Complex Convolution Research Articles

Complex Pseudo 3D Auto-Correlation Network for High-Quality Single-Angle Plane Wave Imaging

Abstract Deep learning has shown potential as an effective beamformer for improving the image quality of plane wave imaging (PWI). But most existing deep learning methods cannot directly handle the complex in-phase and quadrature (IQ) data. And noise in ultrasound signals would significantly damage the performance of regular convolution networks. To address these challenges, we proposed the Complex Pseudo 3D Auto-Correlation Network (CP3AN) which combined complex convolution and pseudo 3D auto-correlation blocks (P3AB) to directly map delayed IQ data from 0° plane wave into PWI pixels. The complex convolution could fully utilize the envelope and phase information of IQ data, while the P3AB used 1D convolution to extract noise in channel and space dimensions, allowing the network to prioritize valid signals with extremely low computational cost. We evaluated the performance of CP3AN through numerical simulations, phantom experiments, and in-vivo experiments, which showed comparable metrics with minimum variance (MV), including contrast (CR), contrast-to-noise ratio (CNR), generalized contrast-to-noise ratio (GCNR), lateral, and axial full-width half maximum (FWHM) at -9.60 dB, 1.12, 0.65, 319 um, and 344 um, respectively. The CP3AN achieved a low computational cost of 0.11 M floating-point operations (FLOPs), significantly lower than the MV or other compared deep learning-based methods. Our proposed method provided a promising solution for improving single-angle PWI imaging, particularly in situations where high frame rates are necessary.

Complex Residual Attention U-Net for Fast Ultrasound Imaging from a Single Plane-Wave Equivalent to Diverging Wave Imaging.

Plane wave imaging persists as a focal point of research due to its high frame rate and low complexity. However, in spite of these advantages, its performance can be compromised by several factors such as noise, speckle, and artifacts that affect the image quality and resolution. In this paper, we propose an attention-based complex convolutional residual U-Net to reconstruct improved in-phase/quadrature complex data from a single insonification acquisition that matches diverging wave imaging. Our approach introduces an attention mechanism to the complex domain in conjunction with complex convolution to incorporate phase information and improve the image quality matching images obtained using coherent compounding imaging. To validate the effectiveness of this method, we trained our network on a simulated phased array dataset and evaluated it using in vitro and in vivo data. The experimental results show that our approach improved the ultrasound image quality by focusing the network's attention on critical aspects of the complex data to identify and separate different regions of interest from background noise.

A method to shorten the time of high-dimensional matrix operations and convolution operations

Serverless computing, or Function-as-a-Service (FaaS), is a cloud computing execution model where the cloud provider dynamically manages the allocation and provisioning of servers which is a new way to solve the problem that the need of client.By serverless computing clients can easily solve their problems anytime,anywhere.However, the complex convolution operations and high-dimensional matrix operations can still consume a lot of resources such as computation time and memory occupancy in serverless computing. In this paper, firstly, the author selects two frequently used models in serverless computing, and then divide them into different numbers of partitions respectively to study the impact of partitioning methods on the computation time and memory occupancy. The author show that different partitioning methods can make an obviously impact on the computation time and memory occupancy,whitch shows that the proper partitioning of high-dimensional matrices and tensors can make a significantly reduction of calculation time and memory occupancy.

Michelson Interferometric Methods for Full Optical Complex Convolution.

Optical real-time data processing is advancing fields like tensor algebra acceleration, cryptography, and digital holography. This technology offers advantages such as reduced complexity through optical fast Fourier transform and passive dot-product multiplication. In this study, the proposed Reconfigurable Complex Convolution Module (RCCM) is capable of independently modulating both phase and amplitude over two million pixels. This research is relevant for applications in optical computing, hardware acceleration, encryption, and machine learning, where precise signal modulation is crucial. We demonstrate simultaneous amplitude and phase modulation of an optical two-dimensional signal in a thin lens's Fourier plane. Utilizing two spatial light modulators (SLMs) in a Michelson interferometer placed in the focal plane of two Fourier lenses, our system enables full modulation in a 4F system's Fourier domain. This setup addresses challenges like SLMs' non-linear inter-pixel crosstalk and variable modulation efficiency. The integration of these technologies in the RCCM contributes to the advancement of optical computing and related fields.

