arXiv subjects

Guoqiang Xiao

Publications and source records attributed to Guoqiang Xiao.

15 recordsLinked to original sources

arXiv2025

Fourth-Order Hierarchical Array: A Novel Scheme for Sparse Array Design Based on Fourth-Order Difference Co-Array

Conventional array designs based on circular fourth-order cumulant typically adopt a single expression form of the fourth-order difference co-array (FODCA), which limits the achievable degrees of freedom (DOFs) and neglects the impact of mutual coupling among physical sensors. To address above issues, this paper proposes a novel scheme to design arrays with increased DOFs by combining different forms of FODCA while accounting for mutual coupling. A novel fourth-order hierarchical array (FOHA) based on different forms of FODCA is constructed using an arbitrary generator set. The analytical expression between the coupling leakage of the generator and the resulting FOHA is derived. Two specific FOHA configurations are presented with closed-form sensor placements. The arrays not only offer increased DOFs for resolving more sources in direction of-arrival (DOA) estimation but also effectively suppress mutual coupling. Moreover, the redundancy of FODCA is examined, and it is shown that arrays based on the proposed scheme achieve lower redundancy compared to existing arrays based on FODCA. Meanwhile, the necessary and sufficient conditions for signal reconstruction by FOHA are derived. Compared with existing arrays based on FODCA, the proposed arrays provide enhanced DOFs and improved robustness against mutual coupling. Numerical simulations verify that FOHAs achieve superior DOA estimation performance compared with other sparse linear arrays.

eess.SP↗

arXiv2025

A Novel Sparse Sum and Difference Co-Array With Low Redundancy and Enhanced DOF for Non-Circular Signals

Array structures based on the sum and difference co-arrays provide more degrees of freedom (DOF). However, since the growth of DOF is limited by a single case of sum and difference co-arrays, the paper aims to design a sparse linear array (SLA) with higher DOF via exploring different cases of second-order cumulants. We present a mathematical framework based on second-order cumulant to devise a second-order extended co-array (SO-ECA) and define the redundancy of SO-ECA. Based on SO-ECA, a novel array is proposed, namely low redundancy sum and difference array (LR-SDA), which can provide closed-form expressions for the sensor positions and enhance DOF in order to resolve more signal sources in the direction of arrival (DOA) estimation of non-circular (NC) signals. For LR-SDA, the maximum DOF under the given number of total physical sensors can be derived and the SO-ECA of LR-SDA is hole-free. Further, the corresponding necessary and sufficient conditions of signal reconstruction for LR-SDA are derived. Additionally, the redundancy and weight function of LR-SDA are defined, and the lower band of the redundancy for LR-SDA is derived. The proposed LR-SDA achieves higher DOF and lower redundancy than those of existing DCAs designed based on sum and difference co-arrays. Numerical simulations are conducted to verify the superiority of LR-SDA on DOA estimation performance and enhanced DOF over other existing DCAs.

eess.SP↗

arXiv2025

A Novel Design Method for Seeking Sparse Linear Arrays With Low Redundancy and Enhanced DOF

Sparse arrays with $N$-sensors can provide up to $O(N^2)$ degrees of freedom (DOF) by second-order cumulants. However, these sparse arrays like minimum-/low-redundancy arrays (MRAs/LRAs), nested arrays and coprime arrays can only provide limited DOF and array aperture with the same number of physical sensors. However, further increasing DOF would increase costs in practical applications. The paper aims to design a sparse linear array (SLA) with higher DOF and lower redundancy via exploring different cases of third-order cumulants. Based on the framework third-order exhaustive co-array (TO-ECA), a general third-order array (GTOA) with any generator is proposed in the paper. Further, three novel arrays are designed based on GTOA with different generators, namely third-order sum and difference array (generator) (TO-SDA(CNA)), (TO-SDA(SCNA)) and (TO-SDA(TNA-II)) which can provide closed-form expressions for the sensor locations and enhance DOF in order to resolve more signal sources in the estimation of direction of arrival (DOA). The three TO-SDAs are all consisted of two sub-arrays, where the first is the generator and another is a ULA with big inter-spacing between sensors. For the three TO-SDAs, the maximum DOF under the given number of total physical sensors can be derived and the TO-ECA of the three TO-SDAs are hole-free. Additionally, the redundancy of the three TO-SDAs is defined, and the lower band of the redundancy for the three TO-SDAs is derived. Furthermore, the proposed TO-SDA(TNA-II) not only achieves higher DOF than those of existing TONA and even SE-FL-NA but also reduces mutual coupling effects. Meanwhile it realizes higher resolution and decreases redundancy. Numerical simulations are conducted to verify the superiority of TO-SDA(TNA-II) on DOA estimation performance and enhanced DOF over other existing DCAs.

