Complex-valued Convolutional Neural Network Research Articles

Global Receptive Field Designed Complex-Valued Convolutional Neural Network Equalizer for Optical Fiber Communications

In this paper, an improved complex-valued convolutional neural network (CvCNN) structure to be placed at the received side is proposed for nonlinearity compensation in a coherent optical system. This complex-valued global convolutional kernel-assisted convolutional neural network equalizer (CvGNN) has been verified in terms of Q-factor performance and complexity compared to seven other related nonlinear equalizers based on both the 64 QAM experimental platform and the QPSK numerical platform. The global convolution operation of the proposed CvGNN is more suitable for the calculation process of perturbation coefficients, and the global receptive field can also be more effective at extracting effective information from perturbation feature maps. The introduction of CvCNN can directly focus on the complex-valued perturbation feature maps themselves without separately processing the real and imaginary parts, which is more in line with the waveform-dependent physical characteristics of optical signals. Based on the experimental platform, compared with the real-valued neural network with small convolutional kernel (RvCNNC), the proposed CvGNNC improves the Q-factor by ∼2.95 dB at the optimal transmission power, while reducing the time complexity by ∼44.7%.

Synthesis of soundfields through irregular loudspeaker arrays based on convolutional neural networks

Most soundfield synthesis approaches deal with extensive and regular loudspeaker arrays, which are often not suitable for home audio systems, due to physical space constraints. In this article, we propose a technique for soundfield synthesis through more easily deployable irregular loudspeaker arrays, i.e., where the spacing between loudspeakers is not constant, based on deep learning. The input are the driving signals obtained through a plane wave decomposition-based technique. While the considered driving signals are able to correctly reproduce the soundfield with a regular array, they show degraded performances when using irregular setups. Through a complex-valued convolutional neural network (CNN), we modify the driving signals in order to compensate the errors in the reproduction of the desired soundfield. Since no ground truth driving signals are available for the compensated ones, we train the model by calculating the loss between the desired soundfield at a number of control points and the one obtained through the driving signals estimated by the network. The proposed model must be retrained for each irregular loudspeaker array configuration. Numerical results show better reproduction accuracy with respect to the plane wave decomposition-based technique, pressure-matching approach, and linear optimizers for driving signal compensation.

PolSAR Image Classification with Active Complex-Valued Convolutional-Wavelet Neural Network and Markov Random Fields

PolSAR image classification has attracted extensive significant research in recent decades. Aiming at improving PolSAR classification performance with speckle noise, this paper proposes an active complex-valued convolutional-wavelet neural network by incorporating dual-tree complex wavelet transform (DT-CWT) and Markov random field (MRF). In this approach, DT-CWT is introduced into the complex-valued convolutional neural network to suppress the speckle noise of PolSAR images and maintain the structures of learned feature maps. In addition, by applying active learning (AL), we iteratively select the most informative unlabeled training samples of PolSAR datasets. Moreover, MRF is utilized to obtain spatial local correlation information, which has been proven to be effective in improving classification performance. The experimental results on three benchmark PolSAR datasets demonstrate that the proposed method can achieve a significant classification performance gain in terms of its effectiveness and robustness beyond some state-of-the-art deep learning methods.

