Search

This communication proposes a novel deep-learning (DL) framework for the electromagnetic inverse scattering (EMIS) problems. Solving EMIS problems is a challenging topic due to various difficulties, such as intrinsic nonlinearity, high computation cost, high contrast, and so on. To overcome these challenges, a novel DL-inspired approach is presented in the context of conditional deep convolutional generative adversarial network (CDCGAN), termed CDCGAN-EMIS. The proposed CDCGAN is based on a generator with an EM forward solver and the corresponding discriminator, both constructed by deep convolutional neural networks (DConvNets). During the offline training step, the generator learns a distribution between the measured scattered field data and the corresponding contrasts (permittivities) of dielectric scatterers, while the discriminator determines whether the presented samples are real or fake. Therefore, such CDCGAN-EMIS can generate contrasts of scatterers from measured scattered field data, by learning the distribution between the known contrasts of scatterers and their corresponding field and generating solutions. Based on the proposed CDCGAN-EMIS, EMIS problems can be accurately solved even for extremely high-contrast scatterers. Numerical examples indicate the accuracy and feasibility of our method. The proposed CDCGAN-EMIS opens a novel path for the DL-inspired real-time quantitative microwave imaging method for high-contrast scatterers.

This communication proposes a novel electromagnetic (EM) inversion solver based on a two-step deep learning (DL) framework. The framework consists of the deep convolutional asymmetric encoder–decoder structure (DCAEDS) followed by the deep residual convolutional neural network (DRCNN). In the first step, DCAEDS utilizes EM scattered field data from a single-frequency one-time measurement to coarsely retrieve the initial contrasts (permittivities) of target scatterers. In the second step, DRCNN employs a mixed input scheme, comprising the initially reconstructed permittivities from the first step and the original EM scattered field data, to significantly improve the retrieved contrasts (permittivities) and refine the reconstruction of targets. Consequently, the proposed EM inversion solver achieves excellent accuracy and efficiency, even for high-contrast targets. The proposed solver is flexible as it is required only for a single-frequency one-time measurement on the EM scattered field. Moreover, the proposed two-step DL-based solver overcomes the limitations of conventional methods, such as high computational costs and ill-posedness. Numerical benchmarks based on various dielectric objects demonstrate the feasibility of the proposed EM inversion solver, highlighting its potential as a candidate for real-time quantitative EM inversion for high-contrast targets.

In this communication, we propose to use a deep learning (DL) approach to detect unit failure in array antennas. Due to natural machine life cycle and/or unexpected accidents, antenna units unavoidably suffer from the risk of failure, leading to the deterioration of array performance. To realize the detection of unit failure, the far-field radiation patterns are used as the input of the deep convolutional neural network (DConvNet) for antenna array diagnosis learning. The proposed DConvNet consists of continuous functional groups of convolution, batch normalization, and activation layers, followed by a fully connected layer to realize recognition, i.e., the fault diagnosis of antenna array. Different from conventional diagnosis techniques, the main advantage of the proposed DL approach does not require intensive computations based on Green’s function. The training data are collected by the electromagnetic (EM) simulation tool. Additionally, the Gaussian noise is added to the training data to imitate the interference in real application scenarios. The proposed DConvNet for array diagnosis is verified by three numerical benchmarks and demonstrates that it can diagnose antenna array in a complex environment with generality.

This article proposes a novel fast electromagnetic (EM) inversion solver for heterogeneous scatterers with high contrast. In order to ensure inversion accuracy, the conventional solvers for the EM inverse scattering (EMIS) problems usually require EM scattered field information originating from multiple incident EM waves, resulting in tedious measurement operation and considerable measurement data for inversion computation. Thus, the conventional solvers are difficult to suit for real-time quantitative EM problems, which require relatively simple measurement operations and small measurement data dimensions. To overcome these challenges, a novel EM inversion solver is proposed based on a conditional deep convolutional generative adversarial network (CDCGAN). The proposed CDCGAN includes the generator with an EM scattering simulator and the corresponding discriminator, both consisting of complex-valued deep convolutional neural networks (DConvNets). The trained CDCGAN can be successfully applied to inhomogeneous and high-contrast scatterers only by employing one single incident EM wave in single-frequency and far-field measurement, which greatly simplifies measurement and reduces the computation complexity for its further inversion computation. Numerical examples have indicated the accuracy and feasibility of the proposed DL-based inversion solver, which acts as the potential candidate for solving real-time quantitative EM problems.

Since higher-order tensors are naturally suitable for representing multi-dimensional data in real-world, e.g., color images and videos, low-rank tensor representation has become one of the emerging areas in machine learning and computer vision. However, classical low-rank tensor representations can solely represent multi-dimensional discrete data on meshgrid, which hinders their potential applicability in many scenarios beyond meshgrid. To break this barrier, we propose a low-rank tensor function representation (LRTFR) parameterized by multilayer perceptrons (MLPs), which can continuously represent data beyond meshgrid with powerful representation abilities. Specifically, the suggested tensor function, which maps an arbitrary coordinate to the corresponding value, can continuously represent data in an infinite real space. Parallel to discrete tensors, we develop two fundamental concepts for tensor functions, i.e., the tensor function rank and low-rank tensor function factorization, and utilize MLPs to paramterize factor functions of the tensor function factorization. We theoretically justify that both low-rank and smooth regularizations are harmoniously unified in LRTFR, which leads to high effectiveness and efficiency for data continuous representation. Extensive multi-dimensional data recovery applications arising from image processing (image inpainting and denoising), machine learning (hyperparameter optimization), and computer graphics (point cloud upsampling) substantiate the superiority and versatility of our method as compared with state-of-the-art methods. Especially, the experiments beyond the original meshgrid resolution (hyperparameter optimization) or even beyond meshgrid (point cloud upsampling) validate the favorable performances of our method for continuous representation.

