A UAV-borne SAR imaging method based on complex convolution Unet

Abstract

This invention relates to the field of UAV-borne SAR imaging technology, specifically to a UAV-borne SAR imaging method based on complex convolution Unet, comprising: inputting a SAR complex feature map into a trained SAR imaging model and outputting a predicted SAR image; in the SAR imaging model: an encoder extracts abstract complex features layer by layer through a series of complex downsampling modules to obtain multi-scale low-resolution complex feature maps; a decoder recovers spatial resolution and image details layer by layer through a series of complex upsampling modules to obtain high-resolution complex feature maps; the low-resolution complex feature map output by the encoder is connected to the corresponding level of the complex upsampling module in the decoder; and the high-resolution complex feature map is converted into a complex image of the same dimension as the input SAR complex feature map as the predicted SAR image. This invention can learn and correct complex nonlinear motion distortions in the raw SAR echo end-to-end, achieving high-precision, well-focused UAV-borne SAR imaging.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) SAR imaging technology, and specifically to an UAV SAR imaging method based on complex convolution Unet. Background Technology

[0002] Synthetic Aperture Radar (SAR) is an active microwave remote sensing imaging system. With its all-weather, all-day operation and high-resolution penetration capabilities, it holds an irreplaceable strategic position in fields such as military reconnaissance, environmental monitoring, geological exploration, and disaster assessment. In recent years, UAV-borne SAR has become a cutting-edge hot topic in the field of remote sensing due to its high mobility, low cost, flexible deployment, and rapid response capabilities.

[0003] The raw echo data received by a SAR system is inherently complex, and its form is as follows: The amplitude reflects the backscattering intensity of the target, while the phase carries the precise distance information (time delay) between the sensor and the target, as well as the coherence characteristics of the signal.

[0004] The high mobility of UAV-borne SAR presents significant technical challenges. The small size and light weight of UAV platforms make them highly susceptible to interference from atmospheric turbulence and wind shear, leading to complex nonlinear motion trajectories and high-frequency vibrations. This non-ideal motion introduces severe and spatially variable phase errors into the raw SAR echo data, posing a primary challenge for UAV-borne SAR. Traditional SAR imaging algorithms (such as RDA and CSA) and their motion compensation (MoCo) methods (such as PGA and sub-aperture methods) are typically based on simplified error models (e.g., linear or low-order polynomials). When faced with the complex, high-order, spatially variable, and nonlinear phase errors introduced by UAVs, these algorithms are severely inadequate in their compensation capabilities, resulting in severe defocusing, geometric distortion, and high sidelobes in the final SAR images, significantly reducing image quality and usability. Especially for subsequent advanced interpretation tasks such as target detection and recognition, this defocusing caused by motion errors can obscure target features (such as strong scattering points and edges) within sidelobes and background clutter, leading to severe false alarms and missed alarms in subsequent algorithms. This is one of the core obstacles currently hindering the application of UAV-borne SAR.

[0005] Deep learning is considered an effective approach to solving this complex nonlinear mapping (i.e., from error-laden echoes to sharp images). However, standard convolutional neural networks (CNNs) are designed for processing real-valued data and face the following problems when dealing with the inherently complex data of SAR:

[0006] 1) Information loss (amplitude processing). Existing methods only extract the amplitude of SAR echo data as network input, completely discarding phase information. In the context of UAV-borne SAR, this causes a "fatal" defect, that is, the model is completely unable to perceive the motion error that causes image defocusing (which is mainly reflected in the phase), and therefore cannot be corrected at its root.

[0007] 2) Algebraic structure disruption (channel separation). Existing methods disrupt complex data... Split into real part and the virtual part Two independent real-valued channels are then fed into a standard real-valued CNN. These approaches have a fundamental flaw: standard real-valued convolution (nn.Conv2d) treats the real and imaginary parts as two unrelated feature maps linearly combined, completely destroying the inherent algebraic structure of complex numbers (e.g., ...). (and its multiplication rules). This processing method leads to severe feature distortion, making it difficult for the network to learn and interpret the true physical meaning contained in the complex echoes (i.e., the complex coupling of target information and motion error information).

[0008] 3) Some existing complex neural networks still have problems with unsuitable component design. For example, applying ReLU (CReLU) to the real and imaginary parts separately will arbitrarily "cut" the complex plane and destroy the phase continuity; applying max pooling to the real and imaginary parts separately is not physically meaningful and leads to the confusion of amplitude and phase information; applying batch normalization (BN) to the real and imaginary parts separately ignores the inherent statistical correlation (covariance) between the two.

[0009] In summary, the core challenge of UAV-borne SAR imaging lies in how to handle and correct the complex phase errors introduced by platform motion. The fundamental bottleneck of existing technologies (whether traditional MoCo or standard real-valued CNN) is that they cannot natively and faithfully process complex data to achieve high-quality imaging while adhering to the rules of complex algebra. Summary of the Invention

[0010] To address the shortcomings of the existing technologies, the technical problem to be solved by this invention is: how to provide an unmanned aerial vehicle (UAV) SAR imaging method based on complex convolution Unet, and to design a new deep learning component (including a deep complex batch normalization layer, a modulus activation function layer, a complex downsampling layer, and a complex upsampling layer) that follows the rules of complex algebra and conforms to the statistical characteristics of complex numbers. This component can learn and correct complex nonlinear motion distortions end-to-end from the raw UAV SAR echoes containing severe phase errors, thereby achieving high-precision, well-focused UAV SAR imaging.

