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THE PERFORMANCE OF ORTHOGONAL MULTI-MATCHING PURSUIT UNDER THE RESTRICTED ISOMETRY PROPERTY

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Journal of Computational Mathematics 2015年第5期33卷 495-516页

作者： zhiqiang xu LSEC Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 CHINA

The orthogonal multi-matching pursuit （OMMP） is a natural extension of the orthogo- nal matching pursuit （OMP）. We denote the OMMP with the parameter M as OMMP（M） where M ≥ 1 is an integer. The main difference between OMP and OMMP（M） is that OMMP（M） selects M atoms per iteration, while OMP only adds one atom to the op- timal atom set. In this paper, we study the performance of orthogonal multi-matching pursuit under RIP. In particular, we show that, when the measurement matrix A satisfies （25s, 1/10）-RIP, OMMP（M0） with M0 = 12 can recover s-sparse signals within s itera- tions. We furthermore prove that OMMP（M） can recover s-sparse signals within O（s/M） iterations for a large class of M.

关键词： Sparse signals Compressed sensing Greedy algorithms

Robustness properties of dimensionality reduction with Gaussian random matrices

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Science China Mathematics 2017年第10期60卷 1753-1778页

作者： HAN Bin xu zhiqiang Department of Mathematical and Statistical Sciences University of Alberta LSEC ICMSEC Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences

In this paper, motivated by the results in compressive phase retrieval, we study the robustness properties of dimensionality reduction with Gaussian random matrices having arbitrarily erased rows. We first study the robustness property against erasure for the almost norm preservation property of Gaussian random matrices by obtaining the optimal estimate of the erasure ratio for a small given norm distortion rate. As a consequence, we establish the robustness property of Johnson-Lindenstrauss lemma and the robustness property of restricted isometry property with corruption for Gaussian random matrices. Secondly, we obtain a sharp estimate for the optimal lower and upper bounds of norm distortion rates of Gaussian random matrices under a given erasure ratio. This allows us to establish the strong restricted isometry property with the almost optimal restricted isometry property(RIP) constants, which plays a central role in the study of phaseless compressed sensing. As a byproduct of our results, we also establish the robustness property of Gaussian random finite frames under erasure.

关键词： phase retrieval finite frames sparse approximation restricted isometry property Johnson-Lindenstrauss lemma

SOLVING SYSTEMS OF QUADRATIC EQUATIONS VIA EXPONENTIAL-TYPE GRADIENT DESCENT ALGORITHM

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Journal of Computational Mathematics 2020年第4期38卷 638-660页

作者： Meng Huang zhiqiang xu LSEC Inst.Comp.Math.Academy of Mathematics and System ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

We consider the rank minimization problem from quadratic measurements,i.e.,recovering a rank r matrix X 2 Rn×r from m scalar measurements yi=ai XX⊤ai,ai 2 Rn,i=1,...,*** problem arises in a variety of applications such as quadratic regression and quantum state *** present a novel algorithm,which is termed exponential-type gradient descent algorithm,to minimize a non-convex objective function f(U)=14m Pm i=1(yi−a⊤i UU⊤ai)*** algorithm starts with a careful initialization,and then refines this initial guess by iteratively applying exponential-type gradient ***,we can obtain a good initial guess of X as long as the number of Gaussian random measurements is O(nr),and our iteration algorithm can converge linearly to the true X(up to an orthogonal matrix)with m=O(nr log(cr))Gaussian random measurements。

关键词： Low-rank matrix recovery Non-convex optimization Phase retrieval

On the l_(1)-Norm Invariant Convex k-Sparse Decomposition of Signals

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Journal of the Operations Research Society of China 2013年第4期1卷 537-541页

作者： Guangwu xu zhiqiang xu Department of EE&CS University of Wisconsin-MilwaukeeMilwaukeeWI 53211USA Inst.Comp.Math. Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

Inspired by an interesting idea of Cai and Zhang,we formulate and prove the convex k-sparse decomposition of vectors that is invariant with respect to the l_(1) *** result fits well in discussing compressed sensing problems under the Restricted Isometry property,but we believe it also has independent *** an application,a simple derivation of the RIP recovery conditionδk+θk,k<1 is presented.

