Complex-valued Convolutional Neural Networks Research Articles

Enhanced noise resilience in passive tone detection via broad-receptive field complex-valued convolutional neural networks.

Tone detection is crucial for passive sonar systems. Numerous algorithms have been developed for passive tone detection, but their effectiveness in detecting weak tones is still limited. To enhance noise resilience in passive tone detection, a broad-receptive field complex-valued structure named attention-driven complex-valued U-Net is proposed. Concretely, two attention mechanisms, namely, temporal attention and harmonic attention, are proposed to broaden the receptive field with high computational efficiency. Complex-valued operators are then introduced to mine both amplitude and phase information of tones. Additionally, a symmetric downsampling and upsampling strategy is proposed to improve the reconstruction accuracy of detailed time-frequency information. Overall, the proposed method demonstrates a strong robustness to noise and a strong ability to generalize. Experimental results on both simulated data and real-world data validate the superiority of the proposed attention-driven complex-valued U-Net against conventional U-shaped structures.

Frequency and phase correction of GABA-edited magnetic resonance spectroscopy using complex-valued convolutional neural networks

PurposeTo determine the significance of complex-valued inputs and complex-valued convolutions compared to real-valued inputs and real-valued convolutions in convolutional neural networks (CNNs) for frequency and phase correction (FPC) of GABA-edited magnetic resonance spectroscopy (MRS) data. MethodsAn ablation study using simulated data was performed to determine the most effective input (real or complex) and convolution type (real or complex) to predict frequency and phase shifts in GABA-edited MEGA-PRESS data using CNNs. The best CNN model was subsequently compared using both simulated and in vivo data to two recently proposed deep learning (DL) methods for FPC of GABA-edited MRS. All methods were trained using the same experimental setup and evaluated using the signal-to-noise ratio (SNR) and linewidth of the GABA peak, choline artifact, and by visually assessing the reconstructed final difference spectrum. Statistical significance was assessed using the Wilcoxon signed rank test. ResultsThe ablation study showed that using complex values for the input represented by real and imaginary channels in our model input tensor, with complex convolutions was most effective for FPC. Overall, in the comparative study using simulated data, our CC-CNN model (that received complex-valued inputs with complex convolutions) outperformed the other models as evaluated by the mean absolute error. ConclusionOur results indicate that the optimal CNN configuration for GABA-edited MRS FPC uses a complex-valued input and complex convolutions. Overall, this model outperformed existing DL models.

Phase Aberration Correction for In Vivo Ultrasound Localization Microscopy Using a Spatiotemporal Complex-Valued Neural Network.

Ultrasound Localization Microscopy (ULM) can map microvessels at a resolution of a few micrometers ( [Formula: see text]). Transcranial ULM remains challenging in presence of aberrations caused by the skull, which lead to localization errors. Herein, we propose a deep learning approach based on recently introduced complex-valued convolutional neural networks (CV-CNNs) to retrieve the aberration function, which can then be used to form enhanced images using standard delay-and-sum beamforming. CV-CNNs were selected as they can apply time delays through multiplication with in-phase quadrature input data. Predicting the aberration function rather than corrected images also confers enhanced explainability to the network. In addition, 3D spatiotemporal convolutions were used for the network to leverage entire microbubble tracks. For training and validation, we used an anatomically and hemodynamically realistic mouse brain microvascular network model to simulate the flow of microbubbles in presence of aberration. The proposed CV-CNN performance was compared to the coherence-based method by using microbubble tracks. We then confirmed the capability of the proposed network to generalize to transcranial in vivo data in the mouse brain (n=3). Vascular reconstructions using a locally predicted aberration function included additional and sharper vessels. The CV-CNN was more robust than the coherence-based method and could perform aberration correction in a 6-month-old mouse. After correction, we measured a resolution of [Formula: see text] for younger mice, representing an improvement of 25.8%, while the resolution was improved by 13.9% for the 6-month-old mouse. This work leads to different applications for complex-valued convolutions in biomedical imaging and strategies to perform transcranial ULM.

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.
 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.
 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.
 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).
 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.
 Keywords – SEFDM; deep complex-valued convolutional neural network; turbocoding.