[0011] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0012] An unmanned aerial vehicle (UAV) SAR imaging method based on complex convolution Unet includes:

[0013] S1: Acquire the SAR complex echo data to be processed, and stack the SAR complex echo data in the form of real part-imaginary part channels to obtain the SAR complex feature map;

[0014] S2: Input the SAR complex feature map into the trained SAR imaging model and output a predicted SAR image with the same dimensions as the SAR complex feature map;

[0015] The processing steps when training a SAR imaging model include:

[0016] S201: Obtain the SAR complex feature map used as training samples and its corresponding ground truth SAR image;

[0017] S202: Input the SAR complex feature map into the encoder, and extract the abstract complex features layer by layer through a series of complex downsampling modules to obtain a multi-scale low-resolution complex feature map;

[0018] S203: Input the low-resolution complex feature map of the last scale into the decoder, and restore the spatial resolution and image details layer by layer through a series of complex upsampling modules to obtain a high-resolution complex feature map; wherein the low-resolution complex feature maps of other scales output by the encoder are connected to the complex upsampling modules of the corresponding levels of the decoder in a skip connection.

[0019] S204: Input the high-resolution complex feature map output by the decoder into the output layer, and convert the high-resolution complex feature map into a predicted SAR image with the same dimensions as the input SAR complex feature map;

[0020] S205: Calculate the loss function based on the predicted SAR image and the corresponding ground truth SAR image, and optimize the parameters of the SAR imaging model in reverse.

[0021] S206: Repeat steps S201 to S205 to iteratively train the SAR imaging model until the model converges or the maximum number of iterations is reached.

[0022] Preferably, in step S202, the encoder includes a cascaded complex double convolution module and four complex downsampling modules; the complex downsampling module includes a cascaded complex downsampling layer and a complex double convolution module; the complex double convolution module includes two cascaded complex double convolution sub-modules;

[0023] The complex double convolution submodule includes a cascaded deep complex convolution submodule, a deep complex batch normalization submodule, and a modulo activation function layer. The input features of the complex double convolution submodule and the output features of the modulo activation function layer are channel-aligned by a complex 1×1 convolution layer and then element-wise added to generate the output features of the complex double convolution submodule. The deep complex convolution submodule includes three cascaded deep complex convolution layers. The deep complex batch normalization submodule includes two cascaded deep complex batch normalization layers.

[0024] Preferably, in step S203, the decoder includes four cascaded complex upsampling modules; each complex upsampling module includes a cascaded complex upsampling layer and a complex double convolution module.

[0025] Preferably, in step S203, the output features of the complex double convolution module in the encoder are made into a skip connection with the input features of the fourth-level complex upsampling module in the decoder;

[0026] The output features of the first-stage complex downsampling module in the encoder are skipped to the input features of the third-stage complex upsampling module in the decoder;

[0027] The output features of the second-stage complex downsampling module in the encoder are skipped to the input features of the second-stage complex upsampling module in the decoder;

[0028] The output features of the third-stage complex downsampling module in the encoder are connected to the input features of the first-stage complex upsampling module in the decoder in a skip connection.

[0029] Preferably, the processing logic for the deep complex batch normalization layer includes:

[0030] S2031: Obtain the set of complex feature maps for the current batch of input to the SAR imaging model; where each complex feature map consists of a real tensor and an imaginary tensor;

[0031] S2032: Calculate the mean of the real tensors of all complex feature maps in the current batch. The mean of the imaginary part tensor of the sum ;

[0032] S2033: For the complex feature map of the current input to the deep complex batch normalized layer, from its real tensor... and imaginary tensor Subtract the mean of the real tensor from each and the mean of the imaginary part tensor The real part after centralization is obtained. and the virtual part ;

[0033] The formula is expressed as:

[0034] ;

[0035] ;

[0036] S2034: Based on the centralized real part and the virtual part Calculate shared variance ;

[0037] The formula is expressed as:

[0038] ;

[0039] In the formula: This indicates the calculation of the expectation;

[0040] S2035: Through the centralized real part and the virtual part Divide by shared variance square root The normalized real tensor is obtained. and imaginary tensor ; Represents a predefined, extremely small positive number;

[0041] S2036: Based on learnability Affine transformation matrix and bias vector Normalized real tensor and imaginary tensor Convert to real tensor and imaginary tensor ;

[0042] The formula is expressed as:

[0043] ;

[0044] In the formula: , , , express Affine transformation matrix Learnable affine transformation coefficients are used to achieve a joint linear transformation of the real and imaginary parts of the normalized complex number. , These represent the bias vectors respectively. The learnable bias parameters corresponding to the real and imaginary parts are used to adjust the translation of the features after linear transformation;

[0045] S2037: Based on Real Tensors and imaginary tensor Construct complex feature maps output by a deep complex batch normalization layer.

[0046] Preferably, the processing logic of the modulo activation function layer includes:

[0047] S2131: Obtain the real tensor of the input to the modulo activation function layer. and imaginary tensor Complex number characteristic diagram;

[0048] S2132: Decompose the input complex feature map into amplitudes. and phase ;

[0049] The formula is expressed as:

[0050] ;

[0051] ;

[0052] In the formula: Represents the two-parameter arctangent function; Represents a predefined, extremely small positive number;

[0053] S2133: Regarding amplitude Perform a nonlinear activation operation to obtain the activation amplitude. ;

[0054] The formula is expressed as:

[0055] ;

[0056] In the formula: express Activation function;

[0057] S2134: Phase-based and the magnitude of activation Calculate the real part tensor and imaginary tensor ;

[0058] The formula is expressed as:

[0059] ;

[0060] ;

[0061] S2135: Based on Real Tensors and imaginary tensor Construct complex feature maps from the output of the modulo activation function layer.