关键词： Convex k-sparse decomposition l_(1)1 minimization Restricted isometry property Sparse recovery

Oxidation of amorphous alloys

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Journal of Materials Science & Technology 2018年第11期34卷 1977-2005页

作者： zhiqiang xu Yifei xu An Zhang Jiangyong Wang Zumin Wang School of Materials Science and Engineering Tianjin University Department of Physics Shantou University

Owing to their unique short-or medium-range ordered microstructures and excellent mechanical, physical, and chemical properties, amorphous alloys have attracted significant interest in recent years. For the application of amorphous alloys, clarifying their oxidation processes and mechanisms is necessary since many of the surface-related properties of amorphous alloys largely depend on the surface oxide *** aim of this paper is to review the recent research on the thermal oxidation behaviors of amorphous alloys under pure oxygen or air condition. The contents are divided into three categories according to the number of components the research considers, i.e., the oxidation of binary, ternary, and multi-component（〉3） amorphous alloys. Each section discusses the thermal stability of the amorphous matrix, oxidation kinetics, and the oxide layer and amorphous substrate, which are strongly affected by internal factors（i.e., alloy elements and microstructure） and external factors（i.e., oxidation temperature, duration, and oxygen partial pressure, etc.）. The general features of the oxidation of amorphous alloys – from simple binary to complex multi-component amorphous alloys – will be summarized. This overview of the current scientific understanding on the fundamentals of these materials may provide guidelines for the development of strongly corrosion-resistant amorphous alloys.

关键词： Amorphous alloys Oxidation Oxidation kinetics Microstructure Surface treatment

A Gradient-Enhanced ℓ_(1)Approach for the Recovery of Sparse Trigonometric Polynomials

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Communications in Computational Physics 2018年第6期24卷 286-308页

作者： zhiqiang xu Tao Zhou LSEC Institute of Computational MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina.

In this paper,we discuss a gradient-enhancedℓ_(1)approach for the recovery of sparse Fourier *** gradient-enhanced approaches we mean that the directional derivatives along given vectors are utilized to improve the sparse *** first consider the case where both the function values and the directional derivatives at sampling points are *** show that,under some mild conditions,the inclusion of the derivatives information can indeed decrease the coherence of measurementmatrix,and thus leads to the improved the sparse recovery conditions of theℓ_(1)*** also consider the case where either the function values or the directional derivatives are known at the sampling points,in which we present a sufficient condition under which the measurement matrix satisfies RIP,provided that the samples are distributed according to the uniform *** result shows that the derivatives information plays a similar role as that of the function *** numerical examples are presented to support the theoretical *** applications to function(Hermite-type)interpolations and uncertainty quantification are also discussed.

关键词： Gradient-enhancedℓ_(1)minimization compressed sensing sparse Fourier expansions restricted isometry property mutual incoherence

Impact time control using biased proportional navigation for missiles with varying velocity

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Chinese Journal of Aeronautics 2020年第3期33卷 956-964页

作者： Guoxin SUN Qiuqiu WEN zhiqiang xu Qunli XIA School of Aerospace Beijing Institute of TechnologyBeijing 100081China Harbin Jiancheng Industry Company Limited Harbin 150030China

A feasible guidance scheme with impact time constraint is proposed for attacking a stationary target by missiles with time-varying *** main idea is to replace the constant velocity with the future mean velocity;therefore, the existing time-to-go estimation algorithm of the proportional navigation guidance law can be improved to adapt to varying *** order to obtain the prediction of the velocity profile, the velocity differential equation to the downrange is derived, which can be numerically integrated between the current downrange and the target position by the on-board ***, a third-order polynomial is introduced to fit the velocity profile in order to calculate the future mean *** the beginning of each guidance loop, the future mean velocity is predicted and the time-to-go information is updated, based on which a novel biased proportional navigation guidance law is established to achieve the impact time ***,numerical simulation results verified the effectiveness of the time-to-go estimation algorithm and the proposed law.