A Novel Complex-Valued Hybrid Neural Network for Automatic Modulation Classification

Currently, dealing directly with in-phase and quadrature time series data using the deep learning method is widely used in signal modulation classification. However, there is a relative lack of methods that consider the complex properties of signals. Therefore, to make full use of the inherent relationship between in-phase and quadrature time series data, a complex-valued hybrid neural network (CV-PET-CSGDNN) based on the existing PET-CGDNN network is proposed in this paper, which consists of phase parameter estimation, parameter transformation, and complex-valued signal feature extraction layers. The complex-valued signal feature extraction layers are composed of complex-valued convolutional neural networks (CNN), complex-valued gate recurrent units (GRU), squeeze-and-excite (SE) blocks, and complex-valued dense neural networks (DNN). The proposed network can improve the extraction of the intrinsic relationship between in-phase and quadrature time series data with low capacity and then improve the accuracy of modulation classification. Experiments are carried out on RML2016.10a and RML2018.01a. The results show that, compared with ResNet, CLDNN, MCLDNN, PET-CGDNN, and CV-ResNet models, our proposed complex-valued neural network (CVNN) achieves the highest average accuracy of 61.50% and 62.92% for automatic modulation classification, respectively. In addition, the proposed CV-PET-CSGDNN has a significant improvement in the misjudgment situation between 64QAM, 128QAM, and 256QAM compared with PET-CGDNN on RML2018.01a.

Spectral complexity-scaled generalisation bound of complex-valued neural networks

Complex-valued neural networks (CVNNs) have been widely applied in various fields, primarily in signal processing and image recognition. Few studies have focused on the generalisation of CVNNs, although it is vital to ensure the performance of CVNNs on unseen data. This study is the first to prove a generalisation bound for complex-valued neural networks. The bounds increase as the spectral complexity increases, with the dominant factor being the product of the spectral norms of the weight matrices. Furthermore, this work provides a generalisation bound for CVNNs trained on sequential data, which is also affected by the spectral complexity. Theoretically, these bounds are derived using the Maurey Sparsification Lemma and Dudley entropy integral. We conducted empirical experiments on various datasets including MNIST, ashionMNIST, CIFAR-10, CIFAR-100, Tiny ImageNet, and IMDB by training complex-valued convolutional neural networks. The Spearman rank-order correlation coefficient and the corresponding p-values on these datasets provide strong proof of the statistically significant correlation between the spectral complexity of a network and its generalisation ability, as measured by the spectral norm product of the weight matrices. The code is available at https://github.com/LeavesLei/cvnn_generalization.

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.

Complex-Valued Neural Networks: A Comprehensive Survey

Complex-valued neural networks (CVNNs) have shown their excellent efficiency compared to their real counter-parts in speech enhancement, image and signal processing. Researchers throughout the years have made many efforts to improve the learning algorithms and activation functions of CVNNs. Since CVNNs have proven to have better performance in handling the naturally complex-valued data and signals, this area of study will grow and expect the arrival of some effective improvements in the future. Therefore, there exists an obvious reason to provide a comprehensive survey paper that systematically collects and categorizes the advancement of CVNNs. In this paper, we discuss and summarize the recent advances based on their learning algorithms, activation functions, which is the most challenging part of building a CVNN, and applications. Besides, we outline the structure and applications of complex-valued convolutional, residual and recurrent neural networks. Finally, we also present some challenges and future research directions to facilitate the exploration of the ability of CVNNs.

A Survey on the Applications of Convolutional Neural Networks for Synthetic Aperture Radar: Recent Advances

In recent years, convolutional neural networks (CNNs) have drawn considerable attention for the analysis of synthetic aperture radar (SAR) data. In this study, major subareas of SAR data analysis that have been tackled by CNNs are systematically reviewed, such as automatic target recognition, land use and land cover classification, segmentation, change detection, object detection, and image denoising. Special emphasis has been given to practical techniques such as data augmentation and transfer learning. Complex-valued CNNs, which have been introduced to exploit phase information embedded in SAR complex images, have also been extensively reviewed. To conclude this review paper, open challenges and future research directions are highlighted.

Robust Beamforming Based on Complex-Valued Convolutional Neural Networks for Sensor Arrays

Robust adaptive beamforming (RAB) plays a vital role in modern communications by ensuring the reception of high-quality signals. This paper proposes a deep learning approach to robust adaptive beamforming. In particular, we propose a novel RAB approach where the sample covariance matrix (SCM) is used as the input of a deep 1D Complex-Valued Convolutional Neural Network (CVCNN). The network employs complex convolutional and pooling layers, as well as a Cartesian Scaled Exponential Linear Unit activation function to directly compute the nearly-optimum weight vector through the training process and without prior knowledge about the direction of arrival of the desired signal. This means that reconstruction of the interference plus noise (IPN) covariance matrix is not required. The trained CVCNN accurately computes the nearly-optimum weight vector for data not used during training. The computed weight vector is employed to estimate the signal-to-interference plus noise ratio. Simulations show that the proposed RAB can provide performance close to that of the optimal beamformer.

