arXiv subjects

Hing Cheung So

Publications and source records attributed to Hing Cheung So.

At least 55 records · Page 3Linked to original sources

arXiv2023

One-Bit Covariance Reconstruction with Non-zero Thresholds: Algorithm and Performance Analysis

Covariance matrix reconstruction is a topic of great significance in the field of one-bit signal processing and has numerous practical applications. Despite its importance, the conventional arcsine law with zero threshold is incapable of recovering the diagonal elements of the covariance matrix. To address this limitation, recent studies have proposed the use of non-zero clipping thresholds. However, the relationship between the estimation error and the sampling threshold is not yet known. In this paper, we undertake an analysis of the mean squared error by computing the Fisher information matrix for a given threshold. Our results reveal that the optimal threshold can vary considerably, depending on the variances and correlation coefficients. As a result, it is inappropriate to use a constant threshold to encompass parameters that vary widely. To mitigate this issue, we present a recovery scheme that incorporates time-varying thresholds. Our approach differs from existing methods in that it utilizes the exact values of the threshold, rather than its statistical properties, to enhance the estimation performance. Our simulations, including the direction-of-arrival estimation problem, demonstrate the efficacy of the developed scheme, especially in complex scenarios where the covariance elements are widely separated.

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arXiv2023

Convergence Analysis of Consensus-ADMM for General QCQP

We analyze the convergence properties of the consensus-alternating direction method of multipliers (ADMM) for solving general quadratically constrained quadratic programs. We prove that the augmented Lagrangian function value is monotonically non-increasing as long as the augmented Lagrangian parameter is chosen to be sufficiently large. Simulation results show that the augmented Lagrangian function is bounded from below when the matrix in the quadratic term of the objective function is positive definite. In such a case, the consensus-ADMM is convergent.

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arXiv2023

Globally Optimized TDOA High Frequency Source Localization Based on Quasi-Parabolic Ionosphere Modeling and Collaborative Gradient Projection

We investigate the problem of high frequency (HF) source localization using the time-difference-of-arrival (TDOA) observations of ionosphere-refracted radio rays based on quasi-parabolic (QP) modeling. An unresolved but pertinent issue in such a field is that the existing gradient-type scheme can easily get trapped in local optima for practical use. This will lead to the difficulty in initializing the algorithm and finally degraded positioning performance if the starting point is inappropriately selected. In this paper, we develop a collaborative gradient projection (GP) algorithm in order to globally solve the highly nonconvex QP-based TDOA HF localization problem. The metaheuristic of particle swarm optimization (PSO) is exploited for information sharing among multiple GP models, each of which is guaranteed to work out a critical point solution to the simplified maximum likelihood formulation. Random mutations are incorporated to avoid the early convergence of PSO. Rather than treating the geolocation of HF transmitter as a pure optimization problem, we further provide workarounds for addressing the possible impairments and challenges when the proposed technique is applied in practice. Numerical results demonstrate the effectiveness of our PSO-assisted re-initialization strategy in achieving the global optimality, and the superiority of our method over its competitor in terms of positioning accuracy.

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arXiv2023

Disproving Sum-Difference Co-Array Property

The recently published paper by Gupta and Agrawal [1] exploited the sum-difference co-array (SDCA) to enhance the virtual aperture of sparse arrays. We argue that the key SDCA property established in [1] requires a critical necessary and sufficient condition that is valid for a very rare case only.

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arXiv2022

Low-Rank and Row-Sparse Decomposition for Joint DOA Estimation and Distorted Sensor Detection

Distorted sensors could occur randomly and may lead to the breakdown of a sensor array system. We consider an array model within which a small number of sensors are distorted by unknown sensor gain and phase errors. With such an array model, the problem of joint direction-of-arrival (DOA) estimation and distorted sensor detection is investigated and the problem is formulated under the framework of low-rank and row-sparse decomposition. We derive an iteratively reweighted least squares (IRLS) algorithm to solve the resulting problem in both noiseless and noisy cases. The convergence property of the IRLS algorithm is analyzed by means of the monotonicity and boundedness of the objective function. Extensive simulations are conducted regarding parameter selection, convergence speed, computational complexity, and performances of DOA estimation as well as distorted sensor detection. Even though the IRLS algorithm is slightly worse than the alternating direction method of multipliers in detecting the distorted sensors, the results show that our approach outperforms several state-of-the-art techniques in terms of convergence speed, computational cost, and DOA estimation performance.