[0062] Preferably, the processing steps for the complex downsampling layer include:

[0063] S2231: Obtain the complex feature map of the input to the complex downsampling layer. , , , This represents the number of channels, height, and width of a complex feature map. Indicates the first Channel, location ( , The complex value of , which includes a real part and an imaginary part;

[0064] S2232: For each channel Calculate the corresponding amplitude diagrams respectively. ;

[0065] S2233: Through Max pooling is performed on the magnitude plot of each channel in a separate max pooling window, and the index of the maximum value position within each pooling window is recorded; where the maximum value position index... Indicates channel amplitude diagram In the middle, position ( , The corresponding maximum value of the original coordinates () );

[0066] S2234: Based on the maximum value position index within each pooling window, from the input complex feature map Extract the complete complex value at the corresponding position to obtain the low-resolution complex feature map output by the complex downsampling layer. , = , = .

[0067] Preferably, the processing steps for the complex upsampling layer include:

[0068] S2331: Obtain the real tensor of the input to the modulo activation function layer. and imaginary tensor Complex number characteristic diagram;

[0069] S2332: Decompose the input complex feature map into amplitudes. and phase ;

[0070] The formula is expressed as:

[0071] ;

[0072] ;

[0073] In the formula: Represents the two-parameter arctangent function; Represents a predefined, extremely small positive number;

[0074] S2333: Amplitude is calculated using standard bilinear interpolation. Magnified to the target resolution, to obtain the high-resolution amplitude. ;

[0075] S2334: Phase Convert to two consecutive real values: the cosine of the phase. Sine of phase ;

[0076] S2335: Cosine of the phase Sine of phase Perform bilinear interpolation separately to obtain the cosine graph. Sine graph ;

[0077] S2336: Based on the two-parameter arctangent function and High-resolution phase recovery ;

[0078] The formula is expressed as:

[0079] ;

[0080] In the formula: Represents the two-parameter arctangent function;

[0081] S2337: Based on high-resolution amplitude and high resolution phase Reconstruct high-resolution complex feature maps from the output of the complex upsampling layer.

[0082] Preferably, in step S204, the calculation formula for the output layer is expressed as follows:

[0083] ;

[0084] In the formula: Represents the predicted SAR image; , This represents the real and imaginary tensors in the high-resolution complex feature map output by the decoder.

[0085] Preferably, in step S205, the loss function The calculation formula is expressed as:

[0086] ;

[0087] In the formula: Represents the predicted SAR image; Represents a true-value SAR image; The L1 loss function minimizes the Manhattan distance between the predicted SAR image and the ground truth SAR image by calculating the difference between their magnitudes.

[0088] Compared with existing technologies, the UAV-borne SAR imaging method based on complex convolution Unet in this invention has the following advantages:

[0089] This invention designs a deep learning component system that follows the rules of complex algebra and conforms to the statistical properties of complex numbers, including a complex batch normalization layer, a modulo activation function layer, a complex downsampling layer, and a complex upsampling layer, for constructing an unmanned aerial vehicle (UAV) SAR imaging network based on complex convolution U-Net.

[0090] By performing end-to-end feature learning and modeling on the raw SAR echo data in the complex domain, the method of this invention can effectively characterize and correct complex nonlinear motion distortions including phase errors, thereby achieving high-resolution, high-focusing-performance UAV-borne SAR imaging.

[0091] Specifically:

[0092] The deep complex batch normalization layer designed in this invention does not independently calculate the variances of the real and imaginary parts. Instead, it calculates the expectation of the magnitude of the centered complex data. Unlike standard Batch Normalization (BN) layers which use two independent scaling factors, this deep complex batch normalization layer employs a learnable affine transformation matrix and a bias vector to achieve normalization. This matrix operation allows the network to explicitly learn and recover the covariance relationship between the real and imaginary parts (modeled by the off-diagonal elements of the affine transformation matrix), solving the core problem of training instability in deep complex networks. The deep complex batch normalization layer designed in this invention significantly enhances the network's representational ability, solves the problem of feature distortion, and improves the network's stability and expressive power under varying complex feature distributions, thereby promoting stable training and convergence of deep complex networks.

[0093] The modulus activation function layer designed in this invention introduces nonlinearity while avoiding disruption of the complex number's inherent structure (e.g., the CReLU's cutting of the complex plane) through an activation function operating in the polar coordinate (amplitude and phase) domain. Furthermore, it decouples the activation operation from the phase, applying nonlinear activation only to the modulus (amplitude) of the complex number while maintaining the phase, thus avoiding damage to the phase structure of the complex features. Compared to activating the real and imaginary parts separately in Cartesian coordinates, this modulus activation strategy helps maintain the structural consistency of complex signals in the polar coordinate domain, reduces phase information distortion, and is more suitable for the feature modeling needs of SAR complex data.

