arXiv subjects

Kui Ren

Publications and source records attributed to Kui Ren.

At least 235 records · Page 13Linked to original sources

arXiv2017

A global stability estimate for the photo-acoustic inverse problem in layered media

This paper is concerned with the stability issue in determining absorption and diffusion coefficients in photoacoustic imaging. Assuming that the medium is layered and the acoustic wave speed is known we derive global Hölder stability estimates of the photo-acoustic inversion. These results show that the reconstruction is stable in the region close to the optical illumination source, and deteriorate exponentially far away. Several experimental pointed out that the resolution depth of the photo-acoustic modality is about tens of millimeters. Our stability estimates confirm these observations and give a rigorous quantification of this depth resolution.

math.AP↗

arXiv2017

Quantitative Photoacoustic Imaging of Two-photon Absorption

Two-photon absorption photoacoustic tomography (TP-PAT) is a recent hybrid imaging modality that aims at reconstructing two-photon absorption properties of heterogeneous media from measured ultrasound signals generated by the photoacoustic effect. While there have been extensive experimental studies in recent years to show the great promises of TP-PAT, very little has been done on developing computational methods for quantitative image reconstruction in this imaging modality. In this work, we present a mathematical model for quantitative TP-PAT in diffusive media. We implemented a computational strategy for the reconstruction of the optical absorption coefficients, and provide numerical simulations based on synthetic acoustic data to demonstrate the feasibility of quantitative reconstructions in TP-PAT.

physics.med-ph↗

arXiv2017

Nonlinear quantitative photoacoustic tomography with two-photon absorption

Two-photon photoacoustic tomography (TP-PAT) is a non-invasive optical molecular imaging modality that aims at inferring two-photon absorption property of heterogeneous media from photoacoustic measurements. In this work, we analyze an inverse problem in quantitative TP-PAT where we intend to reconstruct optical coefficients in a semilinear elliptic PDE, the mathematical model for the propagation of near infra-red photons in tissue-like optical media with two-photon absorption, from the internal absorbed energy data. We derive uniqueness and stability results on the reconstructions of single and multiple optical coefficients, and present some numerical reconstruction results based on synthetic data to complement the theoretical analysis.

math.AP↗

arXiv2017

The phases of large networks with edge and triangle constraints

Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs. We support simulation evidence with mathematical proof of continuity and discontinuity for many of the phase transitions. All but one of themany phase transitions in this model break some form of symmetry, and we use this model to explore how changes in symmetry are related to discontinuities at these transitions.

math.CO↗

arXiv2016

Capacity-achieving and Flicker-free FEC coding scheme for Dimmable Visible Light Communication Based on Polar Codes

Visible light communication (VLC) could provide short-range optical wireless communication together with illumination using LED lighting. However, conventional forward error correction (FEC) codes for reliable communication do not have the features for dimming support and flicker mitigation which are required in VLC for the main functionality of lighting. Therefore, auxiliary coding techniques are usually needed, which eventually reduce the coding efficiency and increase the complexity. In this paper, a polar codes-based FEC coding scheme for dimmable VLC is proposed to increase the coding efficiency and simplify the coding structure. Experimental results show that the proposed scheme has the following advantages: 1) equal probability of 1's and 0's in codewords, which is inherently supporting 50% dimming balance; 2) short run length property (about 90% bits have runs shorter than 5) which can avoid flickers and additional run-length limited line coding; 3) higher coding efficiency about twofold than that of other coding schemes; 4) capacity achieving error correction performance with low-complexity encoding and decoding, which is about 3 dB higher coding gain than that of RS(64,32) in IEEE standard for dimming ratio 50% and about 1 dB higher coding gain than that of LDPC codes for dimming ratio 25% (or 75%).

cs.IT↗

arXiv2016

Numerical algorithms based on Galerkin methods for the modeling of reactive interfaces in photoelectrochemical (PEC) solar cells

This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive semiconductor and electrolyte interfaces. We present three numerical algorithms, mainly based on a mixed finite element and a local discontinuous Galerkin method for spatial discretization, with carefully chosen numerical fluxes, and implicit-explicit time stepping techniques, for solving the time-dependent nonlinear systems of partial differential equations. We perform computational simulations under various model parameters to demonstrate the performance of the proposed numerical algorithms as well as the impact of these parameters on the solution to the model.

math.NA↗

arXiv2016

Multipodal Structure and Phase Transitions in Large Constrained Graphs

We study the asymptotics of large, simple, labeled graphs constrained by the densities of edges and of $k$-star subgraphs, $k\ge 2$ fixed. We prove that under such constraints graphs are "multipodal": asymptotically in the number of vertices there is a partition of the vertices into $M < \infty$ subsets $V_1, V_2, \ldots, V_M$, and a set of well-defined probabilities $g_{ij}$ of an edge between any $v_i \in V_i$ and $v_j \in V_j$. For $2\le k\le 30$ we determine the phase space: the combinations of edge and $k$-star densities achievable asymptotically. For these models there are special points on the boundary of the phase space with nonunique asymptotic (graphon) structure; for the 2-star model we prove that the nonuniqueness extends to entropy maximizers in the interior of the phase space.