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arXiv2022

Off-Grid Direction-of-Arrival Estimation Using Second-Order Taylor Approximation

The problem of off-grid direction-of-arrival (DOA) estimation is investigated. We develop a grid-based method to jointly estimate the closest spatial frequency (the sine of DOA) grids, and the gaps between the estimated grids and the corresponding frequencies. By using a second-order Taylor approximation, the data model under the framework of joint-sparse representation is formulated. We point out an important property of the signals of interest in the model, namely the proportionality relationship, which is empirically demonstrated to be useful in the sense that it increases the probability of the mixing matrix satisfying the block restricted isometry property. Simulation examples demonstrate the effectiveness and superiority of the proposed method against several state-of-the-art grid-based approaches.

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arXiv2022

On Generalisation of Isotropic Central Difference for Higher Order Approximation of Fractional Laplacian

The study of generalising the central difference for integer order Laplacian to fractional order is discussed in this paper. Analysis shows that, in contrary to the conclusion of a previous study, difference stencils evaluated through fast Fourier transform prevents the convergence of the solution of fractional Laplacian. We propose a composite quadrature rule in order to efficiently evaluate the stencil coefficients with the required convergence rate in order to guarantee convergence of the solution. Furthermore, we propose the use of generalised higher order lattice Boltzmann method to generate stencils which can approximate fractional Laplacian with higher order convergence speed and error isotropy. We also review the formulation of the lattice Boltzmann method and discuss the explicit sparse solution formulated using Smolyak's algorithm, as well as the method for the evaluation of the Hermite polynomials for efficient generation of the higher order stencils. Numerical experiments are carried out to verify the error analysis and formulations.

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arXiv2021

Nonlinear Tensor Ring Network

The state-of-the-art deep neural networks (DNNs) have been widely applied for various real-world applications, and achieved significant performance for cognitive problems. However, the increment of DNNs' width and depth in architecture results in a huge amount of parameters to challenge the storage and memory cost, limiting to the usage of DNNs on resource-constrained platforms, such as portable devices. By converting redundant models into compact ones, compression technique appears to be a practical solution to reducing the storage and memory consumption. In this paper, we develop a nonlinear tensor ring network (NTRN) in which both fullyconnected and convolutional layers are compressed via tensor ring decomposition. Furthermore, to mitigate the accuracy loss caused by compression, a nonlinear activation function is embedded into the tensor contraction and convolution operations inside the compressed layer. Experimental results demonstrate the effectiveness and superiority of the proposed NTRN for image classification using two basic neural networks, LeNet-5 and VGG-11 on three datasets, viz. MNIST, Fashion MNIST and Cifar-10.

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arXiv2021

Neurodynamic TDOA localization with NLOS mitigation via maximum correntropy criterion

In this paper, we exploit the maximum correntropy criterion (MCC) to robustify the traditional time-difference-of-arrival (TDOA) location estimator in the presence of non-line-of-sight (NLOS) propagation conditions. For the sake of statistical efficiency, the correntropy-based robust loss is imposed on the underlying time-of-arrival composition via joint estimation of the source position and onset time, instead of the TDOA counterpart generated in the postprocessing of sensor-collected timestamps. We then employ a neurodynamic optimization approach to tackle the highly nonconvex MCC formulation. Furthermore, we examine the local stability of equilibrium for the corresponding projection-type neural network model. Simulation investigations in representative NLOS propagation scenarios demonstrate that our neurodynamic robust TDOA localization solution is capable of outperforming several existing schemes in terms of positioning accuracy.

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arXiv2021

Maximum correntropy criterion for robust TOA-based localization in NLOS environments

We investigate the problem of time-of-arrival (TOA) based localization under possible non-line-of-sight (NLOS) propagation conditions. To robustify the squared-range-based location estimator, we follow the maximum correntropy criterion, essentially the Welsch $M$-estimator with a redescending influence function which behaves like $\ell_0$-minimization towards the grossly biased measurements, to derive the formulation. The half-quadratic technique is then applied to settle the resulting optimization problem in an alternating maximization (AM) manner. By construction, the major computational challenge at each AM iteration boils down to handling an easily solvable generalized trust region subproblem. It is worth noting that the implementation of our localization method requires nothing but merely the TOA-based range measurements and sensor positions as prior information. Simulation and experimental results demonstrate the competence of the presented scheme in outperforming several state-of-the-art approaches in terms of positioning accuracy, especially in scenarios where the percentage of NLOS paths is not large enough.