[0094] In the complex downsampling layer designed in this invention, the max pooling window is only applied to... The algorithm generates amplitude maps, and instead of outputting the pooled amplitude values, it outputs the spatial indices of these maximum amplitude values ​​within the pooling window. These maximum amplitude indices are then used as selectors to precisely extract the complete complex values ​​at corresponding locations from the original, complete complex feature map (containing both real and imaginary parts) through index selection operations. This invention, through this "amplitude index-based complex selection" strategy, ensures that the downsampling process retains the feature points with the strongest signal energy and their complete complex values ​​(real and imaginary parts), avoiding the ambiguity of physical meaning and information confusion caused by separate pooling of the real and imaginary parts, thereby improving the accuracy and quality of UAV-borne SAR imaging.

[0095] In the complex upsampling layer designed in this invention, standard bilinear interpolation is used to amplify the amplitude to the target resolution. Due to phase... exist and There are phase transitions (i.e., phase entanglement) between them, and direct interpolation will lead to severe spatial artifacts. This invention does not use direct interpolation. Instead, it first converts the phase into two consecutive real-valued representations, namely the cosine and sine of the phase. Then, it performs bilinear interpolation on the cosine and sine of the phase, and finally applies a two-parameter arctangent function to accurately recover the interpolated cosine and sine graphs. The complex upsampling layer of this invention uses interpolation... and To avoid phase-wrapping artifacts, and to smooth the interpolated phase map using learnable convolution kernels, the spatial continuity and smoothness of the high-resolution feature map are ensured during the reconstruction (dimensionality upscaling) process, thereby further improving the quality of UAV-borne SAR imaging. Attached Figure Description

[0096] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0097] Figure 1 This is a network structure diagram of the SAR imaging model (complex U-Net).

[0098] Figure 2 This is a network structure diagram of the ComplexDoubleConv submodule.

[0099] Figure 3 The image shows the results of the network experiment. Detailed Implementation

[0100] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Components of the embodiments of the present invention described and illustrated herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0101] The following will be further described in detail through specific embodiments:

[0102] Embodiment:

[0103] In this embodiment, an airborne SAR imaging method based on a complex convolutional Unet is disclosed.

[0104] The airborne SAR imaging method based on a complex convolutional Unet includes:

[0105] S1: Obtain the SAR complex echo data to be processed, and stack the SAR complex echo data in the form of real part - imaginary part channels to obtain a SAR complex feature map; where the SAR complex feature map , , , represent the number of channels, height, and width of the complex feature map; where represents the th channel, the complex value at the position ( , ), and this complex value includes a real part and an imaginary part;

[0106] S2: Input the SAR complex feature map into the trained SAR imaging model (Complex U-Net), and output a complex image (high-resolution) with the same dimension as the SAR complex feature map as the predicted SAR image;

[0107] As Figure 1 shown, the processing steps during training the SAR imaging model include:

[0108] S201: Obtain the SAR complex feature map used as a training sample and its corresponding true SAR image;

[0109] S202: Input the SAR complex feature map into the encoder, and layer by layer extract abstract complex features through a series of complex downsampling modules (ComplexDown) to obtain a multi-scale low-resolution complex feature map;

[0110] S203: Input the low-resolution complex feature map of the last scale into the decoder, and restore the spatial resolution and image details layer by layer through a series of complex upsampling modules (ComplexUp) to obtain a high-resolution complex feature map; the low-resolution complex feature maps of other scales output by the encoder are connected to the complex upsampling modules of the corresponding levels of the decoder in a skip connection.

[0111] S204: Input the high-resolution complex feature map output by the decoder into the output layer, and convert the high-resolution complex feature map into a (high-resolution) complex image with the same dimension as the input SAR complex feature map as the predicted SAR image;

[0112] S205: Calculate the loss function based on the predicted SAR image and the corresponding ground truth SAR image, and optimize the parameters of the SAR imaging model in reverse.

[0113] S206: Repeat steps S201 to S205 to iteratively train the SAR imaging model until the model converges or the maximum number of iterations is reached.

[0114] The entire data flow and computation of the SAR imaging model are completed in the complex domain, enabling the model to learn a nonlinear mapping from complex echoes with phase errors to clear complex images.

[0115] This invention enables the model to implicitly learn and correct complex, nonlinear phase errors introduced by unstable flight of the UAV platform through end-to-end learning in the full complex domain. Compared to traditional algorithms and real-valued CNNs, this invention does not require precise prior motion parameters (such as GPS / INS) to reconstruct high-focus quality images from defocused raw echoes. Furthermore, the innovative components of this invention, such as the deep complex batch normalization layer, modulo activation function layer, complex downsampling layer, and complex upsampling layer, are specifically designed for complex data. This ensures that the network can handle complex signals more effectively during feature extraction, dimensionality reduction, and reconstruction, avoiding the information distortion and structural damage inherent in standard real-valued CNNs when processing complex data (such as channel separation). This is the foundation for its successful achievement of high-quality imaging. Compared to the complex, iterative motion compensation algorithms (such as PGA and autofocus algorithms) in traditional SAR imaging, this invention uses a forward propagation process after training, resulting in fast computation and high efficiency. This gives it the potential for near real-time or onboard / aircraft processing on UAV platforms, greatly improving the rapid response capability of UAV-borne SAR systems.

[0116] To better illustrate the technical solution of the present invention, this embodiment will be described in more detail through the following parts.

[0117] I. Encoder

[0118] like Figure 1 As shown, the encoder includes a cascaded complex double convolution module and four complex downsampling modules; the complex downsampling module includes a cascaded complex downsampling layer and a complex double convolution module; the complex double convolution module includes two cascaded complex double convolution sub-modules (ComplexDoubleConv).