Deep-Learning-Based Multiband Signal Fusion for 3-D SAR Superresolution

Three-dimensional (3-D) synthetic aperture radar (SAR) is widely used in many security and industrial applications requiring high-resolution imaging of concealed or occluded objects. The ability to resolve intricate 3-D targets is essential to the performance of such applications and depends directly on system bandwidth. However, because high-bandwidth systems face several prohibitive hurdles, an alternative solution is to operate multiple radars at distinct frequency bands and fuse the multiband signals. Current multiband signal fusion methods assume a simple target model and a small number of point reflectors, which is invalid for realistic security screening and industrial imaging scenarios wherein the target model effectively consists of a large number of reflectors. To the best of our knowledge, this study presents the first use of deep learning for multiband signal fusion. The proposed network, called <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$kR$</tex-math></inline-formula> -Net, employs a hybrid, dual-domain complex-valued convolutional neural network (CV-CNN) to fuse multiband signals and impute the missing samples in the frequency gaps between subbands. By exploiting the relationships in both the wavenumber domain and wavenumber spectral domain, the proposed framework overcomes the drawbacks of existing multiband imaging techniques for realistic scenarios at a fraction of the computation time of existing multiband fusion algorithms. Our method achieves high-resolution imaging of intricate targets previously impossible using conventional techniques and enables finer resolution capacity for concealed weapon detection and occluded object classification using multiband signaling without requiring more advanced hardware. Furthermore, a fully integrated multiband imaging system is developed using commercially available millimeter-wave (mmWave) radars for efficient multiband imaging. Using two mmWave radars, each with a bandwidth of 4 GHz operating at 60 GHz and 77 GHz, the proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$kR$</tex-math></inline-formula> -Net is employed to achieve an effective bandwidth of 21 GHz by robustly estimating the full-band signal. Additionally, the generalizability of the proposed technique is demonstrated across multiband sensing scenarios in the mmWave and terahertz (THz) frequencies. Extensive numerical simulations and empirical experiments are conducted to illustrate the superiority of our approach over existing methods for a diverse set of realistic 3-D SAR imaging scenarios.

Application of complex-valued convolutional neural networks for equalization and detection of SEFDM systems

Background. The disadvantage of spectrally efficient signals with frequency multiplexing is the occurrence of intersymbol interference, which is further aggravated when these signals propagate in frequency selective channels.&#x0D; Aim. The possibility and effectiveness of using neural network approaches for channel equalization and signal detection in communication systems using SEFDM signals has been assessed.&#x0D; Methods. A receiver structure for SEFDM systems based on a deep complex-valued convolutional neural network is proposed, which allows recovering bits from the temporal representation of the signal without using the fractional Fourier transform and inverting the cross-correlation matrix between frequency subcarriers. A two-stage network training scheme has been developed. Based on simulation modeling, a comparative analysis of the noise immunity of SEFDM systems was carried out both in a channel with white Gaussian noise and in a channel with Rayleigh fading, using classical and neural network receivers.&#x0D; Results. It is shown that there is no loss of noise immunity in channels with additive white Gaussian noise and an increase in noise immunity of the system up to 2 dB in the channel specified by the extended automotive model (3GPP-EVA).&#x0D; Conclusion. The effectiveness of using deep neural complex-valued convolutional networks as receivers for spectrally efficient communication systems, as well as their advantage over classical ones, is shown.&#x0D; Keywords – SEFDM; deep complex-valued convolutional neural network; turbocoding.

Dual-stream complex-valued convolutional network for authentic dehazed image quality assessment.

Effectively evaluating the perceptual quality of dehazed images remains an under-explored research issue. In this paper, we propose a no-reference complex-valued convolutional neural network (CV-CNN) model to conduct automatic dehazed image quality evaluation. Specifically, a novel CV-CNN is employed that exploits the advantages of complex-valued representations, achieving better generalization capability on perceptual feature learning than real-valued ones. To learn more discriminative features to analyze the perceptual quality of dehazed images, we design a dual-stream CV-CNN architecture. The dual-stream model comprises a distortion-sensitive stream that operates on the dehazed RGB image, and a haze-aware stream on a novel dark channel difference image. The distortion-sensitive stream accounts for perceptual distortion artifacts, while the haze-aware stream addresses the possible presence of residual haze. Experimental results on three publicly available dehazed image quality assessment (DQA) databases demonstrate the effectiveness and generalization of our proposed CV-CNN DQA model as compared to state-of-the-art no-reference image quality assessment algorithms.

Real-time High-Quality Computer-Generated Hologram Using Complex-Valued Convolutional Neural Network.

