Explore the vast range of titles available.

Complex neutrosophic set (CNS) is a modified version of the complex fuzzy set, to cope with complicated and inconsistent information in the environment of fuzzy set theory. The CNS is characterised by three functions expressing the degree of complex-valued membership, complex-valued abstinence and degree of complex-valued non-membership. The aim of this manuscript is to initiate the novel dice similarity measures and generalised dice similarity using CNS. The special cases of the investigated measures are discussed with the help of some remarks. Moreover, some distance measures based on CNS are also proposed in this manuscript. Then, the authors applied the generalised dice similarity measures and weighted generalised dice similarity measures using CNS to the pattern recognition model to examine the reliability and superiority of the established approaches. The advantages and comparative analysis of the proposed measures with existing measures are also discussed in detail. At last, a numerical example is provided to illustrate the validity and applicability of the presented measures.

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.

Time-domain backprojection algorithms are widely used in state-of-the-art synthetic aperture radar (SAR) imaging systems that are designed for applications where motion error compensation is required. These algorithms include an interpolation procedure, under which an unknown SAR range-compressed data parameter is estimated based on complex-valued SAR data samples and backprojected into a defined image plane. However, the phase of complex-valued SAR parameters estimated based on existing interpolators does not contain correct information about the range distance between the SAR imaging system and the given point of space in a defined image plane, which affects the quality of reconstructed SAR scenes. Thus, a phase-control procedure is required. This paper introduces extensions of existing linear, cubic, and sinc interpolation algorithms to interpolate complex-valued SAR data, where the phase of the interpolated SAR data value is controlled through the assigned a priori known range time that is needed for a signal to reach the given point of the defined image plane and return back. The efficiency of the extended algorithms is tested at the Nyquist rate on simulated and real data at THz frequencies and compared with existing algorithms. In comparison to the widely used nearest-neighbor interpolation algorithm, the proposed extended algorithms are beneficial from the lower computational complexity perspective, which is directly related to the offering of smaller memory requirements for SAR image reconstruction at THz frequencies.

Polarimetric Synthetic Aperture Radar (PolSAR) images encompass valuable information that can facilitate extensive land cover interpretation and generate diverse output products. Extracting meaningful features from PolSAR data poses challenges distinct from those encountered in optical imagery. Deep Learning (DL) methods offer effective solutions for overcoming these challenges in PolSAR feature extraction. Convolutional Neural Networks (CNNs) play a crucial role in capturing PolSAR image characteristics by exploiting kernel capabilities to consider local information and the complex-valued nature of PolSAR data. In this study, a novel three-branch fusion of Complex-Valued CNN named (CV-ASDF2Net) is proposed for PolSAR image classification. To validate the performance of the proposed method, classification results are compared against multiple state-of-the-art approaches using the Airborne Synthetic Aperture Radar (AIRSAR) datasets of Flevoland, San Francisco, and ESAR Oberpfaffenhofen dataset. Moreover, quantitative and qualitative evaluation measures are conducted to assess the classification performance. The results indicate that the proposed approach achieves notable improvements in Overall Accuracy (OA), with enhancements of 1.30% and 0.80% for the AIRSAR datasets, and 0.50% for the ESAR dataset. However, the most remarkable performance of the CV-ASDF2Net model is observed with the Flevoland dataset; the model achieves an impressive OA of 96.01% with only a 1% sampling ratio. The source code is available at: https://github.com/mqalkhatib/CV-ASDF2Net

We propose the Deep Oscillatory Neural Network (DONN), a brain-inspired network architecture that incorporates oscillatory dynamics into learning. Unlike conventional neural networks with static internal states, DONN neurons exhibit brain-like oscillatory activity through neural Hopf oscillators operating in the complex domain. The network combines neural oscillators with traditional sigmoid and ReLU neurons, all employing complex-valued weights and activations. Input signals can be presented to oscillators in three modes: resonator, amplitude modulation, and frequency modulation. Training uses complex backpropagation to minimize the output error. We extend this approach to convolutional architectures, creating Oscillatory Convolutional Neural Networks (OCNNs). Evaluation on benchmark signal and image processing tasks demonstrates comparable or improved performance over baseline methods. Interestingly, the network exhibits emergent phenomena such as feature and temporal binding during image classification, a key characteristic of biological visual processing, and exhibit STDP (Spike Timing Dependent Plasticity) kernel when trained using Hebbain learning. These phenomena with explicit oscillatory dynamics enhance the interpretability of internal representations.

In this manuscript, the existence theorem for a unique solution to a coupled system of impulsive fractional differential equations in complex-valued fuzzy metric spaces is studied and the fuzzy version of some fixed point results by using the definition and properties of a complex-valued fuzzy metric space is presented. Ultimately, some appropriate examples are constructed to illustrate our theoretical results.