eess.SP↗

arXiv2024

FOGNA: An effective Sum-Difference Co-Array Design Based on Fourth-Order Cumulants

Array structures based on the fourth-order difference co-array (FODCA) provide more degrees of freedom (DOF). However, since the growth of DOF is limited by a single case of fourth-order cumulant in FODCA, this paper aims to design a sparse linear array (SLA) with higher DOF via exploring different cases of fourth-order cumulants. This paper presents a mathematical framework based on fourth-order cumulant to devise a fourth-order extend co-array (FOECA), which is equivalent to FODCA. A novel SLA, namely fourth-order generalized nested array (FOGNA), is proposed based on FOECA to provide closed-form expressions for the sensor locations and enhance DOF to resolve more signal sources in direction of arrival (DOA) estimation. FOGNA is consisted of three subarrays, where the first is a concatenated nested array and the other two subarrays are SLA with big inter-spacing between sensors. When the total physical sensors of FOGNA are given, the number of sensors in each subarray is determined by the designed method, which can obtain the maximum DOF under the proposed array structure and derive closed-form expressions for the sensor locations of FOGNA. The proposed array structure not only achieves higher DOF than those of existing FODCAs but also reduces mutual coupling effects. Numerical simulations are conducted to verify the superiority of FOGNA on DOA estimation performance and enhanced DOF over other existing FODCAs.

eess.SP↗

arXiv2024

Parametric Primitive Analysis of CAD Sketches with Vision Transformer

The design and analysis of Computer-Aided Design (CAD) sketches play a crucial role in industrial product design, primarily involving CAD primitives and their inter-primitive constraints. To address challenges related to error accumulation in autoregressive models and the complexities associated with self-supervised model design for this task, we propose a two-stage network framework. This framework consists of a primitive network and a constraint network, transforming the sketch analysis task into a set prediction problem to enhance the effective handling of primitives and constraints. By decoupling target types from parameters, the model gains increased flexibility and optimization while reducing complexity. Additionally, the constraint network incorporates a pointer module to explicitly indicate the relationship between constraint parameters and primitive indices, enhancing interpretability and performance. Qualitative and quantitative analyses on two publicly available datasets demonstrate the superiority of this method.

cs.CV↗

arXiv2024

PCB-RandNet: Rethinking Random Sampling for LIDAR Semantic Segmentation in Autonomous Driving Scene

Fast and efficient semantic segmentation of large-scale LiDAR point clouds is a fundamental problem in autonomous driving. To achieve this goal, the existing point-based methods mainly choose to adopt Random Sampling strategy to process large-scale point clouds. However, our quantative and qualitative studies have found that Random Sampling may be less suitable for the autonomous driving scenario, since the LiDAR points follow an uneven or even long-tailed distribution across the space, which prevents the model from capturing sufficient information from points in different distance ranges and reduces the model's learning capability. To alleviate this problem, we propose a new Polar Cylinder Balanced Random Sampling method that enables the downsampled point clouds to maintain a more balanced distribution and improve the segmentation performance under different spatial distributions. In addition, a sampling consistency loss is introduced to further improve the segmentation performance and reduce the model's variance under different sampling methods. Extensive experiments confirm that our approach produces excellent performance on both SemanticKITTI and SemanticPOSS benchmarks, achieving a 2.8% and 4.0% improvement, respectively. The source code is available at https://github.com/huixiancheng/PCB-RandNet.

cs.CV↗

arXiv2023

Edge Preserving Implicit Surface Representation of Point Clouds

Learning implicit surface directly from raw data recently has become a very attractive representation method for 3D reconstruction tasks due to its excellent performance. However, as the raw data quality deteriorates, the implicit functions often lead to unsatisfactory reconstruction results. To this end, we propose a novel edge-preserving implicit surface reconstruction method, which mainly consists of a differentiable Laplican regularizer and a dynamic edge sampling strategy. Among them, the differential Laplican regularizer can effectively alleviate the implicit surface unsmoothness caused by the point cloud quality deteriorates; Meanwhile, in order to reduce the excessive smoothing at the edge regions of implicit suface, we proposed a dynamic edge extract strategy for sampling near the sharp edge of point cloud, which can effectively avoid the Laplacian regularizer from smoothing all regions. Finally, we combine them with a simple regularization term for robust implicit surface reconstruction. Compared with the state-of-the-art methods, experimental results show that our method significantly improves the quality of 3D reconstruction results. Moreover, we demonstrate through several experiments that our method can be conveniently and effectively applied to some point cloud analysis tasks, including point cloud edge feature extraction, normal estimation,etc.