Holographic displays are ideal display technologies for virtual and augmented reality because all visual cues are provided. However, real-time high-quality holographic displays are difficult to achieve because the generation of high-quality computer-generated hologram (CGH) is inefficient in existing algorithms. Here, complex-valued convolutional neural network (CCNN) is proposed for phase-only CGH generation. The CCNN-CGH architecture is effective with a simple network structure based on the character design of complex amplitude. A holographic display prototype is set up for optical reconstruction. Experiments verify that state-of-the-art performance is achieved in terms of quality and generation speed in existing end-to-end neural holography methods using the ideal wave propagation model. The generation speed is three times faster than HoloNet and one-sixth faster than Holo-encoder, and the Peak Signal to Noise Ratio (PSNR) is increased by 3 dB and 9 dB, respectively. Real-time high-quality CGHs are generated in 1920×1072 and 3840×2160 resolutions for dynamic holographic displays.

Radial Undersampled MRI Reconstruction Using Deep Learning with Mutual Constraints between Real and Imaginary Components of K-Space.

The deep learning method is an efficient solution for improving the quality of undersampled magnetic resonance (MR) image reconstruction while reducing lengthy data acquisition. Most deep learning methods neglect the mutual constraints between the real and imaginary components of complex-valued k-space data. In this paper, a new complex-valued convolutional neural network (CNN), namely, Dense-U-Dense Net (DUD-Net), is proposed to interpolate the undersampled k-space data and reconstruct MR images. The proposed network comprises dense layers, U-Net, and other dense layers in sequence. The dense layers are used to simulate the mutual constraints between real and imaginary components, and U-Net performs feature sparsity and interpolation estimation for the k-space data. Two MRI datasets were used to evaluate the proposed method: brain magnitude-only MR images and knee complex-valued k-space data. Several operations were conducted to simulate the true undersampled k-space. First, the complex-valued MR images were synthesized by phase modulation on magnitude-only images. Second, a particular radial trajectory based on the golden ratio was used for k-space undersampling, whereby a reversible normalization method was proposed to balance the distribution of positive and negative values in k-space data. The optimal performance of DUD-Net was demonstrated based on a quantitative evaluation of inter-method comparisons of widely used CNNs and intra-method comparisons using an ablation study. When compared with other methods, significant improvements were achieved, PSNRs were increased by 10.78 and 5.74dB, whereas RMSEs were decreased by 71.53% and 30.31% for magnitude and phase image at least, respectively. It is concluded that DUD-Net significantly improves the performance of complex-valued k-space interpolation and MR image reconstruction.

Clutter Covariance Matrix Estimation for Radar Adaptive Detection Based on a Complex-Valued Convolutional Neural Network

In this paper, we address the problem of covariance matrix estimation for radar adaptive detection under non-Gaussian clutter. Traditional model-based estimators may suffer from performance loss due to the mismatch between real data and assumed models. Therefore, we resort to a data-driven deep-learning method and propose a covariance matrix estimation method based on a complex-valued convolutional neural network (CV-CNN). Moreover, a real-valued (RV) network with the same framework as the proposed CV network is also constructed to serve as a natural competitor. The obtained clutter covariance matrix estimation based on the network is applied to the adaptive normalized matched filter (ANMF) detector for performance assessment. The detection results via both simulated and real sea clutter illustrate that the estimator based on CV-CNN outperforms other traditional model-based estimators as well as its RV competitor in terms of probability of detection (PD).

