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Lan Tang

Publications and source records attributed to Lan Tang.

At least 19 recordsLinked to original sources
arXiv2026

Synthesis of Ti2B2Clx MBenes in molten salts from theoretical and experimental perspectives

The unique properties and application possibilities of two-dimensional (2D) materials motivates the exploration of different nanolaminated compounds. Here, by using a molten salt approach, we selectively etch Ti2InB2 with ZnCl2 to produce a multilayer (ml) Ti2B2Clx MBene. Scanning transmission electron microscopy, in combination with energy dispersive X-ray, and electron energy loss spectroscopies show that In atoms are completely removed from the precursor upon etching, being replaced by chlorine surface terminations with a coverage 1.1 < x < 1.4. Further, in situ X-ray diffraction indicates a direct biphasic transformation from Ti2InB2 to ml-MBene, with no signs of intermediate phase formation. A computational framework based on density functional theory further corroborates these experimental observations by showing a negative reaction free energy for the formation of ml-MBene, favourable over all competing processes. In addition, A-element substitution into to the 3D Ti2ZnB2 phase is predicted to be endergonic, consistent with the absence of experimental evidence for its formation. Initial Li-ion battery performance evaluation showed a stable discharge capacity similar or better than MAX phases and other borides. Altogether, the theoretical framework combined with materials synthesis and characterization provides a general approach for 2D materials development, for further expansion of the family of 2D materials.

cond-mat.mtrl-sci↗
arXiv2025

System Synchronization Based on Complex Frequency

The increasing penetration of renewable energy leads to a continuous reduction in system inertia, for which conventional synchronization criteria based solely on frequency consistency can no longer accurately capture the coupled dynamics of frequency and voltage during transients. To address this issue, this paper employs the concept of complex frequency and develops an analysis framework that integrates theory, indices, and simulation for assessing synchronization stability in low-inertia power systems. First, the basic concepts and mathematical formulation of complex frequency and complex-frequency synchronization are introduced. Then, dynamic criteria for local and global complex synchronization are established, upon which a complex inertia index is proposed. This index unifies the supporting role of traditional frequency inertia and the voltage support capability associated with voltage inertia, enabling quantitative evaluation of the strength of coordinated frequency-voltage support and disturbance rejection within a region. Finally, transient simulations on a modified IEEE 9-bus system are carried out to validate the proposed method. The results show that the method can clearly reveal the synchronization relationships between subnetworks and the overall system, providing a useful theoretical reference for stability analysis and control strategy design in low-inertia power systems.

eess.SY↗
arXiv2025

Joint Optimization of Resource Allocation and Radar Receiver Selection in Integrated Communication-Radar Systems

In this paper, we investigate a distributed multi-input multi-output and orthogonal frequency division multiplexing (MIMO-OFDM) dual-function radar-communication (DFRC) system, which enables simultaneous communication and sensing in different subcarrier sets. To obtain the best tradeoff between communication and sensing performance, we first derive Cramer-Rao Bound (CRB) of targets in the detection area, and then maximize the transmission rate by jointly optimizing the power/subcarriers allocation and the selection of radar receivers under the constraints of detection performance and total transmit power. To tackle the non-convex mixed integer programming problem, we decompose the original problem into a semidefinite programming (SDP) problem and a convex quadratic integer problem and solve them iteratively. The numerical results demonstrate the effectiveness of our proposed algorithm, as well as the performance improvement brought by optimizing radar receivers selection.

eess.SP↗
arXiv2023

Enabling surrogate-assisted evolutionary reinforcement learning via policy embedding

Evolutionary Reinforcement Learning (ERL) that applying Evolutionary Algorithms (EAs) to optimize the weight parameters of Deep Neural Network (DNN) based policies has been widely regarded as an alternative to traditional reinforcement learning methods. However, the evaluation of the iteratively generated population usually requires a large amount of computational time and can be prohibitively expensive, which may potentially restrict the applicability of ERL. Surrogate is often used to reduce the computational burden of evaluation in EAs. Unfortunately, in ERL, each individual of policy usually represents millions of weights parameters of DNN. This high-dimensional representation of policy has introduced a great challenge to the application of surrogates into ERL to speed up training. This paper proposes a PE-SAERL Framework to at the first time enable surrogate-assisted evolutionary reinforcement learning via policy embedding (PE). Empirical results on 5 Atari games show that the proposed method can perform more efficiently than the four state-of-the-art algorithms. The training process is accelerated up to 7x on tested games, comparing to its counterpart without the surrogate and PE.