[0119] like Figure 2 As shown, the complex double convolution submodule includes a cascaded deep complex convolution submodule, a deep complex batch normalization submodule, and a modulo activation function layer. The input features of the complex double convolution submodule and the output features of the modulo activation function layer are channel-aligned by a complex 1×1 convolution layer and then element-wise added to generate the output features of the complex double convolution submodule. The deep complex convolution submodule includes three cascaded deep complex convolution layers. The deep complex batch normalization submodule includes two cascaded deep complex batch normalization layers.

[0120] In this embodiment, the deep complex convolutional layer (ComplexConv2d) is an existing module, which essentially belongs to complex convolution operations. Its network structure is consistent with that of a regular two-dimensional convolutional layer, except that during the computation process, convolution operations are performed separately on the real and imaginary parts of the input features, and then combined according to the rules of complex multiplication to achieve a linear transformation of the complex features. The network structure of the complex 1×1 convolutional layer is consistent with that of a regular 1×1 convolutional layer, except that during the computation process, convolution operations are performed separately on the real and imaginary parts of the input features, and then combined according to the rules of complex multiplication.

[0121] II. Decoder

[0122] like Figure 1 As shown, the decoder includes four cascaded complex upsampling modules; each complex upsampling module includes a cascaded complex upsampling layer and a complex double convolution module.

[0123] Specifically, the output features of the complex double convolution module in the encoder are skipped to the input features of the fourth-level complex upsampling module in the decoder;

[0124] The output features of the first-stage complex downsampling module in the encoder are skipped to the input features of the third-stage complex upsampling module in the decoder;

[0125] The output features of the second-stage complex downsampling module in the encoder are skipped to the input features of the second-stage complex upsampling module in the decoder;

[0126] The output features of the third-stage complex downsampling module in the encoder are connected to the input features of the first-stage complex upsampling module in the decoder in a skip connection.

[0127] III. ComplexBN2d Layer with Deep Complex Batch Normalization

[0128] To address the instability issue in training deep complex networks and to correctly model the statistical properties of complex data, this invention designs a deep complex batch normalization layer.

[0129] Specifically, the processing logic of the deep complex batch normalization layer includes:

[0130] S2031: Obtain the set of complex feature maps for the current batch from the input of the SAR imaging model. Each complex feature map , Indicates batch size, , , The number of channels, height, and width of the complex feature map are represented; each complex feature map consists of a real part tensor and an imaginary part tensor.

[0131] S2032: Calculate the mean of the real tensors of all complex feature maps in the current batch. The mean of the imaginary part tensor of the sum ;

[0132] S2033: For the complex feature map of the current input to the deep complex batch normalized layer, from its real tensor... and imaginary tensor Subtract the mean of the real tensor from each and the mean of the imaginary part tensor The real part after centralization is obtained. and the virtual part ;

[0133] The formula is expressed as:

[0134] ;

[0135] ;

[0136] S2034: Based on the centralized real part and the virtual part Calculate shared variance ;

[0137] The formula is expressed as:

[0138] ;

[0139] In the formula: This indicates the calculation of the expectation;

[0140] S2035: Through the centralized real part and the virtual part Divide by shared variance square root The normalized real tensor is obtained. and imaginary tensor ; This is a preset, extremely small positive number, used to prevent the denominator from being zero and to improve the stability of numerical calculations;

[0141] S2036: Based on learnability Affine transformation matrix and bias vector Normalized real tensor and imaginary tensor Convert to real tensor and imaginary tensor ;

[0142] The formula is expressed as:

[0143] ;

[0144] In the formula: , , , express Affine transformation matrix Learnable affine transformation coefficients are used to achieve a joint linear transformation of the real and imaginary parts of the normalized complex number. , These represent the bias vectors respectively. The learnable bias parameters corresponding to the real and imaginary parts are used to translate and adjust the features after linear transformation. Through the above affine transformation, the deep complex batch normalization layer can enhance the network's adaptability to different complex feature distributions while maintaining the complex feature structure.

[0145] S2037: Based on Real Tensors and imaginary tensor Construct complex feature maps output by a deep complex batch normalization layer.

[0146] The deep complex batch normalization layer designed in this invention does not independently calculate the variances of the real and imaginary parts. Instead, it calculates the expectation of the magnitude of the centered complex data. Unlike standard Batch Normalization (BN) layers which use two independent scaling factors, this deep complex batch normalization layer employs a learnable affine transformation matrix and a bias vector to achieve normalization. This matrix operation allows the network to explicitly learn and recover the covariance relationship between the real and imaginary parts (modeled by the off-diagonal elements of the affine transformation matrix), solving the core problem of training instability in deep complex networks. The deep complex batch normalization layer designed in this invention significantly enhances the network's representational ability, solves the problem of feature distortion, and improves the network's stability and expressive power under varying complex feature distributions, thereby promoting stable training and convergence of deep complex networks.

[0147] IV. Modular Activation Function Layer (ModReLU)

[0148] While introducing nonlinearity, this invention employs a transformation method more suitable for SAR complex data structures to facilitate the learning of imaging features. To avoid disrupting the structure of the complex data itself (such as the CReLU's cutting of the complex plane) while introducing nonlinearity, this invention designs an activation function that operates in the polar coordinate (amplitude and phase) domain.