cs.CV↗

arXiv2022

LKD-Net: Large Kernel Convolution Network for Single Image Dehazing

The deep convolutional neural networks (CNNs)-based single image dehazing methods have achieved significant success. The previous methods are devoted to improving the network's performance by increasing the network's depth and width. The current methods focus on increasing the convolutional kernel size to enhance its performance by benefiting from the larger receptive field. However, directly increasing the size of the convolutional kernel introduces a massive amount of computational overhead and parameters. Thus, a novel Large Kernel Convolution Dehaze Block (LKD Block) consisting of the Decomposition deep-wise Large Kernel Convolution Block (DLKCB) and the Channel Enhanced Feed-forward Network (CEFN) is devised in this paper. The designed DLKCB can split the deep-wise large kernel convolution into a smaller depth-wise convolution and a depth-wise dilated convolution without introducing massive parameters and computational overhead. Meanwhile, the designed CEFN incorporates a channel attention mechanism into Feed-forward Network to exploit significant channels and enhance robustness. By combining multiple LKD Blocks and Up-Down sampling modules, the Large Kernel Convolution Dehaze Network (LKD-Net) is conducted. The evaluation results demonstrate the effectiveness of the designed DLKCB and CEFN, and our LKD-Net outperforms the state-of-the-art. On the SOTS indoor dataset, our LKD-Net dramatically outperforms the Transformer-based method Dehamer with only 1.79% #Param and 48.9% FLOPs. The source code of our LKD-Net is available at https://github.com/SWU-CS-MediaLab/LKD-Net.

cs.CV↗

arXiv2021

On the Foundation of Sparse Sensing (Part I): Necessary and Sufficient Sampling Theory and Robust Remaindering Problem

In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation of sparse sensing. It is different from compressed sensing, which exploits the sparse representation of a signal to reduce sample complexity (compressed sampling or acquisition). We use sparse sensing to denote a board concept of methods whose main focus is to improve the efficiency and cost of sampling implementation itself. The "sparse" here is referred to sampling at a low temporal or spatial rate (sparsity constrained sampling or acquisition), which in practice models cheaper hardware such as lower power, less memory and throughput. We take frequency and direction of arrival (DoA) estimation as concrete examples and give the necessary and sufficient requirements of the sampling strategy. Interestingly, we prove that these problems can be reduced to some (multiple) remainder model. As a straightforward corollary, we supplement and complete the theory of co-prime sampling, which receives considerable attention over last decade. On the other hand, we advance the understanding of the robust multiple remainder problem, which models the case when sampling with noise. A sharpened tradeoff between the parameter dynamic range and the error bound is derived. We prove that, for N-frequency estimation in either complex or real waveforms, once the least common multiple (lcm) of the sampling rates selected is sufficiently large, one may approach an error tolerance bound independent of N.

cs.IT↗

arXiv2021

On the Foundation of Sparse Sensing (Part II): Diophantine Sampling and Array Configuration

In the second part of the series papers, we set out to study the algorithmic efficiency of sparse sensing. Stemmed from co-prime sensing, we propose a generalized framework, termed Diophantine sensing, which utilizes generic Diophantine equation theory and higher-order sparse ruler to strengthen the sampling time, the degree of freedom (DoF), and the sampling sparsity, simultaneously. Resorting to higher-moment statistics, the proposed Diophantine framework presents two fundamental improvements. First, on frequency estimation, we prove that given arbitrarily large down-sampling rates, there exist sampling schemes where the number of samples needed is only proportional to the sum of DoF and the number of snapshots required, which implies a linear sampling time. Second, on Direction-of-arrival (DoA) estimation, we propose two generic array constructions such that given N sensors, the minimal distance between sensors can be as large as a polynomial of N, O(N^q), which indicates that an arbitrarily sparse array (with arbitrarily small mutual coupling) exists given sufficiently many sensors. In addition, asymptotically, the proposed array configurations produce the best known DoF bound compared to existing sparse array designs.

