimensional point cloud in this embodiment is as follows: Figure 7 As shown.

[0186] In summary, the method of this invention eliminates the need for complex multi-channel radar system configurations, easing constraints such as stringent system structure and high costs. It enables accurate reconstruction of the 3D structure of moving ships using a low-cost single-channel radar system, reducing system complexity and cost. Addressing the challenge of unknown target motion parameters for non-cooperative ships, the method of this invention designs a joint optimization architecture that transforms the problem of estimating projection transformation into estimating ship motion parameters. Through a reprojection supervision mechanism, the implicit neural network weights are updated synchronously during backpropagation to estimate ship motion parameters, effectively solving the problem of transient and unknown projection matrix caused by non-cooperative motion. Existing single-channel reconstruction mainly relies on keypoint matching, which can easily lead to matching difficulties, position calculation errors, or even reconstruction failure under severe swaying caused by waves. The method of this invention achieves target reconstruction by jointly estimating projection transformation, completely avoiding reliance on keypoint matching in SAR stereo images, and significantly improving the reconstruction success rate and accuracy under complex sea conditions. Existing single-channel methods typically generate sparse point clouds, making it difficult to accurately represent the structure of ship targets. The method of this invention combines electromagnetic propagation mechanisms with a forward rendering model that conforms to SAR imaging characteristics, effectively solving the image occlusion problem and ultimately enabling the inversion of a high-precision, dense, continuous 3D point cloud of the target. This invention cleverly utilizes the multi-angle information naturally provided by the ship's 3D swaying, combining the mapping relationship between spatial position and target density and scattering intensity, successfully achieving an information dimensionality enhancement from a single-channel 2D sequence to a 3D holographic image.

[0187] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A method for 3D reconstruction of moving ships using single-channel SAR based on implicit neural representation, the specific steps of which are as follows: S1. Establish the spatial geometric configuration of the SAR platform and the moving ship target, and complete the parameter initialization; To establish the spatial geometry of the SAR platform and moving ship targets, the global coordinate system is first set. by Let O be the origin of the coordinate system. , and The axes point east, north, and up respectively; then a fixed coordinate system for the ship is established. With center of mass With the origin as the origin, its The shaft is aligned with the ship's longitudinal axis. The axis is perpendicular to the vertical axis. Axis perpendicular to flat; Then, using the ship's center of mass... Establish a local coordinate system with the origin as the origin. In terms of location and time At that time, the coordinate system coincides with the ship's fixed coordinate system, and the radar platform's position coordinates at time zero are... Flight speed is The initial coordinates of the center of mass of the moving target are The center frequency of the transmitted signal is The signal bandwidth is The pulse repetition frequency is PRF, and the electromagnetic wave velocity is ; S2. Based on step S1, establish a motion model of the ship target and complete the motion parameter settings; The motion of a ship target consists of two parts: two-dimensional translation and three-dimensional rotation, as detailed below: 1) The first part is the two-dimensional translation generated by the ship's own power. At that time, the ship's target center of mass was The position vector expression in the coordinate system is as follows: （1）； in, This indicates the transpose operation. The coordinates are in the X-axis direction. Y-axis coordinate Z-axis coordinate; The two-dimensional translational velocity of the ship target The expression is as follows: （2）； in, This represents the velocity component of the ship target along the X direction. This represents the velocity component of the ship target along the Y direction; When setting up two-dimensional translational motion, the ship target is in Centroid position vector in coordinate system The expression is as follows: （3）； 2) The second part is the three-dimensional rotation of the ship around the center of rotation under the action of external forces. This three-dimensional rotation is decomposed into roll, pitch, and yaw, which respectively represent the ship target in a fixed coordinate system. Middle winding axis, shaft and The rotational motion of the axis, which is approximated by a sine function, then with slow time... Variable roll, pitch and yaw angles The expression is as follows: （4）； in, These correspond to the roll, pitch, and yaw angles, respectively. and These represent amplitude and period, respectively. Indicates the initial phase. The set of rotation parameters representing the azimuth and time is denoted as . ; S3. Based on step S2, construct the imaging geometry mapping and obtain the projection mapping relationship from three-dimensional space to two-dimensional imaging plane; exist axis, shaft and