math.CO↗

arXiv2016

A symmetry breaking transition in the edge/triangle network model

Our general subject is the emergence of phases, and phase transitions, in large networks subjected to a few variable constraints. Our main result is the analysis, in the model using edge and triangle subdensities for constraints, of a sharp transition between two phases with different symmetries, analogous to the transition between a fluid and a crystalline solid.

math.CO↗

arXiv2016

Wireless Physical-Layer Identification: Modeling and Validation

The wireless physical-layer identification (WPLI) techniques utilize the unique features of the physical waveforms of wireless signals to identify and classify authorized devices. As the inherent physical layer features are difficult to forge, WPLI is deemed as a promising technique for wireless security solutions. However, as of today it still remains unclear whether existing WPLI techniques can be applied under real-world requirements and constraints. In this paper, through both theoretical modeling and experiment validation, the reliability and differentiability of WPLI techniques are rigorously evaluated, especially under the constraints of state-of-art wireless devices, real operation environments, as well as wireless protocols and regulations. Specifically, a theoretical model is first established to systematically describe the complete procedure of WPLI. More importantly, the proposed model is then implemented to thoroughly characterize various WPLI techniques that utilize the spectrum features coming from the non-linear RF-front-end, under the influences from different transmitters, receivers, and wireless channels. Subsequently, the limitations of existing WPLI techniques are revealed and evaluated in details using both the developed theoretical model and in-lab experiments. The real-world requirements and constraints are characterized along each step in WPLI, including i) the signal processing at the transmitter (device to be identified), ii) the various physical layer features that originate from circuits, antenna, and environments, iii) the signal propagation in various wireless channels, iv) the signal reception and processing at the receiver (the identifier), and v) the fingerprint extraction and classification at the receiver.

cs.CR↗

arXiv2016

User Capacity of Wireless Physical-layer Identification: An Information-theoretic Perspective

Wireless Physical Layer Identification (WPLI) system aims at identifying or classifying authorized devices based on the unique Radio Frequency Fingerprints (RFFs) extracted from their radio frequency signals at the physical layer. Current works of WPLI focus on demonstrating system feasibility based on experimental error performance of WPLI with a fixed number of users. While an important question remains to be answered: what's the user number that WPLI can accommodate using different RFFs and receiving equipment. The user capacity of the WPLI can be a major concern for practical system designers and can also be a key metric to evaluate the classification performance of WPLI. In this work, we establish a theoretical understanding on user capacity of WPLI in an information-theoretic perspective. We apply information-theoretic modeling on RFF features of WPLI. An information-theoretic approach is consequently proposed based on mutual information between RFF and user identity to characterize the user capacity of WPLI. Based on this theoretical tool, the achievable user capacity of WPLI is characterized under practical constrains of off-the-shelf receiving devices. Field experiments on classification error performance are conducted for the validation of the information-theoretic user capacity characterization.

cs.CR↗

arXiv2015

On the modeling and simulation of reaction-transfer dynamics in semiconductor-electrolyte solar cells

The mathematical modeling and numerical simulation of semiconductor-electrolyte systems play important roles in the design of high-performance semiconductor-liquid junction solar cells. In this work, we propose a macroscopic mathematical model, a system of nonlinear partial differential equations, for the complete description of charge transfer dynamics in such systems. The model consists of a reaction-drift-diffusion-Poisson system that models the transport of electrons and holes in the semiconductor region and an equivalent system that describes the transport of reductants and oxidants, as well as other charged species, in the electrolyte region. The coupling between the semiconductor and the electrolyte is modeled through a set of interfacial reaction and current balance conditions. We present some numerical simulations to illustrate the quantitative behavior of the semiconductor-electrolyte system in both dark and illuminated environments. We show numerically that one can replace the electrolyte region in the system with a Schottky contact only when the bulk reductant-oxidant pair density is extremely high. Otherwise, such replacement gives significantly inaccurate description of the real dynamics of the semiconductor-electrolyte system.

math.AP↗

arXiv2015

Inverse transport problems in quantitative PAT for molecular imaging

Fluorescence photoacoustic tomography (fPAT) is a molecular imaging modality that combines photoacoustic tomography (PAT) with fluorescence imaging to obtain high-resolution imaging of fluorescence distributions inside heterogeneous media. The objective of this work is to study inverse problems in the quantitative step of fPAT where we intend to reconstruct physical coefficients in a coupled system of radiative transport equations using internal data recovered from ultrasound measurements. We derive uniqueness and stability results on the inverse problems and develop some efficient algorithms for image reconstructions. Numerical simulations based on synthetic data are presented to validate the theoretical analysis. The results we present here complement these in [Ren-Zhao, SIAM J. Imag. Sci., 2013] on the same problem but in the diffusive regime.