关键词： Guidance Homing missiles Impact time Proportional navigation guidance Time-varying velocity

Effect of Data Augmentation of Renal Lesion Image by Nine-layer Convolutional Neural Network in Kidney CT

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Computer Modeling in Engineering & Sciences 2020年第9期124卷 1001-1015页

作者： Liying Wang zhiqiang xu Shuihua Wang School of Education Science Nanjing Normal UniversityNanjing210097China Unit of Urology Tongliao Hospital of Inner MongoliaTongliao028000China Guangxi Key Laboratory of Trusted Software Guilin University of Electronic TechnologyGuilin541004China School of Mathematics and Actuarial Science University of LeicesterLeicesterLE17RHUK School of Architecture Building and Civil Engineering Loughborough UniversityLoughboroughLE113TUUK

Artificial Intelligence(AI)becomes one hotspot in the field of the medical images analysis and provides rather promising *** some research has been explored in smart diagnosis for the common diseases of urinary system,some problems remain unsolved completely A nine-layer Convolutional Neural Network(CNN)is proposed in this paper to classify the renal Computed Tomography(CT)*** group of comparative experiments prove the structure of this CNN is optimal and can achieve good performance with average accuracy about 92.07±1.67%.Although our renal CT data is not very large,we do augment the training data by affine,translating,rotating and scaling geometric transformation and gamma,noise transformation in color *** results validate the Data Augmentation(DA)on training data can improve the performance of our proposed CNN compared to without DA with the average accuracy about 0.85%.This proposed algorithm gives a promising solution to help clinical doctors automatically recognize the abnormal images faster than manual judgment and more accurately than previous methods.

关键词： Artificial intelligence convolutional neural network data augmentation renal lesion computed tomography image

Accelerated recruitment of copepod Calanus hyperboreus in pelagic slope waters of the western Arctic Ocean

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Acta Oceanologica Sinica 2018年第5期37卷 87-95页

作者： xu zhiqiang ZHANG Guangtao SUN Song Jiaozhou Bay Marine Ecosystem Research Station Institute of Oceanology Chinese Academy of Sciences Qingdao 266071 China University of Chinese Academy of Sciences Beijing 100049 China Key Laboratory of Marine Ecology and Environmental Sciences Institute of Oceanology Chinese Academy of Sciences Qingdao 266071 China

Shelf-basin advection is essential to subsistence of the Arctic copepod Calanus hyperboreus population in high basin area. Its abundance, population structure and body size in pelagic layer were investigated with samples collected over a large range in the western Arctic Ocean during summer 2003, to evaluate the geographical variation in recruitment pattern. Calanus hyperboreus was absent from the shallow areas of the Chukchi Sea and most abundant in the slope area between the Chukchi Sea and Chukchi Abyssal Plain（CS-slope）. Total abundance varied between 1 110.0 and 5 815.0 ind./m^2 in the CS-slope area and ranged from 40.0 to 950.0 ind./m^2 in the other areas. Early stages（CI–IV） dominated in the CS-slope area, whereas CV and adult females were frequently recorded only in deep basin areas. Geographical difference of prosome length was most evident in CIII,with average ranging from 2.48 to 2.61 mm at the CS-slope stations and 2.16–2.37 mm at the others. Abundance of early developmental stages（CI–CIV） correlated positively with Chl a concentration, but negative correlation was observed in late stages（CV–adult）. Our results indicated that C. hyperboreus can benefit from primary production increase through accelerated development in the first growth season and the productive CS-slope area is a potential source for slope-basin replenishment.

关键词： continental slope prosome length population structure food availability life cycle