Under the combined action of axes, the inherent rotation matrix of the ship target The expression is as follows: （5）； in, , and They represent circumference respectively. axis, shaft and Axis rotation , and The rotation matrix of the angle is expressed as follows: （6）； （7）； （8）； In the ship's fixed coordinate system In the middle, for the scattering point on the ship target , its in The position vector at time is denoted as After three-dimensional rotation, the scattering point In the local coordinate system Position vector in The expression is as follows: （9）； in, Represents the scattering point Position component along the U-axis Represents the scattering point Position component on the V-axis Represents the scattering point Position component on the W-axis; Then, by combining two-dimensional translation and three-dimensional rotation, the scattering point is obtained. In the global coordinate system of the ship target Position vector in The expression is as follows: （10）； in, Indicates from the local coordinate system To the global coordinate system The rotation matrix; In the global coordinate system, both the SAR platform and the ship target are in motion; the total angular velocity of the system is... It consists of two parts: one part is the angular velocity generated by the relative translation between the SAR platform and the ship target. The other part is the angular velocity generated by the rotational motion of the ship target. The specific expression is as follows: （11）； At the initial moment, the position vector of the SAR platform in the global coordinate system is defined as... Platform speed is Then, at any given time, the platform position is represented as: The equivalent line of sight and equivalent direction RLOS expression is as follows: （12）； in, This represents the distance vector between the radar platform and the center point of the ship target; The angular velocity generated by translation The expression is as follows: （13）； in, Indicates the platform's translational velocity The component of RLOS perpendicular to the equivalent line-of-sight and equivalent direction. Indicates the ship's translational speed The component of RLOS perpendicular to the equivalent line-of-sight and equivalent direction; In the local coordinate system, angular velocity The calculation expression is as follows: （14）； in, This represents the angular velocity component along the U-axis. This represents the angular velocity component along the V-axis. This represents the angular velocity component along the W-axis. In the global coordinate system, The calculation expression is as follows: （15）； effective angular velocity This can be expressed as subtracting the projected component of the total angular velocity vector along the radar line-of-sight direction from the total angular velocity vector, as shown in the following expression: （16）； in, This represents the angular velocity component parallel to the equivalent line-of-sight direction, RLOS. This represents the angular velocity component perpendicular to the equivalent line-of-sight direction RLOS. In the local coordinate system, the basis vectors of the imaging coordinate system are expressed as follows: （17）； in, , Represents the distance vector. Represents the orientation vector. Indicates perpendicular to the imaging plane; then the scattering point The position expression in the imaging coordinate system is as follows: （18）； in, Represents the scattering point Distance coordinates, Represents the scattering point The azimuth coordinates, Represents the scattering point Coordinates in the normal direction of the imaging plane; Represents the rotation matrix from the local coordinate system to the imaging coordinate system; This represents the global projection transformation from the local coordinate system to the imaging coordinate system; Then set the point on the imaging plane The two-dimensional coordinate expression is as follows: （19）； in, The projection matrix from the initial three-dimensional space to the two-dimensional imaging plane is represented by... The first two lines constitute the structure; and Establish geometric constraints for the projection mapping used for reprojection supervision; S4. Based on step S3, construct a SAR imaging rendering model based on radar electromagnetic propagation; By establishing a mapping relationship for scattering intensity, i.e., the contribution of a target point in space to the scattering intensity in the two-dimensional imaging result, and considering that the equivalent line-of-sight direction and the imaging projection direction are orthogonal during SAR imaging, the analytical representation of SAR imaging rendering is established by combining the SAR imaging mechanism and the electromagnetic propagation process as follows: （20）； Among them, setting Indicates radar ray, This represents the sampling point on the two-dimensional imaging plane. This indicates a distance-oriented mesh partition, with the nearest boundary being... The far boundary is , Indicates the equivalent observation direction; Indicates the position along the IPP normal direction. This indicates a height-based mesh partitioning, with the near-boundary being... The far boundary is , Indicates the direction of accumulation; This represents the contribution of scattered energy. Indicates density; This represents the amplitude value of a pixel; It represents the cumulative transmittance along the equivalent line-of-sight direction. This represents the distance vector