CSI Feedback Based on Complex Neural Network for Massive MIMO Systems

In order to solve the problem of large channel state information (CSI) feedback overhead and low feedback accuracy in massive multiple-input multiple-output (MIMO) systems. We propose a CSI feedback method based on complex-valued convolutional neural networks to improve the representation capability of the network. In this method, a complex-valued encoder-decoder structure is constructed considering the fact that CSI exists in the form of complex numbers. We use complex convolutional downsampling (CCD) to extract CSI features in the encoder, and reconstruct the compressed CSI with high accuracy in the decoder by using a complex dense block (CDBlock). Simulation results show that the average accuracy is improved by 17.5% compared with several classical deep learning CSI feedback methods. Our proposed CSI feedback method has higher feedback accuracy and better system performance in massive MIMO systems.

Fast Complex-Valued CNN for Radar Jamming Signal Recognition

Jamming is a big threat to the survival of a radar system. Therefore, the recognition of radar jamming signal type is a part of radar countermeasure. Recently, convolutional neural networks (CNNs) have shown their effectiveness in radar signal processing, including jamming signal recognition. However, most of existing CNN methods do not regard radar jamming as a complex value signal. In this study, a complex-valued CNN (CV-CNN) is investigated to fully explore the inherent characteristics of a radar jamming signal, and we find that we can obtain better recognition accuracy using this method compared with a real-valued CNN (RV-CNN). CV-CNNs contain more parameters, which need more inference time. To reduce the parameter redundancy and speed up the recognition time, a fast CV-CNN (F-CV-CNN), which is based on pruning, is proposed for radar jamming signal fast recognition. The experimental results show that the CV-CNN and F-CV-CNN methods obtain good recognition performance in terms of accuracy and speed. The proposed methods open a new window for future research, which shows a huge potential of CV-CNN-based methods for radar signal processing.

A novel complex-valued convolutional neural network for medical image denoising

Several applications of complex-valued networks have been reported for computer vision tasks like image processing and classification. However, complex-valued convolutional neural networks are yet to be explored for medical image denoising. In this paper, a novel complex-valued convolutional neural network-based model, termed as CVMIDNet, is investigated for medical image denoising. Unlike traditional approaches, which learn clean images from noisy images, the proposed model utilizes residual learning, which learns noise from noisy images and then subtracts it from noisy images so as to obtain clean images. To assess the denoising performance of CVMIDNet, standard image quality metrics, namely, peak signal to noise ratio and the structural similarity index, have been used for five different additive white Gaussian noise levels in chest X-ray images. Chest X-ray denoising performance of CVMIDNet was compared with four recent state-of-the-art models, namely, Block-Matching and 3D (BM3D) filtering, DnCNN, Feature-guided Denoising Convolutional Neural Network (FDCNN), and deep CNN with residual learning. Additionally, it is also benchmarked against its real-valued counterpart, termed RVMIDNet. In all the reported performance investigations, CVMIDNet was found to be superior. For instance, for a Gaussian noise level of σ = 15, peak signal to noise ratio and structural similarity index values achieved by the CVMIDNet are 37.2010 and 0.9227, respectively, against the 36.2292 and 0.9086, 36.3203 and 0.9139, 35.0995 and 0.9005, 36.1830 and 0.8968, 34.2436 and 0.8874 achieved by BM3D filtering, DnCNN, RVMIDNet, FDCNN, and deep CNN with residual learning, respectively. Therefore, based on the presented investigations, it is concluded that CVMIDNet is a potential deep learning model for medical image denoising.

Gaussian-type activation function for complex-valued CNN and its application in polar-SAR image classification

Activation functions play increasingly important roles in deep learning. The activation functions give the neural network the ability to learn complex patterns by introducing non-linearity. Complex-valued activation functions for complex-valued neural networks are extended from real-valued activation functions like sigmoid, tanh, rectified linear unit, and exponential linear unit. Recently, the most widely used complex-valued activation function is the real-imaginary-type activation function (RIAF), which applies separate real-valued activation functions on both the real and the imaginary parts of a neuron. This separate activation method ignores the internal relationship between the real and imaginary parts of the complex input and loses the integrity of activation. In this work, a complex-valued activation function called Gaussian-type activation function (GTAF) is proposed to activate the real and imaginary parts of a neuron jointly and enhance the learning ability and learning speed. GTAF consists of an ordinary real-valued activation function and a Gaussian function and is suitable for any given complex-valued neural network. Two polar-SAR image classification experiments on complex-valued convolutional neural networks show that GTAF converges faster than RIAF and has higher accuracy.

Analysis of deep complex-valued convolutional neural networks for MRI reconstruction and phase-focused applications.