[0149] Specifically, the processing logic of the modulo activation function layer includes:

[0150] S2131: Obtain the real tensor of the input to the modulo activation function layer. and imaginary tensor Complex number characteristic diagram;

[0151] S2132: Decompose the input complex feature map into amplitudes. (Magnitude) and phase (Phase);

[0152] The formula is expressed as:

[0153] ;

[0154] ;

[0155] In the formula: Represents the two-parameter arctangent function; Represents a predefined, extremely small positive number;

[0156] S2133: Regarding amplitude Perform a nonlinear activation operation to obtain the activation amplitude. ;

[0157] The formula is expressed as:

[0158] ;

[0159] In the formula: express Activation function;

[0160] S2134: Phase-based and the magnitude of activation Calculate the real part tensor and imaginary tensor ;

[0161] The formula is expressed as:

[0162] ;

[0163] ;

[0164] S2135: Based on Real Tensors and imaginary tensor Construct complex feature maps from the output of the modulo activation function layer.

[0165] The modulus activation function layer designed in this invention introduces nonlinearity while avoiding disruption of the complex number's inherent structure (e.g., the CReLU's cutting of the complex plane) through an activation function operating in the polar coordinate (amplitude and phase) domain. Furthermore, it decouples the activation operation from the phase, applying nonlinear activation only to the modulus (amplitude) of the complex number while maintaining the phase, thus avoiding damage to the phase structure of the complex features. Compared to activating the real and imaginary parts separately in Cartesian coordinates, this modulus activation strategy helps maintain the structural consistency of complex signals in the polar coordinate domain, reduces phase information distortion, and is more suitable for the feature modeling needs of SAR complex data.

[0166] V. Complex Downsampling Layer Based on Amplitude Index

[0167] In order to preserve the most important complex signal information during dimensionality reduction (pooling), this invention designs a complex pooling method.

[0168] Specifically, the processing steps of the complex downsampling layer include:

[0169] S2231: Obtain the complex feature map of the input to the complex downsampling layer. , , , This represents the number of channels, height, and width of a complex feature map. Indicates the first Channel, location ( , The complex value of , which includes a real part and an imaginary part;

[0170] S2232: For each channel Calculate the corresponding amplitude diagrams respectively. ;

[0171] S2233: Through Max pooling windows perform max pooling operations on the magnitude plots of each channel separately, and record the index of the maximum value position within each pooling window; where the maximum value position index... Indicates channel amplitude diagram In the middle, position ( , The corresponding maximum value of the original coordinates () );

[0172] S2234: Based on the maximum value position index within each pooling window, from the input complex feature map Extract the complete complex value at the corresponding position to obtain the low-resolution complex feature map output by the complex downsampling layer. , = , = .

[0173] In the complex downsampling layer designed in this invention, the max pooling window is only applied to... The algorithm generates amplitude maps, and instead of outputting the pooled amplitude values, it outputs the spatial indices of these maximum amplitude values ​​within the pooling window. These maximum amplitude indices are then used as selectors to precisely extract the complete complex values ​​at corresponding locations from the original, complete complex feature map (containing both real and imaginary parts) through index selection operations. This invention, through this "amplitude index-based complex selection" strategy, ensures that the downsampling process retains the feature points with the strongest signal energy and their complete complex values ​​(real and imaginary parts), avoiding the ambiguity of physical meaning and information confusion caused by separate pooling of the real and imaginary parts, thereby improving the accuracy and quality of UAV-borne SAR imaging.

[0174] VI. Complex Upsampling Layer Based on Trigonometric Function Domain Interpolation (ComplexUp)

[0175] In high-resolution reconstruction (upsampling), it is necessary to achieve smoother and more accurate complex feature reconstruction, avoid artifacts, and ensure high-quality imaging. To solve the phase interpolation problem, this invention designs a method for upsampling in the continuous trigonometric function domain.

[0176] Specifically, the processing steps of the complex upsampling layer include:

[0177] S2331: Obtain the real tensor of the input to the modulo activation function layer. and imaginary tensor Complex number characteristic diagram;

[0178] S2332: Decompose the input complex feature map into amplitudes. (Magnitude) and phase (Phase);

[0179] The formula is expressed as:

[0180] ;

[0181] ;

[0182] In the formula: Represents the two-parameter arctangent function; Represents a predefined, extremely small positive number;

[0183] S2333: Amplitude is calculated using standard bilinear interpolation. Magnified to the target resolution, to obtain the high-resolution amplitude. ;

[0184] S2334: Phase Convert to two consecutive real values: the cosine of the phase. Sine of phase ;

[0185] S2335: Cosine of the phase Sine of phase Perform bilinear interpolation separately to obtain the cosine graph. Sine graph ;

[0186] S2336: Based on the two-parameter arctangent function and High-resolution phase recovery ;

[0187] The formula is expressed as:

[0188] ;

[0189] In the formula: This represents the two-parameter arctangent function, used to calculate the corresponding phase angle based on the input sine and cosine components. Its output phase range is (−π,π] to ensure the continuity and uniqueness of phase recovery.

[0190] S2337: Based on high-resolution amplitude and high resolution phase Reconstruct high-resolution complex feature maps from the output of the complex upsampling layer.

[0191] In the complex upsampling layer designed in this invention, standard bilinear interpolation is used to amplify the amplitude to the target resolution. Due to phase... exist and There are phase transitions (i.e., phase entanglement) between them, and direct interpolation will lead to severe spatial artifacts. This invention does not use direct interpolation. Instead, it first converts the phase into two consecutive real-valued representations, namely the cosine and sine of the phase. Then, it performs bilinear interpolation on the cosine and sine of the phase, and finally applies a two-parameter arctangent function to accurately recover the interpolated cosine and sine graphs. The complex upsampling layer of this invention uses interpolation... and To avoid phase-wrapping artifacts, and to smooth the interpolated phase map using learnable convolution kernels, the spatial continuity and smoothness of the high-resolution feature map are ensured during the reconstruction (dimensionality upscaling) process, thereby further improving the quality of UAV-borne SAR imaging.

