Noise Vector Research Articles

Performance analysis of random angle based quantization modulation

The random angle based quantization modulation (RAQM) is a new watermarking method invariant to valumetric scaling attack. In this paper, the performance of RAQM is theoretically evaluated in two aspects: the embedding distortion and the decoding performance against additive noise attack. The analyses are developed under the assumptions that the host and noise vectors are mutually independent and both of them have independently and identically distributed components. We establish the stochastic models for several concerned signals. Based on them, the expressions of the embedding distortion and the decoding bit-error probability are derived in closed form. We also present the simplified but effective approximations to these analytical results. The analyses allow us to get more insight into the impact of various factors on the performance of RAQM. Numerical simulations confirm the validity of our analyses and exhibit the performance advantage of RAQM over similar modulation techniques.

Optimal Non-regenerative Linear MIMO Relay for Orthogonal Space Time Codes

We consider a multi-input multi-output (MIMO) communication system in which a linear non-regenerative MIMO relay assists the data transmission between a source and a destination node using orthogonal space time block codes (OSTBC). We derive the relay transformation matrix (RTM) by minimizing the symbol error rate (or maximizing the capacity) of the system under a constraint on the relay's transmitted power. The RTM is derived in the presence of the direct source-destination path and for spatially-correlated additive noise vectors. We show that the proposed RTM can significantly enhance the performance of the system in terms of the capacity/symbol error rate. Interestingly, our simulation results, in various conditions, reveal that the proposed method provides close to the optimum data rate even for the system without OSTBC. This suboptimal approach is justified, as the complexity of computing the proposed RTM is significantly less than the computation complexity of the RTM which maximizes the non-regenerative capacity.

Evaluation of disconnected quark loops for hadron structure using GPUs

A number of stochastic methods developed for the calculation of fermion loops are investigated and compared, in particular with respect to their efficiency when implemented on Graphics Processing Units (GPUs). We assess the performance of the various methods by studying the convergence and statistical accuracy obtained for observables that require a large number of stochastic noise vectors, such as the isoscalar nucleon axial charge. The various methods are also examined for the evaluation of sigma-terms where noise reduction techniques specific to the twisted mass formulation can be utilized thus reducing the required number of stochastic noise vectors.

Decoding Binary Node Labels from Censored Edge Measurements: Phase Transition and Efficient Recovery

We consider the problem of clustering a graph G into two communities by observing a subset of the vertex correlations. Specifically, we consider the inverse problem with observed variables Y = B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</sub> x ⊕ Z, where B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</sub> is the incidence matrix of a graph G, x is the vector of unknown vertex variables (with a uniform prior), and Z is a noise vector with Bernoulli (ε) i.i.d. entries. All variables and operations are Boolean. This model is motivated by coding, synchronization, and community detection problems. In particular, it corresponds to a stochastic block model or a correlation clustering problem with two communities and censored edges. Without noise, exact recovery (up to global flip) of x is possible if and only the graph G is connected, with a sharp threshold at the edge probability log (n)/n for Erdos-Renyi random graphs. The first goal of this paper is to determine how the edge probabilityp needs to scale to allow exact recovery in the presence of noise. Defining the degree rate of the graph by α = np/log(n), it is shown that exact recovery is possible if and only if α > 2/(1 - 2ε) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> + o(1/(1 - 2ε) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). In other words, 2/(1 - 2ε) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> is the information theoretic threshold for exact recovery at low-SNR. In addition, an efficient recovery algorithm based on semidefinite programming is proposed and shown to succeed in the threshold regime up to twice the optimal rate. For a deterministic graph G, defining the degree rate as α = d/log(n), where d is the minimum degree of the graph, it is shown that the proposed method achieves the rate α > 4((1 + λ)/(1 - λ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /(1 - 2ε) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> + o(1/(1 - 2ε) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), where 1-λ is the spectral gap of the graph G.