math.AP↗

arXiv2015

Bipodal structure in oversaturated random graphs

We study the asymptotics of large simple graphs constrained by the limiting density of edges and the limiting subgraph density of an arbitrary fixed graph $H$. We prove that, for all but finitely many values of the edge density, if the density of $H$ is constrained to be slightly higher than that for the corresponding Erdős-Rényi graph, the typical large graph is bipodal with parameters varying analytically with the densities. Asymptotically, the parameters depend only on the degree sequence of $H$.

math.CO↗

arXiv2015

A one-step reconstruction algorithm for quantitative photoacoustic imaging

Quantitative photoacoustic tomography (QPAT) is a recent hybrid imaging modality that couples optical tomography with ultrasound imaging to achieve high resolution imaging of optical properties of scattering media. Image reconstruction in QPAT is usually a two-step process. In the first step, the initial pressure field inside the medium, generated by the photoacoustic effect, is reconstructed using measured acoustic data. In the second step, this initial ultrasound pressure field datum is used to reconstruct optical properties of the medium. We propose in this work a one-step inversion algorithm for image reconstruction in QPAT that reconstructs the optical absorption coefficient directly from measured acoustic data. The algorithm can be used to recover simultaneously the absorption coefficient and the ultrasound speed of the medium from \emph{multiple} acoustic data sets, with appropriate \emph{a priori} bounds on the unknowns. We demonstrate, through numerical simulations based on synthetic data, the feasibility of the proposed reconstruction method.

math.AP↗

arXiv2014

Inverse transport calculations in optical imaging with subspace optimization algorithms

Inverse boundary value problems for the radiative transport equation play important roles in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid progress in the mathematical theory and numerical computation of these inverse problems in recent years, developing robust and efficient reconstruction algorithms remains as a challenging task and an active research topic. We propose here a robust reconstruction method that is based on subspace minimization techniques. The method splits the unknown transport solution (or a functional of it) into low-frequency and high-frequency components, and uses singular value decomposition to analytically recover part of low-frequency information. Minimization is then applied to recover part of the high-frequency components of the unknowns. We present some numerical simulations with synthetic data to demonstrate the performance of the proposed algorithm.

math.NA↗

arXiv2014

The Asymptotics of Large Constrained Graphs

We show, through local estimates and simulation, that if one constrains simple graphs by their densities $\varepsilon$ of edges and $τ$ of triangles, then asymptotically (in the number of vertices) for over $95\%$ of the possible range of those densities there is a well-defined typical graph, and it has a very simple structure: the vertices are decomposed into two subsets $V_1$ and $V_2$ of fixed relative size $c$ and $1-c$, and there are well-defined probabilities of edges, $g_{jk}$, between $v_j\in V_j$, and $v_k\in V_k$. Furthermore the four parameters $c, g_{11}, g_{22}$ and $g_{12}$ are smooth functions of $(\varepsilon,τ)$ except at two smooth `phase transition' curves.

math.CO↗

arXiv2013

All Your Location are Belong to Us: Breaking Mobile Social Networks for Automated User Location Tracking

Many popular location-based social networks (LBSNs) support built-in location-based social discovery with hundreds of millions of users around the world. While user (near) realtime geographical information is essential to enable location-based social discovery in LBSNs, the importance of user location privacy has also been recognized by leading real-world LBSNs. To protect user's exact geographical location from being exposed, a number of location protection approaches have been adopted by the industry so that only relative location information are publicly disclosed. These techniques are assumed to be secure and are exercised on the daily base. In this paper, we question the safety of these location-obfuscation techniques used by existing LBSNs. We show, for the first time, through real world attacks that they can all be easily destroyed by an attacker with the capability of no more than a regular LBSN user. In particular, by manipulating location information fed to LBSN client app, an ill-intended regular user can easily deduce the exact location information by running LBSN apps as location oracle and performing a series of attacking strategies. We develop an automated user location tracking system and test it on the most popular LBSNs including Wechat, Skout and Momo. We demonstrate its effectiveness and efficiency via a 3 week real-world experiment with 30 volunteers. Our evaluation results show that we could geo-locate a target with high accuracy and can readily recover users' Top 5 locations. We also propose to use grid reference system and location classification to mitigate the attacks. Our work shows that the current industrial best practices on user location privacy protection are completely broken, and it is critical to address this immediate threat.

cs.SI↗

arXiv2012

Quantitative photoacoustic imaging in radiative transport regime

The objective of quantitative photoacoustic tomography (QPAT) is to reconstruct optical and thermodynamic properties of heterogeneous media from data of absorbed energy distribution inside the media. There have been extensive theoretical and computational studies on the inverse problem in QPAT, however, mostly in the diffusive regime. We present in this work some numerical reconstruction algorithms for multi-source QPAT in the radiative transport regime with energy data collected at either single or multiple wavelengths. We show that when the medium to be probed is non-scattering, explicit reconstruction schemes can be derived to reconstruct the absorption and the Gruneisen coefficients. When data at multiple wavelengths are utilized, we can reconstruct simultaneously the absorption, scattering and Gruneisen coefficients. We show by numerical simulations that the reconstructions are stable.

physics.med-ph↗