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Enhanced Radar Imaging Using a Complex-valued Convolutional Neural Network
Jingkun Gao, Bin Deng, Yuliang Qin, Hongqiang Wang, Xiang Li
TL;DR
Radar imaging needs methods that avoid the computational burden and modeling sensitivity of sparsity-driven reconstruction while improving image quality. The paper proposes a CV-CNN framework with radar-specific modifications and reports superior imaging quality and computational efficiency in simulations and experiments.
Problem
Sparsity-driven radar imaging can be time-consuming and sensitive to inaccurate modeling or unsuitable constraints, motivating investigation of CNN for radar imaging.
Method
The paper replaces the conventional imaging processor with a supervised CV-CNN and introduces radar-specific activation and output-layer modifications.
Results
For all SNR levels, CV-CNN achieves the best RMSE performance, with 0.0245 RMSE and 0.071 s time at 10dB.
Takeaways & Limitations
The proposed method shows superiority in radar imaging quality and computational efficiency, with recent results also indicating robustness and efficiency.
Abstract
from arXiv · showhide
Convolutional neural networks (CNN) have been successfully employed to tackle several remote sensing tasks such as image classification and show better performance than previous techniques. For the radar imaging community, a natural question is: Can CNN be introduced to radar imaging and enhance its performance? The presented letter gives an affirmative answer to this question. We firstly propose a processing framework by which a complex-valued CNN (CV-CNN) is used to enhance radar imaging. Then we introduce two modifications to the CV-CNN to adapt it to radar imaging tasks. Subsequently, the method to generate training data is shown and some implementation details are presented. Finally, simulations and experiments are carried out, and both results show the superiority of the proposed method on imaging quality and computational efficiency.
I. INTRODUCTION
Radar imaging quality can be improved with signal processing, but sparsity-driven methods face high computational cost and sensitivity to modeling accuracy. This motivates examining CNN as an adaptive, parallel, non-iterative alternative for radar imaging.
- I. INTRODUCTION: Sparsity-driven radar imaging transforms reconstruction into a constrained optimization problem using prior knowledge about the image.The model represents the echo as y = Ax + n and estimates x under a prior constraint and noise-energy bound.
- I. INTRODUCTION: Conventional back projection and FFT imaging suffer from limited resolution, high side-lobes, and strong speckle.
- I. INTRODUCTION: Sparsity-driven methods can improve imaging quality but require many iterations, making real-time imaging difficult.Their nonlinear optimization generally needs substantial computation to converge.
- I. INTRODUCTION: Their results also depend on accurate sensing-matrix modeling and suitable constraints, so modeling errors can substantially degrade imaging quality.
- I. INTRODUCTION: CNN offers data-adaptive learning, highly parallel structure, and an iteration-free feedforward process for regression-type imaging tasks.The introduction connects these properties with potential gains in accuracy and efficiency over sparsity-based methods.
A. Overall framework of CV-CNN-enhanced radar imaging
The proposed framework replaces a conventional radar imaging processor with a CV-CNN trained through supervised input-output examples. Radar echoes are used as inputs and expected images as outputs during the imaging or testing process.
- A. Overall framework of CV-CNN-enhanced radar imaging: The framework uses CV-CNN as the radar imaging processor, replacing conventionally designed imaging algorithms.The imaging model supplies the configurations and parameters needed by the imaging task.
- A. Overall framework of CV-CNN-enhanced radar imaging: Radar echoes form the CV-CNN input, while expected or formed images provide the output targets.Training uses given input-output examples, and testing uses the learned processor for imaging.
- A. Overall framework of CV-CNN-enhanced radar imaging: The framework follows supervised learning by learning the imaging processor from paired echo and image examples.
B. Modifications on the CV-CNN
The CV-CNN is adapted to radar imaging with a complex-valued ReLU activation and a specialized real-valued output neuron. These changes target efficient backpropagation and amplitude-focused radar images.