Deep learning has had success with MRI reconstruction, but previously published works use real-valued networks. The few works which have tried complex-valued networks have not fully assessed their impact on phase. Therefore, the purpose of this work is to fully investigate end-to-end complex-valued convolutional neural networks (CNNs) for accelerated MRI reconstruction and in several phase-based applications in comparison to 2-channel real-valued networks. Several complex-valued activation functions for MRI reconstruction were implemented, and their performance was compared. Complex-valued convolution was implemented and tested on an unrolled network architecture and a U-Net-based architecture over a wide range of network widths and depths with knee, body, and phase-contrast datasets. Quantitative and qualitative results demonstrated that complex-valued CNNs with complex-valued convolutions provided superior reconstructions compared to real-valued convolutions with the same number of trainable parameters for both an unrolled network architecture and a U-Net-based architecture, and for 3 different datasets. Complex-valued CNNs consistently had superior normalized RMS error, structural similarity index, and peak SNR compared to real-valued CNNs. Complex-valued CNNs can enable superior accelerated MRI reconstruction and phase-based applications such as fat-water separation, and flow quantification compared to real-valued convolutional neural networks.

Superpixel-Oriented Classification of PolSAR Images Using Complex-Valued Convolutional Neural Network Driven by Hybrid Data

Recently, convolutional neural networks (CNNs) have been successfully developed and used in the classification of polarimetric synthetic aperture radar (PolSAR) images. However, they often suffer from some problems, such as time-consuming, unsatisfactory detail-preservation, and bad effectiveness given limited training samples. Focusing on these problems, we propose a complex-valued CNN (CV-CNN)-based algorithm for PolSAR image classification in this article. On the one hand, a superpixel-oriented (SPO) scheme is employed to reduce the computational cost of the algorithm and preserve image details simultaneously, which takes superpixels instead of single pixels as classification units. In particular, to meet the input requirement of CV-CNN, three alternative methods of superpixel regularization are designed and compared. On the other hand, considering that both measured data (MD) and manually designed polarimetric features (PFs) have their own advantages, the hybrid data (HD) combining them is employed to drive CV-CNN, which is helpful to improve the effectiveness of the algorithm. We perform experiments on three actual PolSAR image data sets acquired by AIRSAR and Radarsat-2 systems as well as a semisimulated data set. The experimental results demonstrate that, compared to conventional pixel-oriented methods, the proposed SPO scheme is much more time-efficient and is also beneficial to detail preservation. Moreover, the CV-CNN driven by HD generally obtains consistently better classification results than that driven by pure MD or manually designed PFs.

Image denoising using complex-valued deep CNN

While complex-valued transforms have been widely used in image processing and have their deep connections to biological vision systems, complex-valued convolutional neural networks (CNNs) have not seen their applications in image recovery. This paper aims at investigating the potentials of complex-valued CNNs for image denoising. A CNN is developed for image denoising with its key mathematical operations defined in the complex number field to exploit the merits of complex-valued operations, including the compactness of convolution given by the tensor product of 1D complex-valued filters, the nonlinear activation on phase, and the noise robustness of residual blocks. The experimental results show that, the proposed complex-valued denoising CNN performs competitively against existing state-of-the-art real-valued denoising CNNs, with better robustness to possible inconsistencies of noise models between training samples and test images. The results also suggest that complex-valued CNNs provide another promising deep-learning-based approach to image denoising and other image recovery tasks.

Complex-Valued Convolutional Neural Networks Design and its Application on UAV DOA Estimation in Urban Environments

Direction-of-arrival (DOA) estimation is an important task in many unmanned aerial vehicle (UAV) applications. However, the complicated electromagnetic wave propagation in urban environments substantially deteriorates the performance of many conventional model-driven DOA estimation approaches. To alleviate this, a deep learning based DOA estimation approach is proposed in this paper. Specifically, a complex-valued convolutional neural network (CCNN) is designed to fit the electromagnetic UAV signal with complex envelope better. In the CCNN design, we construct some mapping functions using quantum probabilities, and further analyze some factors which may impact the convergence of complex-valued neural networks. Numerical simulations show that the proposed CCNN converges faster than the real convolutional neural network, and the DOA estimation result is more accurate and robust.

Land Form Classification and Similar Land-Shape Discovery by Using Complex-Valued Convolutional Neural Networks

This paper proposes a complex-valued convolutional neural network for land form classification and discovery in interferometric synthetic aperture radar (InSAR). Since the amount of satellite-borne SAR data has been increasing drastically, it is necessary to structurize the local features contained in observation data prior to utilization in the so-called big data framework for higher usability. Convolutional neural networks have such potential in general. However, there exists no network that can deal with complex amplitude data obtained in InSAR consistently. In this paper, we propose a complex-valued convolutional neural network to deal with InSAR. We demonstrate that the network classifies slopes and plains adaptively and, moreover, indicates small volcanos similar to a sample volcano (Omuroyama) included in the InSAR data. We also find their characteristic features emerging in the kernels in the convolution layers. These results reveal that the proposed complex-valued convolutional neural network is capable of successfully discovering unidentified lands similar to a prepared sample, which is highly useful for the InSAR data structurization.

Enhanced Radar Imaging Using a Complex-Valued Convolutional Neural Network

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.