Deep Learning-Based Multi-Feature Fusion for Communication and Radar Signal Sensing

Recent years witness the rapid development of communication and radar technologies, and many transmitters are equipped with both communication and radar functionalities. To keep track of the working state of a target dual-functional transmitter, it is crucial to sense the modulation mode of the emitted signals. In this paper, we propose a deep learning-based intelligent modulation sensing technique for dual-functional transmitters. Different from existing modulation sensing methods, which usually focus on communication signals, we take both communication and radar signals into consideration. Typically, the dominant features of communication signals lie in the time domain, while those of radar signals lie in both time and frequency domains. To enhance the sensing accuracy, we first exploit real and complex value convolution operations to extract both time-domain and frequency-domain features of emitted signals from the target transmitter. Then, we fuse the extracted features by assigning proper weights with the attention mechanism. Simulation results reveal that the proposed technique can improve the sensing accuracy by up to 4% on average compared with benchmarks.

Source localization in deep ocean based on complex convolutional neural network

To solve the problem that phase information cannot be used effectively in underwater acoustic localization, a deep learning network based on complex convolutional neural network is proposed in this paper. The complex convolution layer is used to effectively utilize the phase features favorable to the source localization problem, and the phase information is used to improve the feature extraction performance. Through simulation, the performance of the network for source localization in deep-sea direct arrival region under different SNR conditions is analyzed. The results show that the complex convolutional network proposed in this paper can locate the sound source with less computation and has better performance under the condition of low SNR.

A cross-domain complex convolution neural network for undersampled magnetic resonance image reconstruction

To introduce a new cross-domain complex convolution neural network for accurate MR image reconstruction from undersampled k-space data. Most reconstruction methods utilize neural networks or cascade neural networks in either the image domain and/or the k-space domain. However, these methods encounter several challenges: 1) Applying neural networks directly in the k-space domain is suboptimal for feature extraction; 2) Classic image-domain networks have difficulty in fully extracting texture features; and 3) Existing cross-domain methods still face challenges in extracting and fusing features from both image and k-space domains simultaneously. In this work, we propose a novel deep-learning-based 2-D single-coil complex-valued MR reconstruction network termed TEID-Net. TEID-Net integrates three modules: 1) TE-Net, an image-domain-based sub-network designed to enhance contrast in input features by incorporating a Texture Enhancement Module; 2) ID-Net, an intermediate-domain sub-network tailored to operate in the image-Fourier space, with the specific goal of reducing aliasing artifacts realized by leveraging the superior incoherence property of the decoupled one-dimensional signals; and 3) TEID-Net, a cross-domain reconstruction network in which ID-Nets and TE-Nets are combined and cascaded to boost the quality of image reconstruction further. Extensive experiments have been conducted on the fastMRI and Calgary-Campinas datasets. Results demonstrate the effectiveness of the proposed TEID-Net in mitigating undersampling-induced artifacts and producing high-quality image reconstructions, outperforming several state-of-the-art methods while utilizing fewer network parameters. The cross-domain TEID-Net excels in restoring tissue structures and intricate texture details. The results illustrate that TEID-Net is particularly well-suited for regular Cartesian undersampling scenarios.

DMCNet-Pro: A Model-Driven Multi-Pilot Convolution Neural Network for MIMO-OFDM Receivers