- B. Modifications on the CV-CNN: The complex-valued network is trained through complex-valued backpropagation using the defined neuron variables, weights, biases, and cost function.
- B. Modifications on the CV-CNN: The radar-imaging CV-CNN introduces two modifications: a new activation function and a new output-layer neuron.
- B. Modifications on the CV-CNN: cReLU applies ReLU independently to the real and imaginary parts of each complex-valued neuron input.This simplifies the backpropagation process.
- B. Modifications on the CV-CNN: The output layer uses a specialized neuron because radar imaging primarily uses image amplitude and therefore seeks real-valued outputs.
C. Generation of the training data
Training data are generated from a simplified turntable radar model using random continuous scatterer coordinates and complex scattering coefficients, with expected images formed by convolution with an ideal point-spread function.
- The turntable model simplifies scattering to ideal point targets confined to 2D, while neglecting attenuation and propagation phase.
- The radar echo is generated from the simplified turntable scattering model, providing the CV-CNN input data.
- Expected images are defined as the convolution of the scattering distribution with an ideal point-spread function.
- The point-spread function uses Gaussian widths σ_x and σ_y, corresponding to resolutions of 1.18σ_x and 1.18σ_y under the −3 dB definition.
- Random continuous coordinates are sampled uniformly within the imaging area, and each scatterer receives a standard complex Gaussian coefficient.
A. Network structure and implementation details
The implementation combines implicit fast imaging operators with a complex-valued CNN and compares it against a real-valued counterpart and SPGL1.
- The network comparison includes the proposed CV-CNN and a counterpart RV-CNN with real and imaginary data components treated as independent channels.
- The fully connected imaging transformation is implemented implicitly with FFT-based operators rather than explicitly storing the sensing matrix.
- The RV-CNN is designed with higher total degrees of freedom than the CV-CNN for comparison.
- Training uses 50,000 generated examples for 5 epochs, with a batch size of 50 and approximately 16 hours on one NVIDIA TITAN Xp.
- SPGL1 is selected as the sparsity-driven baseline because it supports implicit operators, complex-valued problems, and relatively efficient execution.
B. Numerical simulations
Numerical simulations compare FFT, SPGL1, RV-CNN, and CV-CNN on synthetic point-scatterer data using image quality and runtime measures.
- CV-CNN produces higher-quality images than FFT and SPGL1 and more closely resembles the groundtruth image alongside RV-CNN.
- FFT images show high side-lobes and relatively low resolution, while modeling errors also affect SPGL1 results.
- CV-CNN is more robust to modeling errors because its adaptive convolutional layers can compensate for errors introduced by FFT-based operators.
- For all SNR levels, CV-CNN has the best RMSE, including 0.0245 at 10 dB, while its imaging time is 0.071 s.
C. Laboratory results
Laboratory experiments with an airplane target show that CNN-based methods improve resolution and suppress side-lobes relative to FFT, while the paper notes unresolved image-quality assessment and model-scope limitations.
- The laboratory experiment uses an airplane model with the same imaging parameters as the numerical setup.
- FFT produces relatively low resolution and extremely high side-lobes, whereas the other methods enhance resolution and suppress side-lobes.
- The visual quality of the non-FFT methods differs substantially in the laboratory images.
- Radar-image quality assessment remains an open question, although recent results show the proposed method’s robustness and efficiency.
- The proposed CV-CNN is trained under an ideal point-scattering assumption and is therefore oriented toward point-feature enhancement.
IV. CONCLUSION
The paper concludes that CV-CNNs can enhance radar imaging and may broaden the role of deep learning in radar imaging.
- The proposed method uses a complex-valued convolutional neural network to enhance radar imaging.
- Feedforward CNN processing makes enhanced imaging faster and potentially suitable for real-time operation than iterative-based imaging.
- CV-CNN achieves better performance with fewer parameters than its real-valued counterpart.
- The authors expect radar imaging to benefit from deep learning techniques such as CNNs in the future.