Compared to traditional real-valued neural networks, which process only amplitude information, complex-valued neural networks handle both amplitude and phase information, leading to superior performance in polarimetric synthetic aperture radar (PolSAR) image classification tasks. This paper proposes a multi-scale feature extraction (MSFE) method based on a 3D complex-valued network to improve classification accuracy by fully leveraging multi-scale features, including phase information. We first designed a complex-valued three-dimensional network framework combining complex-valued 3D convolution (CV-3DConv) with complex-valued squeeze-and-excitation (CV-SE) modules. This framework is capable of simultaneously capturing spatial and polarimetric features, including both amplitude and phase information, from PolSAR images. Furthermore, to address robustness degradation from limited labeled samples, we introduced a multi-scale learning strategy that jointly models global and local features. Specifically, global features extract overall semantic information, while local features help the network capture region-specific semantics. This strategy enhances information utilization by integrating multi-scale receptive fields, complementing feature advantages. Extensive experiments on four benchmark datasets demonstrated that the proposed method outperforms various comparison methods, maintaining high classification accuracy across different sampling rates, thus validating its effectiveness and robustness.

Complex-valued models have been applied to several fields as a result of their advantages in modeling and processing uncertain information, but few studies have addressed the uncertainty associated with them. It is therefore the main contribution of this paper to propose a complex-valued Deng entropy in the complex-valued evidence theory (One of the complex-valued models). Complex-valued Deng entropy effectively measures the uncertainty of the mass function in the complex-valued framework. It involves uncertainty related to phase angle information, inconsistency and non-specificity. Additionally, complex-valued Deng entropy is a generalization of the Deng entropy and Shannon entropy. In other words, complex-valued Deng entropy may collapse to classical Deng entropy if the complex-valued mass function collapses to a mass function in real space. If the complex-valued mass function collapses into the probability distribution in real space, the complex-valued Deng entropy also collapses into Shannon entropy. There are also a number of numerical examples illustrating the compatibility and effectiveness of the complex-valued Deng entropy. Finally, this article presents a classification experiment involving entropy. Results of classification experiments indicate that results associated with the core parameter of complex-valued Deng entropy are more accurate than results associated with the core parameter of Deng entropy in some data sets.

Driven by deep learning, three-dimensional (3-D) target reconstruction from two-dimensional (2-D) synthetic aperture radar (SAR) images has been developed. However, there is still room for improvement in the reconstruction quality. In this paper, we propose a structurally flexible occupancy network (SFONet) to achieve high-quality reconstruction of a 3-D target using one or more 2-D SAR images. The SFONet consists of a basic network and a pluggable module that allows it to switch between two input modes: one azimuthal image and multiple azimuthal images. Furthermore, the pluggable module is designed to include a complex-valued (CV) long short-term memory (LSTM) submodule and a CV attention submodule, where the former extracts structural features of the target from multiple azimuthal SAR images, and the latter fuses these features. When two input modes coexist, we also propose a two-stage training strategy. The basic network is trained in the first stage using one azimuthal SAR image as the input. In the second stage, the basic network trained in the first stage is fixed, and only the pluggable module is trained using multiple azimuthal SAR images as the input. Finally, we construct an experimental dataset containing 2-D SAR images and 3-D ground truth by utilizing the publicly available Gotcha echo dataset. Experimental results show that once the SFONet is trained, a 3-D target can be reconstructed using one or more azimuthal images, exhibiting higher quality than other deep learning-based 3-D reconstruction methods. Moreover, when the composition of a training sample is reasonable, the number of samples required for the SFONet training can be reduced.

Deep learning has significantly advanced synthetic aperture radar (SAR) ship detection in recent years. However, existing approaches predominantly rely on amplitude information while largely overlooking the critical phase component, limiting further performance improvements. Additionally, unlike optical images, which benefit from a variety of enhancement techniques, complex-valued SAR images lack effective processing methods. To address these challenges, we propose Complex-Valued You Only Look Once (CV-YOLO), an anchor-free, oriented bounding box (OBB)-based ship detection network that fully exploits both amplitude and phase information from single-polarization, single-look complex SAR images. Furthermore, we introduce novel complex-valued data augmentation strategies—including complex-valued Gaussian filtering, complex-valued Mosaic data augmentation, and complex-valued mixed sample data augmentation—to enhance sample diversity and significantly improve the generalization capability of complex-valued networks. Experimental evaluations of the Complex-Valued SAR Images Rotation Ship Detection Dataset (CSRSDD) demonstrate that our method surpasses real-valued networks with identical architectures and outperforms leading real-valued approaches, validating the effectiveness of our proposed methodology.