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arXiv2021

Arbitrary order of convergence for Riesz fractional derivative via central difference method

We propose a novel method to compute a finite difference stencil for Riesz derivative for artibitrary speed of convergence. This method is based on applying a pre-filter to the Grünwald-Letnikov type central difference stencil. The filter is obtained by solving for the inverse of a symmetric Vandemonde matrix and exploiting the relationship between the Taylor's series coefficients and fast Fourier transform. The filter costs O\left(N^{2}\right) operations to evaluate for O\left(h^{N}\right) of convergence, where h is the sampling distance. The higher convergence speed should more than offset the overhead with the requirement of the number of nodal points for a desired error tolerance significantly reduced. The benefit of progressive generation of the stencil coefficients for adaptive grid size for dynamic problems with the Grünwald-Letnikov type difference scheme is also kept because of the application of filtering. The higher convergence rate is verified through numerical experiments.

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arXiv2020

TDOA-based localization with NLOS mitigation via robust model transformation and neurodynamic optimization

This paper revisits the problem of locating a signal-emitting source from time-difference-of-arrival (TDOA) measurements under non-line-of-sight (NLOS) propagation. Many currently fashionable methods for NLOS mitigation in TDOA-based localization tend to solve their optimization problems by means of convex relaxation and, thus, are computationally inefficient. Besides, previous studies show that manipulating directly on the TDOA metric usually gives rise to intricate estimators. Aiming at bypassing these challenges, we turn to retrieve the underlying time-of-arrival framework by treating the unknown source onset time as an optimization variable and imposing certain inequality constraints on it, mitigate the NLOS errors through the $\ell_1$-norm robustification, and finally apply a hardware realizable neurodynamic model based on the redefined augmented Lagrangian and projection theorem to solve the resultant nonconvex optimization problem with inequality constraints. It is validated through extensive simulations that the proposed scheme can strike a nice balance between localization accuracy, computational complexity, and prior knowledge requirement.

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arXiv2019

Target Localization with Jammer Removal Using Frequency Diverse Array

A foremost task in frequency diverse array multiple-input multiple-output (FDA-MIMO) radar is to efficiently obtain the target signal in the presence of interferences. In this paper, we employ a novel "low-rank + low-rank + sparse" decomposition model to extract the low-rank desired signal and suppress the jamming signals from both barrage and burst jammers. In the literature, the barrage jamming signals, which are intentionally interfered by enemy jammer radar, are usually assumed Gaussian distributed. However, such assumption is oversimplified to hold in practice as the interferences often exhibit non-Gaussian properties. Those non-Gaussian jamming signals, known as impulsive noise or burst jamming, are involuntarily deviated from friendly radar or other working radio equipment including amplifier saturation and sensor failures, thunderstorms and man-made noise. The estimation performance of the existing estimators, relied crucially on the Gaussian noise assumption, may degrade substantially since the probability density function (PDF) of burst jamming has heavier tails that exceed a few standard deviations than the Gaussian distribution. To capture a more general signal model with burst jamming in practice, both barrage jamming and burst jamming are included and a two-step "Go Decomposition" (GoDec) method via alternating minimization is devised for such mixed jamming signal model, where the $a$ $priori$ rank information is exploited to suppress two kinds of jammers and estimate the desired target. Simulation results verify the robust performance of the devised scheme.

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arXiv2019

Image Denoising by Random Interpolation Average with Low-Rank Matrix Approximation

With the wide deployment of digital image capturing equipment, the need of denoising to produce a crystal clear image from noisy capture environment has become indispensable. This work presents a novel image denoising method that can tackle both impulsive noise, such as salt and pepper noise (SAPN), and additive white Gaussian noise (AWGN), such as hot carrier noise from CMOS sensor, at the same time. We propose to use low-rank matrix approximation to form the basic denoising framework, as it has the advantage of preserving the spatial integrity of the image. To mitigate the SAPN, the original noise corrupted image is randomly sampled to produce sampled image sets. Low-rank matrix factorization method (LRMF) via alternating minimization denoising method is applied to all sampled images, and the resultant images are fused together via a wavelet fusion with hard threshold denoising. Since the sampled image sets have independent but identical noise property, the wavelet fusion serves as the effective mean to remove the AWGN, while the LRMF method suppress the SAPN. Simulation results are presented which vividly show the denoised images obtained by the proposed method can achieve crystal clear image with strong structural integrity and showing good performance in both subjective and objective metrics.