between the radar platform and the sampling point. Indicates the equivalent line-of-sight direction; In the local coordinate system In this scenario, both the radar platform and the ship target are in motion; an initial time of 0 is chosen as the reference time for 3D reconstruction; the reconstructed scattering point locations... Position at the initial moment; observation direction The equivalent observation direction is expressed as follows: （21）； Similarly, cumulative direction The equivalent cumulative direction of writing is expressed as follows: （22）； Then combine and Equivalent azimuth direction The specific expression is as follows: （23）； Then along the height direction Distance and direction and direction Discretizing the imaging space yields the following discrete-form expression for the analytical representation of SAR imaging rendering: （24）； in, Represents the number of spatial sampling points, variable and These represent sampling points in the height and distance directions, respectively. Indicates the interval used for distance direction. Indicates the interval for height-direction sampling. Indicates density, Indicates the contribution of scattered energy; S5. Based on step S4, design the implicit neural network and extract the three-dimensional point cloud to complete the three-dimensional reconstruction of the single-channel SAR moving ship. Scattering energy contribution Position of discrete points in space and radar observation direction Strong correlation, and density Only with position If they are related, their implicit expressions are as follows: （25）； （26）； in, Representing spatial coordinates and observation direction Contribution of Scattered Energy The implicit mapping relationship, Representing spatial coordinates With density The implicit mapping relationship; Fitting using implicit neural representation and The mapping relationship between them, and and The mapping relationship between them is used to construct an implicit neural network including a multilayer perceptron; the implicit neural network includes three cooperating modules: a motion parameter module, a neural representation module, and a joint optimization module; The motion parameter module uses platform parameters and ship motion parameters to construct a projection matrix. The neural representation module is essentially an improved multilayer perceptron (MLP), whose input is spatial coordinates. and observation direction The output is the contribution of scattering energy. With density A joint optimization module with skip connections is used to establish the loss function. Based on the recorded gradient information, two Adam optimizers are used to synchronously update the MLP parameters in the neural representation module and the ship motion parameters in the motion parameter module. The implicit neural network transforms the problem of estimating projection transformation into the problem of estimating ship motion parameters. It treats the ship's motion parameters as learnable variables and sets up two optimizers to jointly optimize the network weights and ship motion parameters, thereby obtaining the three-dimensional point cloud of the ship target and realizing the three-dimensional reconstruction of a moving ship using single-channel SAR.

2. The single-channel SAR moving ship three-dimensional reconstruction method according to claim 1, characterized in that, In step S5, the joint optimization by the two optimizers is as follows: 1) Utilizing ship motion parameters ( Generate a two-dimensional SAR image, and based on the calibration results, convert the pixel coordinate system of the two-dimensional SAR image into an imaging coordinate system with real physical scale; 2) with the first The center of the SAR image is the origin. Spatially discrete sampling is performed along the propagation and accumulation directions. The projection transformation formula of equation (19) is used to transform the imaging coordinate system to the local coordinate system. In the middle, obtain the position coordinates and observation direction ; 3) The implicit neural network will and As input, obtain and The reprojection process of the two-dimensional SAR image is completed using the imaging rendering formula of equation (20); 4) The joint optimization module uses mean squared error as the loss function in the implicit neural network training process to supervise the consistency between reprojected SAR images and other SAR images. The expression is as follows: （27）； in, Indicates reprojected pixels. Indicates the number of pixels in the input image. Indicates the image height. This represents the image width; and during backpropagation, the two optimizers synchronously update the network parameters and ship motion parameters. 5) Using the acquired long sequence of 2D images of the moving SAR ship target as input, initialize the ship motion parameters. Train the network according to the optimization criteria provided by the loss function. The optimizer synchronously updates the implicit neural network weight parameters and the ship motion parameters. After training, perform discrete sampling in the 3D space to obtain... and The output; based on The nonnegativity of the judgment space determines whether a point belongs to the reconstruction target. It is assumed that there are scattering points in space, and these points are preserved. The spatial network is traversed one by one to finally obtain the three-dimensional point cloud of the ship target.

Images