Nowadays, wireless communication technology is evolving towards high data rates, a low latency, and a high throughput to meet increasingly complex business demands. Key technologies in this direction include multiple-input multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM). This research is based on our previous work DMCNet. In this article, we focus on studying the deep learning (DL) application of neural networks to solve the reception of single-antenna OFDM signals. Specifically, in multi-antenna scenarios, the channel model is more complex compared to single-antenna cases. By leveraging the characteristics of DL, such as automatic learning of parameters using deep neural networks, we treat the reception process of MIMO-OFDM signals as a black box and utilize neural networks to accomplish the signal reception task. Moreover, we propose a data-driven multi-pilot convolution neural network for MIMO-OFDM receivers (DMCNet). By incorporating complex convolution and complex fully connected structures, we design a receiver network to recover the transmitted signals from the received signals. We validate the accuracy and robustness of DMCNet under different channel conditions, comparing the bit error rates with different schemes. Additionally, we discuss the factors influencing various channel effects. At the same time, we also propose a model-driven scheme, DMCNet-pro, which has a higher accuracy and fewer parameters in some scenarios. The experimental results demonstrate that the DL-based reception scheme exhibits promising feasibility in terms of accuracy and interference resistance when compared to traditional approaches.

Error correction algorithm for grating Moiré fringes based on QM-ANN

Many interference factors of the complex and changeable working environment of the grating sensor are the main factors affecting the accuracy; a grating Moiré fringe error correction model based on the quartile method (QM) and artificial neural network (ANN) is proposed in this paper. Firstly, the grating sensor's signals in the working process are collected, and three kinds of interference signals (temperature, humidity and vibration) from the grating sensor working environment are collected simultaneously. Secondly, the QM is used to detect outliers from the collected data and delete data outliers directly. Subsequently, the processed data are input into the ANN model for training. The model is lightweight and stable, because it adopts the cascaded structure of full connection layer-normalization layer-full connection layer, which does not need deploy the complex convolution layer module etc. Finally, the corrected data are output after being processed by the QM-ANN error correction model. The experimental results show that the mean absolute error (MAE) of the proposed QM-ANN error correction model is better than QM-convolutional neural network (CNN), QM-long short-term memory (LSTM) and ANN, CNN, LSTM models without QM. It shows that the proposed model has better robustness and practicability.

Complex spherical-wave seismic inversion in anelastic media for the P-wave minimum quality factor

Attenuation always exists when seismic waves propagate in underground anelastic media, especially in hydrocarbon-bearing reservoirs. Quality factor Q or attenuation factor 1/ Q can be used to quantify the seismic wave attenuation and has become an important hydrocarbon indicator. The relationship between the plane-wave reflection coefficient ([Formula: see text]) in anelastic media and P- and S-wave quality factors has been widely used in the plane-wave seismic inversion to estimate the quality factors. The [Formula: see text] provides an adequate approximation for the deeper subsurface. However, for the shallow subsurface and anelastic wavefields excited by point sources, the [Formula: see text] is inaccurate and its meaning involves some fundamental difficulties. In view of this, a Q-dependent P-P spherical-wave reflection coefficient ([Formula: see text]) in anelastic media is used here. Considering that having too many parameters to be inverted will lead to unstable and inaccurate inversion results, we further derive an approximate anelastic [Formula: see text] and anelastic spherical-wave impedance ([Formula: see text]), which are frequency dependent and are the functions of P- and S-wave velocities, density, and P-wave minimum quality factor ([Formula: see text]). Finally, a complex spherical-wave seismic inversion approach in anelastic media for the P-wave minimum quality factor is developed. Using the Bayesian inversion approach and complex convolution model, we first estimate the multilayer [Formula: see text] from the complex seismic traces with different frequencies and incidence angles. Based on the inverted angle- and frequency-dependent [Formula: see text], the P- and S-wave velocities, density, and P-wave minimum quality factor are further estimated using a nonlinear inversion tool. Synthetic examples verify the feasibility and robustness of the complex spherical-wave seismic inversion approach in anelastic media. In the shallow subsurface, the spherical-wave inversion is superior to plane-wave inversion. A field example further demonstrates the accuracy and great potential of our approach in hydrocarbon-bearing reservoir prediction.

A Novel Lightweight Human Activity Recognition Method Via L-CTCN.