[0192] VII. Output Layer

[0193] The final layer of the SAR imaging model (complex U-Net) outputs a high-resolution complex image with the same dimensions as the input echo data.

[0194] Specifically, the calculation formula for the output layer is expressed as follows:

[0195] ;

[0196] In the formula: express The real-valued, high-focus quality prediction map is the predicted SAR image; , This represents the real and imaginary tensors in the high-resolution complex feature map output by the decoder.

[0197] VIII. Loss Function

[0198] During the training phase, the prediction graph This will be compared with the corresponding ideal, motion-error-free "ground truth" image. The differences between them are compared. The L1 loss is used to calculate the difference. This loss value is then passed through multiple complex modules via backpropagation to update all learnable parameters in the network (including complex convolutional kernels and parameters in ComplexBN2d layers). Affine transformation matrix and bias ).

[0199] Specifically, loss function The calculation formula is expressed as:

[0200] ;

[0201] In the formula: Represents the predicted SAR image; Represents a true-value SAR image; The L1 loss function minimizes the Manhattan distance between the predicted SAR image and the ground truth SAR image by calculating the difference between their magnitudes.

[0202] III. Experimental Instructions

[0203] In this embodiment, experiments were conducted on the UAV-borne SAR imaging method based on complex convolution Unet proposed in this invention. The experimental results are as follows: Figure 3 As shown. Wherein:

[0204] The predicted values ​​of the method of the present invention are as follows: Range: Peak sidelobe ratio (PSLR) = -13.32 dB, Integrated sidelobe ratio (ISLR) = -10.03 dB; Azimuth: Peak sidelobe ratio (PSLR) = -13.65 dB, Integrated sidelobe ratio (ISLR) = -10.75 dB.

[0205] The corresponding actual values ​​are as follows: Range: Peak sidelobe ratio (PSLR) = -13.31 dB, Integrated sidelobe ratio (ISLR) = -9.96 dB; Azimuth: Peak sidelobe ratio (PSLR) = -13.60 dB, Integrated sidelobe ratio (ISLR) = -10.54 dB.

[0206] Combination Figure 3 As shown, the method of the present invention achieves superior sidelobe suppression in both the range and azimuth directions compared to traditional methods, demonstrating superior point target focusing and anti-interference capabilities.

[0207] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit the technical solutions. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. An unmanned aerial vehicle (UAV) SAR imaging method based on complex convolution Unet, characterized in that, include: S1: Acquire the SAR complex echo data to be processed, and stack the SAR complex echo data in the form of real part-imaginary part channels to obtain the SAR complex feature map; S2: Input the SAR complex feature map into the trained SAR imaging model and output a predicted SAR image with the same dimensions as the SAR complex feature map; The processing steps when training a SAR imaging model include: S201: Obtain the SAR complex feature map used as training samples and its corresponding ground truth SAR image; S202: Input the SAR complex feature map into the encoder, and extract the abstract complex features layer by layer through a series of complex downsampling modules to obtain a multi-scale low-resolution complex feature map; S203: Input the low-resolution complex feature map of the last scale into the decoder, and restore the spatial resolution and image details layer by layer through a series of complex upsampling modules to obtain a high-resolution complex feature map; wherein the low-resolution complex feature maps of other scales output by the encoder are connected to the complex upsampling modules of the corresponding levels of the decoder in a skip connection. S204: Input the high-resolution complex feature map output by the decoder into the output layer, and convert the high-resolution complex feature map into a predicted SAR image with the same dimensions as the input SAR complex feature map; S205: Calculate the loss function based on the predicted SAR image and the corresponding ground truth SAR image, and optimize the parameters of the SAR imaging model in reverse. S206: Repeat steps S201 to S205 to iteratively train the SAR imaging model until the model converges or the maximum number of iterations is reached.

2. The UAV-borne SAR imaging method based on complex convolution Unet as described in claim 1, characterized in that: In step S202, the encoder includes a cascaded complex double convolution module and four complex downsampling modules; the complex downsampling module includes a cascaded complex downsampling layer and a complex double convolution module; the complex double convolution module includes two cascaded complex double convolution sub-modules; The complex double convolution submodule includes a cascaded deep complex convolution submodule, a deep complex batch normalization submodule, and a modulo activation function layer. The input features of the complex double convolution submodule and the output features of the modulo activation function layer are channel-aligned by a complex 1×1 convolution layer and then element-wise added to generate the output features of the complex double convolution submodule. The deep complex convolution submodule includes three cascaded deep complex convolution layers. The deep complex batch normalization submodule includes two cascaded deep complex batch normalization layers.

3. The UAV-borne SAR imaging method based on complex convolution Unet as described in claim 2, characterized in that: In step S203, the decoder includes four cascaded complex upsampling modules; each complex upsampling module includes a cascaded complex upsampling layer and a complex double convolution module.