Multi-Label Radar Compound Jamming Signal Recognition Using Complex-Valued CNN with Jamming Class Representation Fusion

In the complex battlefield electromagnetic environment, multiple jamming signals can enter the radar receiver simultaneously due to the development of jammers and modulation technology. The received compound jamming signals aggravate the difficulty of recognition and subsequent counter-countermeasure. In the face of strong overlapping signals and unseen jamming signal combinations, the performance of existing recognition methods usually seriously degrades. In this paper, an end-to-end multi-label classification framework combining a complex-valued convolutional neural network (CV-CNN) and jamming class representations is proposed to automatically recognize the jamming signal components of compound jamming signals. A basic multi-label CV-CNN (ML-CV-CNN) is first designed to directly process time–domain complex signals and fully retain jamming signal information. Then, the jamming class representations are generated using prototype clustering implemented by learning vector quantization, and they are fused with the ML-CV-CNN using class decoupling implemented by the attention mechanism to construct a multi-label class representation CV-CNN (ML-CR-CV-CNN), which can better learn the class-related features required for recognition. Finally, an adaptive threshold calibration is adopted to obtain optimal recognition results by multi-threshold discrimination. Simulation results verify that the proposed method has superior recognition performance, which is reflected in the strong robustness to the varying jamming-to-noise ratio (JNR) and power ratio, faster convergence speed with high JNRs, and better generalization for unseen jamming signal combinations.

A New Architecture of a Complex-Valued Convolutional Neural Network for PolSAR Image Classification

Polarimetric synthetic aperture radar (PolSAR) image classification has been an important area of research due to its wide range of applications. Traditional machine learning methods were insufficient in achieving satisfactory results before the advent of deep learning. Results have significantly improved with the widespread use of deep learning in PolSAR image classification. However, the challenge of reconciling the complex-valued inputs of PolSAR images with the real-valued models of deep learning remains unsolved. Current complex-valued deep learning models treat complex numbers as two distinct real numbers, providing limited assistance in PolSAR image classification results. This paper proposes a novel, complex-valued deep learning approach for PolSAR image classification to address this issue. The approach includes amplitude-based max pooling, complex-valued nonlinear activation, and a cross-entropy loss function based on complex-valued probability. Amplitude-based max pooling reduces computational effort while preserving the most valuable complex-valued features. Complex-valued nonlinear activation maps feature into a high-dimensional complex-domain space, producing the most discriminative features. The complex-valued cross-entropy loss function computes the classification loss using the complex-valued model output and dataset labels, resulting in more accurate and robust classification results. The proposed method was applied to a shallow CNN, deep CNN, FCN, and SegNet, and its effectiveness was verified on three public datasets. The results showed that the method achieved optimal classification results on any model and dataset.

Deep learning-based position detection for hydraulic cylinders using scattering parameters

Position detection of hydraulic cylinder pistons is crucial for numerous industrial automation applications. A typical traditional method is to excite electromagnetic waves in the cylinder structure and analytically solve the piston position based on the scattering parameters measured by a sensor. The core of this approach is a physical model that outlines the relationship between the measured scattering parameters and the targeted piston position. However, this physical model has shortcomings in accuracy and adaptability, especially in extreme conditions. To address these limitations, we propose machine learning and deep learning-based methods to learn the relationship directly in a data-driven manner. As a result, all deep learning models in this paper consistently outperform the physical one by a large margin. We further deliberate on the choice of models based on domain knowledge and provide in-depth analyses combining model performance with real-world physical characteristics. Specifically, we use Convolutional Neural Network (CNN) to discover local interactions of input among adjacent frequencies, apply Complex-Valued Neural Network (CVNN) to exploit the complex-valued nature of electromagnetic scattering parameters, and introduce a novel technique named Frequency Encoding to add weighted frequency information to the model input. The combination of these techniques results in our best-performing model, a complex-valued CNN with Frequency Encoding, which exhibits substantial improvement in accuracy with an error reduction of 1/12 compared to the traditional physical model.