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arXiv2019

A Survey on Matrix Completion: Perspective of Signal Processing

Matrix completion (MC) is a promising technique which is able to recover an intact matrix with low-rank property from sub-sampled/incomplete data. Its application varies from computer vision, signal processing to wireless network, and thereby receives much attention in the past several years. There are plenty of works addressing the behaviors and applications of MC methodologies. This work provides a comprehensive review for MC approaches from the perspective of signal processing. In particular, the MC problem is first grouped into six optimization problems to help readers understand MC algorithms. Next, four representative types of optimization algorithms solving the MC problem are reviewed. Ultimately, three different application fields of MC are described and evaluated.

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arXiv2018

l0-norm Based Centers Selection for Training Fault Tolerant RBF Networks and Selecting Centers

The aim of this paper is to train an RBF neural network and select centers under concurrent faults. It is well known that fault tolerance is a very attractive property for neural networks. And center selection is an important procedure during the training process of an RBF neural network. In this paper, we devise two novel algorithms to address these two issues simultaneously. Both of them are based on the ADMM framework. In the first method, the minimax concave penalty (MCP) function is introduced to select centers. In the second method, an l0-norm term is directly used, and the hard threshold (HT) is utilized to address the l0-norm term. Under several mild conditions, we can prove that both methods can globally converge to a unique limit point. Simulation results show that, under concurrent fault, the proposed algorithms are superior to many existing methods.

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arXiv2018

Robust MIMO Radar Target Localization based on Lagrange Programming Neural Network

This paper focuses on target localization in a widely distributed multiple-input-multiple-output (MIMO) radar system. In this system, range measurements, which include the sum of distances between transmitter and target and the distances from the target to receivers, are used. We can obtain an accurate estimated position of the target by minimizing the measurement errors. In order to make our model come closer to reality, we introduce two kinds of noises, namely, Gaussian noise and outliers. When we evaluate a target localization algorithm, its localization accuracy and computational complexity are two main criteria. To improve the positioning accuracy, the original problem is formulated as solving a non-smooth constrained optimization problem in which the objective function is either l1-norm or l0-norm term. To achieve a real-time solution, the Lagrange programming neural network (LPNN) is utilized to solve this problem. However, it is well known that LPNN requires twice-differentiable objective function and constraints. Obviously, the l1-norm or l0-norm term in the objective function does not satisfy this requirement. To address this non-smooth optimization problem, this paper proposes two modifications based on the LPNN framework. In the first method, a differentiable proximate l1-norm function is introduced. While in the second method, locally competitive algorithm is utilized. Simulation and experimental results demonstrate that the performance of the proposed algorithms outperforms several existing schemes.

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arXiv2018

Robust Real-time Ellipse Fitting Based on Lagrange Programming Neural Network and Locally Competitive Algorithm

Given a set of 2-dimensional (2-D) scattering points, which are usually obtained from the edge detection process, the aim of ellipse fitting is to construct an elliptic equation that best fits the collected observations. However, some of the scattering points may contain outliers due to imperfect edge detection. To address this issue, we devise a robust real-time ellipse fitting approach based on two kinds of analog neural network, Lagrange programming neural network (LPNN) and locally competitive algorithm (LCA). First, to alleviate the influence of these outliers, the fitting task is formulated as a nonsmooth constrained optimization problem in which the objective function is either an l1-norm or l0-norm term. It is because compared with the l2-norm in some traditional ellipse fitting models, the lp-norm with p<2 is less sensitive to outliers. Then, to calculate a real-time solution of this optimization problem, LPNN is applied. As the LPNN model cannot handle the non-differentiable term in its objective, the concept of LCA is introduced and combined with the LPNN framework. Simulation and experimental results show that the proposed ellipse fitting approach is superior to several state-of-the-art algorithms.

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