In recent years, neural network-based methods have shown promising results in hyperspectral image (HSI) denoising areas. Real HSIs exhibit the substantial variations in noise distribution due to various factors, such as different imaging techniques, camera variations, imaging environments, and hardware aging. In this article, we develop an eigenimage plus eigennoise level map-guided convolutional neural network (CNN) for HSI denoising. Our main idea is to perform eigendecomposition on HSIs, utilize the low-rank property of HSIs in the spectral dimension and approximate the spectral vectors in a low-dimensional orthogonal subspace, where representation coefficients are called eigenimages. Besides eigenimages, we make use of estimated eigennoise level map as an input to guide the network for denoising. The proposed network can be constructed without restriction in the number of eigencomponents by using all eigenimages and eigennoise level maps of training noisy-clean pairs. In the inference part, the trained network can be used to remove noise in observed eigenimages without restriction in the number of eigencomponents, and an underlying clean image HSI can be estimated by performing orthogonal projection back. Experimental results on both simulated and real HSIs demonstrate the effectiveness of our trained Eigen-CNN compared with state-of-the-art HSI denoising methods. A MATLAB demo of this work is available at: https://github.com/LinaZhuang/HSI-denoiser-Eigen-CNN for the sake of reproducibility.

Graph-structured data, where nodes exhibit either pair-wise or high-order relations, are ubiquitous and essential in graph learning. Despite the great achievement made by existing graph learning models, these models use the direct information (edges or hyperedges) from graphs and do not adopt the underlying indirect information (hidden pair-wise or high-order relations). To address this issue, in this paper, we propose a general framework named Simplicial Complex Neural (SCN) network, in which we construct a simplicial complex based on the direct and indirect graph information from a graph so that all information can be employed in the complex network learning. Specifically, we learn representations of simplices by aggregating and integrating information from all the simplices together via layer-by-layer simplicial complex propagation. In consequence, the representations of nodes, edges, and other high-order simplices are obtained simultaneously and can be used for learning purposes. By making use of block matrix properties, we derive the theoretical bound of the simplicial complex filter learnt by the propagation and establish the generalization error bound of the proposed simplicial complex network. We perform extensive experiments on node (0-simplex), edge (1-simplex), and triangle (2-simplex) classifications, and promising results demonstrate the performance of the proposed method is better than that of existing graph and hypergraph network approaches.

Unmixing is a crucial technique in analyzing hyperspectral imaging (HSI) data, which involves identifying the endmembers present in the data and estimating their abundance maps. Due to some practical constraints in the atmospheric environment, HSI data is usually nonuniformly distributed along the spectral domain, which brings incomplete spectral information in the hyperspectral unmixing. To overcome this issue, we propose, in this article, nonnegative matrix functional factorization (NMFF) which is an extension of classical nonnegative matrix factorization (NMF) for hyperspectral unmixing. In particular, we present a novel functional factorization model by incorporating the implicit neural representations (INRs) to learn about endmembers. Our method effectively characterizes endmembers by learning a continuous representation through INR with positional encoding, capturing the nonuniform distribution of spectral wavelengths. This distinct approach streamlines NMFF’s iterative process for abundance extraction, bypassing the conventionally complex and cumbersome processing. When tested on various datasets, our hyperspectral unmixing approach consistently outperforms established techniques, showcasing the enhanced capabilities of our proposed model.

Modern datasets often exhibit heavy-tailed behavior, while quantization is inevitable in digital signal processing and many machine learning problems. This paper studies the quantization of heavy-tailed data in several fundamental statistical estimation problems where the underlying distributions have bounded moments of some order (no greater than 4). We propose to truncate and properly dither the data prior to a uniform quantization. Our major standpoint is that (near) minimax rates of estimation error could be achieved by computationally tractable estimators based on the quantized data produced by the proposed scheme. In particular, concrete results are worked out for covariance estimation, compressed sensing (also interpreted as sparse linear regression), and matrix completion, all agreeing that the quantization only slightly worsens the multiplicative factor. Additionally, while prior results focused on the quantization of responses (i.e., measurements), we study compressed sensing where the covariates (i.e., sensing vectors) are also quantized; in this case, though our recovery program is non-convex (since our covariance matrix estimator lacks positive semi-definiteness), we prove that all local minimizers enjoy near-optimal estimation error. Moreover, by the concentration inequality of the product process and a covering argument, we establish a near minimax uniform recovery guarantee for quantized compressed sensing with heavy-tailed noise. Finally, numerical simulations are provided to corroborate our theoretical results.

In this article, we develop a new alternating projection method to compute nonnegative low rank matrix approximation for nonnegative matrices. In the nonnegative low rank matrix approximation method, the projection onto the manifold of fixed rank matrices can be expensive as the singular value decomposition is required. We propose to use the tangent space of the point in the manifold to approximate the projection onto the manifold in order to reduce the computational cost. We show that the sequence generated by the alternating projections onto the tangent spaces of the fixed rank matrices manifold and the nonnegative matrix manifold, converge linearly to a point in the intersection of the two manifolds where the convergent point is sufficiently close to optimal solutions. This convergence result based inexact projection onto the manifold is new and is not studied in the literature. Numerical examples in data clustering, pattern recognition and hyperspectral data analysis are given to demonstrate that the performance of the proposed method is better than that of nonnegative matrix factorization methods in terms of computational time and accuracy.