Enhance Terahertz Image Resolution via Complex-valued convolutional neural networks

Terahertz imaging technology is widely used in nondestructive testing (NDT), human security inspection, far-field imaging systems, and so on. Improving image resolution is always a topic of discussion. For visible image and image super-resolution, the convolutional neural network (CNN) has achieved a better improvement effect than the traditional algorithm. Compared to optics, it is quite feasible to gain both the amplitude and phase information in THz imaging, the Complex-valued convolutional neural network (CV-CNN) is better suited for the field of terahertz imaging than the real-valued neural network. In this paper, A lightweight complex-valued neural network is constructed which enhances terahertz imaging in a vector network analyzer (VNA) imaging system. Compared to CNN, CV-CNN has a better peak signal-to-noise ratio (PSNR) and structural similarity (SSIM), and it is significantly less vulnerable to overfitting. Phase information can be used well at the same time, which is impossible for CNN. The network is trained using the MNIST dataset and verified by using simulated and measured data obtained from a 200Ghz imager.

Atmospheric turbulence removal with complex-valued convolutional neural network

Atmospheric turbulence distorts visual imagery and is always problematic for information interpretation by both human and machine. Most well-developed approaches to remove atmospheric turbulence distortion are model-based. However, these methods require high computation and large memory making real-time operation infeasible. Deep learning-based approaches have hence gained more attention but currently work efficiently only on static scenes. This paper presents a novel learning-based framework offering short temporal spanning to support dynamic scenes. We exploit complex-valued convolutions as phase information, altered by atmospheric turbulence, is captured better than using ordinary real-valued convolutions. Two concatenated modules are proposed. The first module aims to remove geometric distortions and, if enough memory, the second module is applied to refine micro details of the videos. Experimental results show that our proposed framework efficiently mitigates the atmospheric turbulence distortion and significantly outperforms existing methods.

Deep Learning-Based Speech Enhancement of an Extrinsic Fabry-Perot Interferometric Fiber Acoustic Sensor System.

To achieve high-quality voice communication technology without noise interference in flammable, explosive and strong electromagnetic environments, the speech enhancement technology of a fiber-optic external Fabry-Perot interferometric (EFPI) acoustic sensor based on deep learning is studied in this paper. The combination of a complex-valued convolutional neural network and a long short-term memory (CV-CNN-LSTM) model is proposed for speech enhancement in the EFPI acoustic sensing system. Moreover, the 3 × 3 coupler algorithm is used to demodulate voice signals. Then, the short-time Fourier transform (STFT) spectrogram features of voice signals are divided into a training set and a test set. The training set is input into the established CV-CNN-LSTM model for model training, and the test set is input into the trained model for testing. The experimental findings reveal that the proposed CV-CNN-LSTM model demonstrates exceptional speech enhancement performance, boasting an average Perceptual Evaluation of Speech Quality (PESQ) score of 3.148. In comparison to the CV-CNN and CV-LSTM models, this innovative model achieves a remarkable PESQ score improvement of 9.7% and 11.4%, respectively. Furthermore, the average Short-Time Objective Intelligibility (STOI) score witnesses significant enhancements of 4.04 and 2.83 when contrasted with the CV-CNN and CV-LSTM models, respectively.

Recognition of Micro-Motion Jamming Based on Complex-Valued Convolutional Neural Network.

Micro-motion jamming is a new jamming method to inverse synthetic aperture radar (ISAR) in recent years. Compared with traditional jamming methods, it is more flexible and controllable, and is a great threat to ISAR. The prerequisite of taking relevant anti-jamming measures is to recognize the patterns of micro-motion jamming. In this paper, a method of micro-motion jamming pattern recognition based on complex-valued convolutional neural network (CV-CNN) is proposed. The micro-motion jamming echo signals are serialized and input to the network, and the result of recognition is output. Compared with real-valued convolutional neural network (RV-CNN), it can be found that the proposed method has a higher recognition accuracy rate. Additionally, the recognition accuracy rate is analyzed with different signal-to-noise ratio (SNR) and number of training samples. Simulation results prove the effectiveness of the proposed recognition method.

Classifying epileptic phase-amplitude coupling in SEEG using complex-valued convolutional neural network.