cs.IT↗

arXiv2019

From Co-prime to the Diophantine Equation Based Sparse Sensing

With a careful design of sample spacings either in temporal and spatial domain, co-prime sensing can reconstruct the autocorrelation at a significantly denser set of points based on Bazout theorem. However, still restricted from Bazout theorem, it is required O(M1 + M2) samples to estimate frequencies in the case of co-prime sampling, where M1 and M2 are co-prime down-sampling rates. Besides, for Direction-of-arrival (DOA) estimation, the sensors can not be arbitrarily sparse in co-prime arrays. In this letter, we restrain our focus on complex waveforms and present a framework under multiple samplers/sensors for both frequency and DOA estimation based on Diophantine equation, which is essentially to estimate the autocorrelation with higher order statistics instead of the second order one. We prove that, given arbitrarily high down-sampling rates, there exist sampling schemes with samples to estimate autocorrelation only proportional to the sum of degrees of freedom (DOF) and the number of snapshots required. In the scenario of DOA estimation, we show there exist arrays of N sensors with O(N^3) DOF and O(N) minimal distance between sensors.

math.ST↗

arXiv2019

Statistical Robust Chinese Remainder Theorem for Multiple Numbers

Generalized Chinese Remainder Theorem (CRT) is a well-known approach to solve ambiguity resolution related problems. In this paper, we study the robust CRT reconstruction for multiple numbers from a view of statistics. To the best of our knowledge, it is the first rigorous analysis on the underlying statistical model of CRT-based multiple parameter estimation. To address the problem, two novel approaches are established. One is to directly calculate a conditional maximum a posteriori probability (MAP) estimation of the residue clustering, and the other is based on a generalized wrapped Gaussian mixture model to iteratively search for MAP of both estimands and clustering. Residue error correcting codes are introduced to improve the robustness further. Experimental results show that the statistical schemes achieve much stronger robustness compared to state-of-the-art deterministic schemes, especially in heavy-noise scenarios.

stat.OT↗

arXiv2019

Multiple Independent Subspace Clusterings

Multiple clustering aims at discovering diverse ways of organizing data into clusters. Despite the progress made, it's still a challenge for users to analyze and understand the distinctive structure of each output clustering. To ease this process, we consider diverse clusterings embedded in different subspaces, and analyze the embedding subspaces to shed light into the structure of each clustering. To this end, we provide a two-stage approach called MISC (Multiple Independent Subspace Clusterings). In the first stage, MISC uses independent subspace analysis to seek multiple and statistical independent (i.e. non-redundant) subspaces, and determines the number of subspaces via the minimum description length principle. In the second stage, to account for the intrinsic geometric structure of samples embedded in each subspace, MISC performs graph regularized semi-nonnegative matrix factorization to explore clusters. It additionally integrates the kernel trick into matrix factorization to handle non-linearly separable clusters. Experimental results on synthetic datasets show that MISC can find different interesting clusterings from the sought independent subspaces, and it also outperforms other related and competitive approaches on real-world datasets.

cs.LG↗

arXiv2018

On Solving Ambiguity Resolution with Robust Chinese Remainder Theorem for Multiple Numbers

Chinese Remainder Theorem (CRT) is a powerful approach to solve ambiguity resolution related problems such as undersampling frequency estimation and phase unwrapping which are widely applied in localization. Recently, the deterministic robust CRT for multiple numbers (RCRTMN) was proposed, which can reconstruct multiple integers with unknown relationship of residue correspondence via generalized CRT and achieves robustness to bounded errors simultaneously. Naturally, RCRTMN sheds light on CRT-based estimation for multiple objectives. In this paper, two open problems arising that how to introduce statistical methods into RCRTMN and deal with arbitrary errors introduced in residues are solved. We propose the extended version of RCRTMN assisted with Maximum Likelihood Estimation (MLE), which can tolerate unrestricted errors and bring considerable improvement in robustness.

cs.IT↗

arXiv2017

Robustness in Chinese Remainder Theorem

Chinese Remainder Theorem (CRT) has been widely studied with its applications in frequency estimation, phase unwrapping, coding theory and distributed data storage. Since traditional CRT is greatly sensitive to the errors in residues due to noises, the problem of robustly reconstructing integers via the erroneous residues has been intensively studied in the literature. In order to robustly reconstruct integers, there are two kinds of traditional methods: the one is to introduce common divisors in the moduli and the other is to directly decrease the dynamic range. In this paper, we take further insight into the geometry property of the linear space associated with CRT. Echoing both ways to introduce redundancy, we propose a pseudo metric to analyze the trade-off between the error bound and the dynamic range for robust CRT in general. Furthermore, we present the first robust CRT for multiple numbers to solve the problem of the CRT-based undersampling frequency estimation in general cases. Based on symmetric polynomials, we proved that in most cases, the problem can be solved in polynomial time efficiently. The work in this paper is towards a complete theoretical solution to the open problem over 20 years.

cs.IT↗