cs.NE↗
arXiv2022

Performance Optimization and Parameters Estimation for MIMO-OFDM Dual-functional Communication-radar Systems

In dual-functional communication-radar systems, common radio frequency (RF) signals are used for both communication and detection. For better compatibility with existing communication systems, we adopt multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) signals as integrated signals and investigate the estimation performance of MIMO-OFDM signals. We first analyze the Cramer-Rao lower bound (CRLB) of parameters estimation. Then, transmit powers over different subcarriers are optimized to achieve the best tradeoff between transmission rate and estimation performance. Finally, we propose a more accurate estimation method which utilizes canonical polyadic decomposition (CPD) of three-order tensor to obtain the parameter matrices. Due to the characteristic of the column structure of the parameter matrices, we just need to use DFT / IDFT to recover the parameters of multiple targets. The simulation results show that the estimation method based on tensor can achieve performance close to CRLB and the estimation performance can be improved by optimizing the transmit powers.

cs.IT↗
arXiv2021

Regularity of free boundary for the Monge-Amp\`ere obstacle problem

In this paper, we prove the regularity of the free boundary in the Monge-Amp\`ere obstacle problem $\det D^2 v= f(y)\chi_{\{v>0\}}. $ By duality, the regularity of the free boundary is equivalent to that of the asymptotic cone of the solution to the singular Monge-Amp\`ere equation $\det D^2 u = 1/f (Du)+\delta_0$ at the origin. We first establish an asymptotic estimate for the solution $u$ near the singular point, then use a partial Legendre transform to change the Monge-Amp\`ere equation to a singular, fully nonlinear elliptic equation, and establish the regularity of solutions to the singular elliptic equation.

math.AP↗
arXiv2021

Boundary homogenization of a class of obstacle problems

We study homogenization of a boundary obstacle problem on $ C^{1,\alpha} $ domain $D$ for some elliptic equations with uniformly elliptic coefficient matrices $\gamma$. For any $ \epsilon\in\mathbb{R}_+$, $\partial D=\Gamma \cup \Sigma$, $\Gamma \cap \Sigma=\emptyset $ and $ S_{\epsilon}\subset \Sigma $ with suitable assumptions,\ we prove that as $\epsilon$ tends to zero, the energy minimizer $ u^{\epsilon} $ of $ \int_{D} |\gamma\nabla u|^{2} dx $, subject to $ u\geq \varphi $ on $ S_{\varepsilon} $, up to a subsequence, converges weakly in $ H^{1}(D) $ to $ \widetilde{u} $ which minimizes the energy functional $\int_{D}|\gamma\nabla u|^{2}+\int_{\Sigma} (u-\varphi)^{2}_{-}\mu(x) dS_{x}$, where $\mu(x)$ depends on the structure of $S_{\epsilon}$ and $ \varphi $ is any given function in $C^{\infty}(\overline{D})$.

math.AP↗
arXiv2020

Variational structure and two-dimensional subsonic jet flows for compressible Euler system with general incoming flows

In this paper, we proved the well-posedness theory of compressible subsonic jet flows for two-dimensional steady Euler system with {\it general} incoming horizontal velocity as long as the flux is larger than a critical value. One of the key observations is that the stream function formulation for two-dimensional compressible steady Euler system enjoys a variational structure even when the flows have nontrivial vorticity, so that the jet problem can be reformulated as a domain variation problem. This variational structure helps to adapt the framework developed by Alt, Caffarelli, and Friedman to study {the jet problem, which is a Bernoulli type free boundary problem. A major technical point to analyze the jet flows is that the inhomogeneous terms in the rescaled equation near the free boundary are always small, even when the vorticity of the flows is big.

math.AP↗
arXiv2018

Group Sparsity Residual with Non-Local Samples for Image Denoising

Inspired by group-based sparse coding, recently proposed group sparsity residual (GSR) scheme has demonstrated superior performance in image processing. However, one challenge in GSR is to estimate the residual by using a proper reference of the group-based sparse coding (GSC), which is desired to be as close to the truth as possible. Previous researches utilized the estimations from other algorithms (i.e., GMM or BM3D), which are either not accurate or too slow. In this paper, we propose to use the Non-Local Samples (NLS) as reference in the GSR regime for image denoising, thus termed GSR-NLS. More specifically, we first obtain a good estimation of the group sparse coefficients by the image nonlocal self-similarity, and then solve the GSR model by an effective iterative shrinkage algorithm. Experimental results demonstrate that the proposed GSR-NLS not only outperforms many state-of-the-art methods, but also delivers the competitive advantage of speed.