Wi-Fi-based human activity recognition has attracted significant attention. Deep learning methods are widely used to achieve feature representation and activity sensing. While more learnable parameters in the neural networks model lead to richer feature extraction, it results in significant resource consumption, rendering the model unsuitable for lightweight Internet of Things (IoT) devices. Furthermore, the sensing performance heavily relies on the quality and quantity of data, which is a time-consuming and labor-intensive task. Therefore, there is a need to explore methods that reduce the dependence on the quality and quantity of the dataset while ensuring recognition performance and decreasing model complexity to adapt to ubiquitous lightweight IoT devices. In this paper, we propose a novel Lightweight-Complex Temporal Convolution Network (L-CTCN) for human activity recognition. Specifically, this approach effectively combines complex convolution with a Temporal Convolution Network (TCN). Complex convolution can extract richer information from limited raw complex data, reducing the reliance on the quality and quantity of training samples. Based on the designed TCN framework with 1D convolution and residual blocks, the proposed model can achieve lightweight human activity recognition. Extensive experiments verify the effectiveness of the proposed method. We can achieve an average recognition accuracy of 96.6% with only 0.17 M parameter size. This method performs well under conditions of low sampling rates and a low number of subcarriers and samples.

Complex Transformer Network for Single-Angle Plane-Wave Imaging.

Plane-wave imaging (PWI) is a high-frame-rate imaging technique that sacrifices image quality. Deep learning can potentially enhance plane-wave image quality, but processing complex in-phase and quadrature (IQ) data and suppressing incoherent signals pose challenges. To address these challenges, we present a complex transformer network (CTN) that integrates complex convolution and complex self-attention (CSA) modules. The CTN operates in a four-step process: delaying complex IQ data from a 0° single-angle plane wave for each pixel as CTN input data; extracting reconstruction features with a complex convolution layer; suppressing irrelevant features derived from incoherent signals with two CSA modules; and forming output images with another complex convolution layer. The training labels are generated by minimum variance (MV). Simulation, phantom and in vivo experiments revealed that CTN produced comparable- or even higher-quality images than MV, but with much shorter computation time. Evaluation metrics included contrast ratio, contrast-to-noise ratio, generalized contrast-to-noise ratio and lateral and axial full width at half-maximum and were -11.59 dB, 1.16, 0.68, 278 μm and 329 μm for simulation, respectively, and 9.87 dB, 0.96, 0.62, 357 μm and 305 μm for the phantom experiment, respectively. In vivo experiments further indicated that CTN could significantly improve details that were previously vague or even invisible in DAS and MV images. And after being accelerated by GPU, the CTN runtime (76.03 ms) was comparable to that of delay-and-sum (DAS, 61.24 ms). The proposed CTN significantly improved the image contrast, resolution and some unclear details by the MV beamformer, making it an efficient tool for high-frame-rate imaging.

Estimating Monthly River Discharges from GRACE/GRACE-FO Terrestrial Water Storage Anomalies

Simulating river discharge is a complex convolution depending on precipitation, runoff generation and transformation, and network attenuation. Terrestrial water storage anomalies (TWSA) from NASA’s Gravity Recovery and Climate Experiment (GRACE) and its follow-on mission can be used to estimate monthly river discharge (Q). Monthly discharges for the period April 2002–January 2022 are estimated at 2870 U.S. Geological Survey gauge locations (draining 1K to 3M km2) throughout the continental U.S. (CONUS) using two-parameter exponential relationships between TWSA and Q. Roughly 70% of the study sites have a model performance exceeding the expected performance of other satellite-derived discharge products. The results show how the two model parameters vary based on hydrologic characteristics (annual precipitation and range in TWSA) and that model performance can be affected by snow accumulation/melt, water regulation (dams/reservoirs) or GRACE signal leakage. The generally favorable model performance and our understanding of variability in model applicability and associated parameters suggest that this concept can be expanded to other regions and ungauged locations.

