arXiv subjects

Chi-Sing Leung

Publications and source records attributed to Chi-Sing Leung.

6 recordsLinked to original sources

arXiv2024

A semidefinite programming approach for robust elliptic localization

This short communication addresses the problem of elliptic localization with outlier measurements. Outliers are prevalent in various location-enabled applications, and can significantly compromise the positioning performance if not adequately handled. Instead of following the common trend of using $M$-estimation or adjusting the conventional least squares formulation by integrating extra error variables, we take a different path. Specifically, we explore the worst-case robust approximation criterion to bolster resistance of the elliptic location estimator against outliers. From a geometric standpoint, our method boils down to pinpointing the Chebyshev center of a feasible set, which is defined by the available bistatic ranges with bounded measurement errors. For a practical approach to the associated min-max problem, we convert it into the convex optimization framework of semidefinite programming (SDP). Numerical simulations confirm that our SDP-based technique can outperform a number of existing elliptic localization schemes in terms of positioning accuracy in Gaussian mixture noise.

eess.SP↗

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.

cs.LG↗

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.

eess.SP↗

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.

eess.IV↗

arXiv2018

Fast L1-Minimization Algorithm for Sparse Approximation Based on an Improved LPNN-LCA framework

The aim of sparse approximation is to estimate a sparse signal according to the measurement matrix and an observation vector. It is widely used in data analytics, image processing, and communication, etc. Up to now, a lot of research has been done in this area, and many off-the-shelf algorithms have been proposed. However, most of them cannot offer a real-time solution. To some extent, this shortcoming limits its application prospects. To address this issue, we devise a novel sparse approximation algorithm based on Lagrange programming neural network (LPNN), locally competitive algorithm (LCA), and projection theorem. LPNN and LCA are both analog neural network which can help us get a real-time solution. The non-differentiable objective function can be solved by the concept of LCA. Utilizing the projection theorem, we further modify the dynamics and proposed a new system with global asymptotic stability. Simulation results show that the proposed sparse approximation method has the real-time solutions with satisfactory MSEs.

eess.SP↗

arXiv2018

ADMM-MCP Framework for Sparse Recovery with Global Convergence

In compressed sensing, the l0-norm minimization of sparse signal reconstruction is NP-hard. Recent work shows that compared with the best convex relaxation (l1-norm), nonconvex penalties can better approximate the l0-norm and can reconstruct the signal based on fewer observations. In this paper, the original problem is relaxed by using minimax concave penalty (MCP). Then alternating direction method of multipliers (ADMM) and modified iterative hard thresholding method are used to solve the problem. Under certain reasonable assumptions, the global convergence of the proposed method is proved. The parameter setting is also discussed. Finally, through simulations and comparisons with several state-of-the-art algorithms, the effectiveness of proposed method is confirmed.

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