EEG phase-amplitude coupling (PAC), the amplitude of high-frequency oscillations modulated by the phase of low-frequency oscillations (LFOs), is a useful biomarker to localize epileptogenic tissue. It is commonly represented in a comodulogram of coupling strength but without coupled phase information. The phase-amplitude coupling is also found in the normal brain, and it is difficult to discriminate pathological phase-amplitude couplings from normal ones. This study proposes a novel approach based on complex-valued phase-amplitude coupling (CV-PAC) for classifying epileptic phase-amplitude coupling. The CV-PAC combines both the coupling strengths and the coupled phases of low-frequency oscillations. The complex-valued convolutional neural network (CV-CNN) is then used to classify epileptic CV-PAC. Stereo-electroencephalography (SEEG) recordings from nine intractable epilepsy patients were analyzed. The leave-one-out cross-validation is performed, and the area-under-curve (AUC) value is used as the indicator of the performance of different measures. Our result shows that the area-under-curve value is .92 for classifying epileptic CV-PAC using CV-CNN. The area-under-curve value decreases to .89, .80, and .88 while using traditional convolutional neural networks, support vector machine, and random forest, respectively. The phases of delta (1-4Hz) and alpha (8-10Hz) bands are different between epileptic and normal CV-PAC. The phase information of CV-PAC is important for improving classification performance. The proposed approach of CV-PAC/CV-CNN promises to identify more accurate epileptic brain activities for potential surgical intervention.

CVGG-Net: Ship Recognition for SAR Images Based on Complex-Valued Convolutional Neural Network

CVGG-Net: Ship Recognition for SAR Images Based on Complex-Valued Convolutional Neural Network

Capsule Network With Multiscale Feature Fusion for Hidden Human Activity Classification

This article considers the problem of human activity classification behind the walls using ultrawideband (UWB) radar. The complex-valued multiscale feature fusion capsule network (CV-MCNet) is proposed, which consists of a feature extractor, a multiscale feature fusion (MFF) block, and a capsule block. Specifically, the feature extractor with two complex-valued convolutional layers is designed to extract the deep features from the range profiles. Then, the MFF block is developed to enrich the feature representation of the activity. Finally, a capsule block is applied to implicitly encode the spatial relationship among the features in vector form and aggregate the vectors to get accurate classification results. The proposed CV-MCNet is evaluated by real data, and the results show that it achieves better classification performance compared with the deep convolutional neural network (DCNN), convolutional autoencoder (CAE), and complex-valued convolutional neural network (CV-CNN).

Few-Shot Specific Emitter Identification via Deep Metric Ensemble Learning

Specific emitter identification (SEI) is a highly potential technology for physical-layer authentication that is one of the most critical supplements for the upper-layer authentication. SEI is based on radio frequency (RF) features from circuit difference, rather than cryptography. These features are inherent characteristics of hardware circuits, which are difficult to counterfeit. Recently, various deep learning (DL)-based conventional SEI methods have been proposed, and achieved advanced performances. However, these methods are proposed for close-set scenarios with massive RF signal samples for training, and they generally have poor performance under the condition of limited training samples. Thus, we focus on few-shot SEI (FS-SEI) for aircraft identification via automatic dependent surveillance-broadcast (ADS-B) signals, and a novel FS-SEI method is proposed, based on deep metric ensemble learning (DMEL). Specifically, the proposed method consists of feature embedding and classification. The former is based on metric learning with a complex-valued convolutional neural network (CVCNN) for extracting discriminative features with compact intracategory distance and separable intercategory distance, while the latter is realized by an ensemble classifier. Simulation results show that if the number of samples per category is more than 5, the average accuracy of our proposed method is higher than 98%. Moreover, feature visualization demonstrates the advantages of our proposed method in both discriminability and generalization. The code and the dataset can be downloaded from <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/BeechburgPieStar/FS-SEI</uri> .