4. The UAV-borne SAR imaging method based on complex convolution Unet as described in claim 3, characterized in that: In step S203, the output features of the complex double convolution module in the encoder are made into a skip connection with the input features of the fourth-level complex upsampling module in the decoder; The output features of the first-stage complex downsampling module in the encoder are skipped to the input features of the third-stage complex upsampling module in the decoder; The output features of the second-stage complex downsampling module in the encoder are skipped to the input features of the second-stage complex upsampling module in the decoder; The output features of the third-stage complex downsampling module in the encoder are connected to the input features of the first-stage complex upsampling module in the decoder in a skip connection.

5. The UAV-borne SAR imaging method based on complex convolution Unet as described in claim 3, characterized in that: The processing logic of the deep complex batch normalization layer includes: S2031: Obtain the set of complex feature maps for the current batch of input to the SAR imaging model; where each complex feature map consists of a real tensor and an imaginary tensor; S2032: Calculate the mean of the real tensors of all complex feature maps in the current batch. The mean of the imaginary part tensor of the sum ; S2033: For the complex feature map of the current input to the deep complex batch normalized layer, from its real tensor... and imaginary tensor Subtract the mean of the real tensor from each and the mean of the imaginary part tensor The real part after centralization is obtained. and the virtual part ; The formula is expressed as: ； ； S2034: Based on the centralized real part and the virtual part Calculate shared variance ; The formula is expressed as: ； In the formula: This indicates the calculation of the expected value; S2035: Through the centralized real part and the virtual part Divide by shared variance square root The normalized real tensor is obtained. and imaginary tensor ; Represents a predefined, extremely small positive number; S2036: Based on learnability Affine transformation matrix and bias vector Normalized real tensor and imaginary tensor Convert to real tensor and imaginary tensor ; The formula is expressed as: ； In the formula: , , , express Affine transformation matrix Learnable affine transformation coefficients are used to achieve a joint linear transformation of the real and imaginary parts of the normalized complex number. , These represent the bias vectors respectively. The learnable bias parameters corresponding to the real and imaginary parts are used to adjust the translation of the features after linear transformation; S2037: Based on Real Tensors and imaginary tensor Construct complex feature maps output by a deep complex batch normalization layer.

6. The UAV-borne SAR imaging method based on complex convolution Unet as described in claim 3, characterized in that: The processing logic of the modulo activation function layer includes: S2131: Obtain the real tensor of the input to the modulo activation function layer. and imaginary tensor Complex number characteristic diagram; S2132: Decompose the input complex feature map into amplitudes. and phase ; The formula is expressed as: ； ； In the formula: Represents the two-parameter arctangent function; Represents a predefined, extremely small positive number; S2133: Regarding amplitude Perform a nonlinear activation operation to obtain the activation amplitude. ; The formula is expressed as: ； In the formula: express Activation function; S2134: Phase-based and the magnitude of activation Calculate the real part tensor and imaginary tensor ; The formula is expressed as: ； ； S2135: Based on Real Tensors and imaginary tensor Construct complex feature maps from the output of the modulo activation function layer.

7. The UAV-borne SAR imaging method based on complex convolution Unet as described in claim 3, characterized in that: The processing steps for complex downsampling layers include: S2231: Obtain the complex feature map of the input to the complex downsampling layer. , , , This represents the number of channels, height, and width of a complex feature map. Indicates the first Channel, location ( , The complex value of , which includes a real part and an imaginary part; S2232: For each channel Calculate the corresponding amplitude diagrams respectively. ; S2233: Through Max pooling is performed on the magnitude plot of each channel in a separate max pooling window, and the index of the maximum value position within each pooling window is recorded; where the maximum value position index... Indicates channel amplitude diagram In the middle, position ( , The corresponding maximum value of the original coordinates () ); S2234: Based on the maximum value position index within each pooling window, from the input complex feature map Extract the complete complex value at the corresponding position to obtain the low-resolution complex feature map output by the complex downsampling layer. , = , = .

8. The UAV-borne SAR imaging method based on complex convolution Unet as described in claim 3, characterized in that: The processing steps of the complex upsampling layer include: S2331: Obtain the real tensor of the input to the modulo activation function layer. and imaginary tensor Complex number characteristic diagram; S2332: Decompose the input complex feature map into amplitudes. and phase ; The formula is expressed as: ； ； In the formula: Represents the two-parameter arctangent function; Represents a predefined, extremely small positive number; S2333: Amplitude is calculated using standard bilinear interpolation. Magnified to the target resolution, to obtain the high-resolution amplitude. ; S2334: Phase Convert to two consecutive real values: the cosine of the phase. Sine of phase ; S2335: Cosine of the phase Sine of phase Perform bilinear interpolation separately to obtain the cosine graph. Sine diagram ; S2336: Based on the two-parameter arctangent function and High-resolution phase recovery ; The formula is expressed as: ； In the formula: Represents the two-parameter arctangent function; S2337: Based on high-resolution amplitude and high resolution phase Reconstruct high-resolution complex feature maps from the output of the complex upsampling layer.

9. The UAV-borne SAR imaging method based on complex convolution Unet as described in claim 1, characterized in that: In step S204, the calculation formula for the output layer is expressed as follows: ； In the formula: Represents the predicted SAR image; , This represents the real and imaginary tensors in the high-resolution complex feature map output by the decoder.

10. The UAV-borne SAR imaging method based on complex convolution Unet as described in claim 1, characterized in that: In step S205, the loss function The calculation formula is expressed as: ； In the formula: Represents the predicted SAR image; Represents a true-value SAR image; The L1 loss function minimizes the Manhattan distance between the predicted SAR image and the ground truth SAR image by calculating the difference between their magnitudes.

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