Spherical-wave elastic inversion in transversely isotropic media with a vertical symmetry axis

SUMMARY Although subsurface media are usually assumed to be isotropic, anisotropy is ubiquitous in crustal rocks and leads to the variation of seismic response with direction. Transversely isotropic media with a vertical symmetry axis (VTI media) are widely found in the real world, such as in textured shale reservoirs. Plane-wave reflection coefficients (PRCs) in VTI media have been widely exploited in amplitude variation with offset (AVO) inversion to estimate the elastic and anisotropy parameters of subsurface media. However, the PRCs in VTI media meet some fundamental problems, especially at near-critical or post-critical incidence angles where the spherical-wave effect is significant. To consider the wave front curvature, a complex spherical-wave reflection coefficient (SRC) in VTI media is derived. To better understand the spherical-wave seismic response in VTI media, we investigate the dependence of the complex SRC on frequency, reflector depth and Thomsen anisotropy parameters ($\varepsilon $ and $\delta $). Based on a complex convolution model, a spherical-wave AVO inversion approach in VTI media is proposed to estimate the vertical (symmetry-axis) compressional and shear wave velocities (P and S waves), density and Thomsen anisotropy parameters from observed seismic data with different incidence angle and frequency components. Synthetic data with Gaussian random noise are used to verify the robustness of the spherical-wave AVO inversion approach in VTI media. Field data examples show that the proposed approach can produce reasonable inversion results that match well with the well-logging data.

A high‐efficient information extraction mechanism based on complex convolution for wireless signal recognition

AbstractIn the integration of terrestrial and non‐terrestrial networks, massive access to wireless signals poses a significant threat to communication systems. However, existing signal recognition models cannot accurately identify signals with low signal‐to‐noise ratios (SNRs). To alleviate this issue, this paper proposes a high‐efficient information extraction mechanism based on complex convolution. Specifically, complex convolution and complex max‐pooling operations have been integrated into a real‐value network to efficiently acquire anti‐noise information. The extracted features contain both in‐phase and quadrature (IQ) structure information and complex relationship information. Experiments on the public RML2016.04C dataset indicated that the model exhibits rapid convergence and superior noise‐robustness under low SNRs. When SNR =0 dB, the model outperforms the suboptimal model by 4.05%. Furthermore, our model demonstrates excellent generalization performance at high SNRs.

DCT based densely connected convolutional GRU for real-time speech enhancement

Over the past ten years, deep learning has enabled significant advancements in the improvement of noisy speech. Due to the short time stability of speech signal, previous speech enhancement (SE) methods concentrated only on magnitude estimation, and these methods added a phase of the mixture in reconstructing the speech. The performance is limited in these approaches since the phase will also carry some of the speech information. Some of the speech enhancement approaches were developed later to jointly estimate both magnitudes as well as phases. Recently, complex-valued models, like deep complex convolution recurrent network (DCCRN), are proposed, but the computation of the model is very huge. In this work, we propose a Discrete Cosine Transform-based Densely Connected Convolutional Gated Recurrent Unit (DCTDCCGRU) model using dilated dense block and stacked GRU. The dense connectivity strengthens the gradient propagation by concatenating features from previous layers at the input. The advantage of the dense block is that at various resolutions, the dilated convolutions aid with context aggregation, and the dense connectivity provides a feature map with more precise target information by passing through multiple layers. To represent the correlation between neighboring noisy speech frames, a two Layer GRU is added in the bottleneck of U-Net. The experimental findings demonstrate that the proposed model outperformed the other existing models in terms of STOI (short-time objective intelligibility), PESQ (perceptual evaluation of the speech quality), and output SNR (signal-to-noise ratio).

A multi-head residual connection GCN for EEG emotion recognition

Electroencephalography (EEG) emotion recognition is a crucial aspect of human-computer interaction. However, conventional neural networks have limitations in extracting profound EEG emotional features. This paper introduces a novel multi-head residual graph convolutional neural network (MRGCN) model that incorporates complex brain networks and graph convolution networks. The decomposition of multi-band differential entropy (DE) features exposes the temporal intricacy of emotion-linked brain activity, and the combination of short and long-distance brain networks can explore complex topological characteristics. Moreover, the residual-based architecture not only enhances performance but also augments classification stability across subjects. The visualization of brain network connectivity offers a practical technique for investigating emotional regulation mechanisms. The MRGCN model exhibits average classification accuracies of 95.8% and 98.9% for the DEAP and SEED datasets, respectively, highlighting its excellent performance and robustness.