cs.CV↗
arXiv2017

Group-based Sparse Representation for Image Compressive Sensing Reconstruction with Non-Convex Regularization

Patch-based sparse representation modeling has shown great potential in image compressive sensing (CS) reconstruction. However, this model usually suffers from some limits, such as dictionary learning with great computational complexity, neglecting the relationship among similar patches. In this paper, a group-based sparse representation method with non-convex regularization (GSR-NCR) for image CS reconstruction is proposed. In GSR-NCR, the local sparsity and nonlocal self-similarity of images is simultaneously considered in a unified framework. Different from the previous methods based on sparsity-promoting convex regularization, we extend the non-convex weighted Lp (0 < p < 1) penalty function on group sparse coefficients of the data matrix, rather than conventional L1-based regularization. To reduce the computational complexity, instead of learning the dictionary with a high computational complexity from natural images, we learn the principle component analysis (PCA) based dictionary for each group. Moreover, to make the proposed scheme tractable and robust, we have developed an efficient iterative shrinkage/thresholding algorithm to solve the non-convex optimization problem. Experimental results demonstrate that the proposed method outperforms many state-of-the-art techniques for image CS reconstruction.

cs.CV↗
arXiv2017

Non-Convex Weighted Lp Nuclear Norm based ADMM Framework for Image Restoration

Since the matrix formed by nonlocal similar patches in a natural image is of low rank, the nuclear norm minimization (NNM) has been widely used in various image processing studies. Nonetheless, nuclear norm based convex surrogate of the rank function usually over-shrinks the rank components and makes different components equally, and thus may produce a result far from the optimum. To alleviate the above-mentioned limitations of the nuclear norm, in this paper we propose a new method for image restoration via the non-convex weighted Lp nuclear norm minimization (NCW-NNM), which is able to more accurately enforce the image structural sparsity and self-similarity simultaneously. To make the proposed model tractable and robust, the alternative direction multiplier method (ADMM) is adopted to solve the associated non-convex minimization problem. Experimental results on various types of image restoration problems, including image deblurring, image inpainting and image compressive sensing (CS) recovery, demonstrate that the proposed method outperforms many current state-of-the-art methods in both the objective and the perceptual qualities.

cs.CV↗
arXiv2017

Non-Convex Weighted Lp Minimization based Group Sparse Representation Framework for Image Denoising

Nonlocal image representation or group sparsity has attracted considerable interest in various low-level vision tasks and has led to several state-of-the-art image denoising techniques, such as BM3D, LSSC. In the past, convex optimization with sparsity-promoting convex regularization was usually regarded as a standard scheme for estimating sparse signals in noise. However, using convex regularization can not still obtain the correct sparsity solution under some practical problems including image inverse problems. In this paper we propose a non-convex weighted $\ell_p$ minimization based group sparse representation (GSR) framework for image denoising. To make the proposed scheme tractable and robust, the generalized soft-thresholding (GST) algorithm is adopted to solve the non-convex $\ell_p$ minimization problem. In addition, to improve the accuracy of the nonlocal similar patches selection, an adaptive patch search (APS) scheme is proposed. Experimental results have demonstrated that the proposed approach not only outperforms many state-of-the-art denoising methods such as BM3D and WNNM, but also results in a competitive speed.

cs.CV↗
arXiv2017

Group Sparsity Residual Constraint for Image Denoising

Group-based sparse representation has shown great potential in image denoising. However, most existing methods only consider the nonlocal self-similarity (NSS) prior of noisy input image. That is, the similar patches are collected only from degraded input, which makes the quality of image denoising largely depend on the input itself. However, such methods often suffer from a common drawback that the denoising performance may degrade quickly with increasing noise levels. In this paper we propose a new prior model, called group sparsity residual constraint (GSRC). Unlike the conventional group-based sparse representation denoising methods, two kinds of prior, namely, the NSS priors of noisy and pre-filtered images, are used in GSRC. In particular, we integrate these two NSS priors through the mechanism of sparsity residual, and thus, the task of image denoising is converted to the problem of reducing the group sparsity residual. To this end, we first obtain a good estimation of the group sparse coefficients of the original image by pre-filtering, and then the group sparse coefficients of the noisy image are used to approximate this estimation. To improve the accuracy of the nonlocal similar patch selection, an adaptive patch search scheme is designed. Furthermore, to fuse these two NSS prior better, an effective iterative shrinkage algorithm is developed to solve the proposed GSRC model. Experimental results demonstrate that the proposed GSRC modeling outperforms many state-of-the-art denoising methods in terms of the objective and the perceptual metrics.