A New Approach to the Evaluation of the Lightning Horizontal Electric Field Over a Lossy Ground Based on the Time-Domain Cooray–Rubinstein Formula Fitted by Orthogonal Polynomials

The calculation of lightning return stroke electromagnetic field is the basis for evaluating transmission line lightning-induced voltages. The Cooray–Rubinstein formula in the time domain is widely used to evaluate the horizontal electric field of lightning return stroke on a lossy ground, but the evaluation of the formula requires high computation cost. Therefore, this study presents a new approach to evaluate the Cooray–Rubinstein formula based on orthogonal polynomial fitting. This method converts the complex convolution in the Cooray–Rubinstein formula into the sum of multiple simple convolutions by using an effective truncation scheme of Legendre orthogonal polynomial and the second Chebyshev orthogonal polynomial. The objective is to realize an efficient evaluation method to the horizontal electric field of the lightning return stroke. On the premise of ensuring the calculation accuracy, the effectiveness and correctness of the proposed method are verified through numerical experiments. Moreover, the application of the time-domain Cooray–Rubinstein formula based on two orthogonal polynomial fitting methods is discussed. Compared with the existing numerical methods for solving the Cooray–Rubinstein formula, the proposed method is easy to implement and efficient, which provides a new idea for evaluating the horizontal electric field of lightning return stroke above the lossy ground in the time domain.

Data-Driven-Based Terahertz Image Restoration

Terahertz (THz) has been widely used in radar, remote sensing, atmospheric and environmental monitoring, real-time biological information extraction, and medical diagnosis. However, the long-wavelength property of THz leads to low imaging resolution. Due to the expensive nature of experimental equipment and the difficulty of obtaining terahertz sources, most scientific institutions have difficulty in obtaining large amounts of terahertz dataset. In addition, it is difficult for convolution neural networks to recover low-resolution complex images because of the phase information contained in the images. In this paper, we build a terahertz imaging system and propose a Progressive Multi-scale Augmented Neural Network (PMANN) to address this problem. PMANN integrates self-attention and channel-attention for image contextual feature extraction by the proposed progressive network. Compared with the Complex convolution Neural Network (CCNN) in private cartoon datasets, PMANN improves the quantitative metrics on PSNR by about 18.6%. It also obtains better visual quality than CCNN. Moreover, we publicly and synthesize the first grayscale image MinistTHz dataset. Compared to SwinTransformer, PMANN improves the PSNR by 28.2%. The experimental results on the THz dataset demonstrate that the proposed model achieves better performances than the state-of-the-art models. Our synthetic THz dataset is open at https://github.com/szpxmu/PMANN.

A Robust Complex-Valued Deep Neural Network for Target Recognition of UAV SAR Imagery

Unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) plays an important role in modern remote sensing for its characteristics of all weather, all day-and-night, zero casualty, flying flexibility and low cost. However, the atmospheric turbulence will cause motion errors to UAV SAR, resulting in unmodeled phase errors. The phase errors will degrade the focusing quality of the image and bring difficulties to the recognition task. Meanwhile, it is difficult for convolution neural network (CNN) to extract and utilize the back-scattering information for the target recognition. To this end, a novel Defocusing Adaptive Complex Convolution Neural Network (DA-CCNN) is proposed, which can realize the overall computation of the network in the complex-valued data domain and effectively extract the phase history information of the complex-valued data. Furthermore, it is the first time that the image entropy metric is introduced into the fully complex deep neural network to improve the focusing quality of the image and the interpretability of the network. The experiment is carried out using the benchmark dataset of MSTAR 10. In order to simulate the defocused images generated by UAV SAR and certificate the robustness to phase errors, datasets with the contamination are also applied. The results show that on the benchmark data, the recognition accuracy of DA-CCNN is comparable to that of the existing methods. On the data with phase errors, DA-CCNN shows stronger robustness and higher accuracy in terms of recognition than the reported networks.