cs.CV↗
arXiv2017

Analyzing the Weighted Nuclear Norm Minimization and Nuclear Norm Minimization based on Group Sparse Representation

Rank minimization methods have attracted considerable interest in various areas, such as computer vision and machine learning. The most representative work is nuclear norm minimization (NNM), which can recover the matrix rank exactly under some restricted and theoretical guarantee conditions. However, for many real applications, NNM is not able to approximate the matrix rank accurately, since it often tends to over-shrink the rank components. To rectify the weakness of NNM, recent advances have shown that weighted nuclear norm minimization (WNNM) can achieve a better matrix rank approximation than NNM, which heuristically set the weight being inverse to the singular values. However, it still lacks a sound mathematical explanation on why WNNM is more feasible than NNM. In this paper, we propose a scheme to analyze WNNM and NNM from the perspective of the group sparse representation. Specifically, we design an adaptive dictionary to bridge the gap between the group sparse representation and the rank minimization models. Based on this scheme, we provide a mathematical derivation to explain why WNNM is more feasible than NNM. Moreover, due to the heuristical set of the weight, WNNM sometimes pops out error in the operation of SVD, and thus we present an adaptive weight setting scheme to avoid this error. We then employ the proposed scheme on two low-level vision tasks including image denoising and image inpainting. Experimental results demonstrate that WNNM is more feasible than NNM and the proposed scheme outperforms many current state-of-the-art methods.

cs.CV↗
arXiv2017

Image denoising using group sparsity residual and external nonlocal self-similarity prior

Nonlocal image representation has been successfully used in many image-related inverse problems including denoising, deblurring and deblocking. However, a majority of reconstruction methods only exploit the nonlocal self-similarity (NSS) prior of the degraded observation image, it is very challenging to reconstruct the latent clean image. In this paper we propose a novel model for image denoising via group sparsity residual and external NSS prior. To boost the performance of image denoising, the concept of group sparsity residual is proposed, and thus the problem of image denoising is transformed into one that reduces the group sparsity residual. Due to the fact that the groups contain a large amount of NSS information of natural images, we obtain a good estimation of the group sparse coefficients of the original image by the external NSS prior based on Gaussian Mixture model (GMM) learning and the group sparse coefficients of noisy image is used to approximate the estimation. Experimental results have demonstrated that the proposed method not only outperforms many state-of-the-art methods, but also delivers the best qualitative denoising results with finer details and less ringing artifacts.

cs.CV↗
arXiv2016

Analyzing the group sparsity based on the rank minimization methods

Sparse coding has achieved a great success in various image processing studies. However, there is not any benchmark to measure the sparsity of image patch/group because sparse discriminant conditions cannot keep unchanged. This paper analyzes the sparsity of group based on the strategy of the rank minimization. Firstly, an adaptive dictionary for each group is designed. Then, we prove that group-based sparse coding is equivalent to the rank minimization problem, and thus the sparse coefficient of each group is measured by estimating the singular values of each group. Based on that measurement, the weighted Schatten $p$-norm minimization (WSNM) has been found to be the closest solution to the real singular values of each group. Thus, WSNM can be equivalently transformed into a non-convex $\ell_p$-norm minimization problem in group-based sparse coding. To make the proposed scheme tractable and robust, the alternating direction method of multipliers (ADMM) is used to solve the $\ell_p$-norm minimization problem. Experimental results on two applications: image inpainting and image compressive sensing (CS) recovery have shown that the proposed scheme outperforms many state-of-the-art methods.

cs.CV↗
arXiv2016

A note on the Monge-Amp\`ere type equations with general source terms

In this paper we consider the generalised solutions to the Monge-Amp{\`{e}}re type equations with general source terms. We firstly prove the so-called comparison principle and then give some important propositions for the border of generalised solutions. Furthermore, we design well-posed finite element methods for the generalised solutions with the classical and weak Dirichlet boundary conditions respectively.

math.AP↗