An improved method for density-based clustering

Knowledge discovery in large multimedia databases which usually contain large amounts of noise and high-dimensional feature vectors is an increasingly important research issue. Density-based clustering is proved to be much more efficient when dealing with such databases. However, its clustering quality mainly depends on the parameter setting. For the adequate choice of the parameters to be preset, it has difficulty in its operability without enough domain knowledge. To solve such problem, in this paper it proposed a new approach to immediately inference an appropriate value for one of the parameters named bandwidth. Based on the Bayesian Theorem, it is to infer the suitable parameter value by the constructed parameter estimation model. Then the user only has to preset the other parameter noise threshold. As a result, the clusters can be identified by the determined parameter values. The experimental results show that the proposed method has complementary advantages in the density-based clustering algorithm.

On-board wet road surface identification using tyre/road noise and Support Vector Machines

Changes in weather have a major influence on driving safety. On wet pavement, tyre grip is reduced and drivers must adapt their driving style accordingly. The correct operation of this adaptation mechanism depends on the perception the driver has of the asphalt status. Due to certain effects, this perception does not always correspond with reality. To improve this perception, it is essential to inform the driver about the asphalt status, efficiently and as quickly as possible. This could be achieved by installing an asphalt status detection system on the vehicle itself. The system could display asphalt status information in the vehicle’s console, allowing drivers to adapt their driving style accordingly.In this paper we propose an asphalt status classification system based on real-time acoustic analysis of tyre/road noise. The proposed system uses a practical approach that allows it to be integrated into a real vehicle. We present the system architecture used to measure the noise and the signal processing algorithms used for the classification of the asphalt state. A practical implementation of the proposed system has been developed and tested. For this preliminary prototype, only wet and dry asphalt states have been covered. Obtained wet/dry classification results have been reported, showing very high success rates.

Multi-feature gradient vector flow snakes for adaptive segmentation of the ultrasound images of breast cancer

Segmentation of ultrasound (US) images of breast cancer is one of the most challenging problems of the modern medical image processing. A number of popular codes for US segmentation are based on a generalized gradient vector flow (GGVF) method proposed by Xu and Prince. The GGVF equations include a smoothing term (diffusion) applied to regions of small gradients of the edge map and a stopping term to fix and extend large gradients appearing at the boundary of the object.The paper proposes two new directions. The first component is diffusion as a polynomial function of the intensity of the edge map. The second component is the orientation score of the vector field. The new features are integrated into the GGVF equations in the smoothing and the stopping term.The algorithms, having been tested by a set of ground truth images, show that the proposed techniques lead to a better convergence and better segmentation accuracy with the reference to conventional GGVF snakes. The adaptive multi-feature snake does not require any hand-tuning. However, it is as efficient as the standard GGVF with the parameters selected by the “brutal force approach”. Finally, proposed approach has been tested against recent modifications of GGVF, i.e. the Poisson gradient vector flow, the mixed noise vector flow and the convolution vector flow. The numerical tests employing 195 synthetic and 48 real ultrasound images show a tangible improvement in the accuracy of segmentation.

Linear Transceiver Design for Downlink Multiuser MIMO Systems: Downlink-Interference Duality Approach

This paper considers linear transceiver design for downlink multiuser multiple-input multiple-output (MIMO) systems. We examine different transceiver design problems. We focus on two groups of design problems. The first group is the weighted sum mean-square-error (WSMSE) (i.e., symbol-wise or user-wise WSMSE) minimization problems and the second group is the minimization of the maximum weighted mean-square-error (WMSE) (symbol-wise or user-wise WMSE) problems. The problems are examined for the practically relevant scenario where the power constraint is a combination of per base station (BS) antenna and per symbol (user), and the noise vector of each mobile station is a zero-mean circularly symmetric complex Gaussian random variable with arbitrary covariance matrix. For each of these problems, we propose a novel downlink-interference duality based iterative solution. Each of these problems is solved as follows. First, we establish a new mean-square-error (MSE) downlink-interference duality. Second, we formulate the power allocation part of the problem in the downlink channel as a Geometric Program (GP). Third, using the duality result and the solution of GP, we utilize alternating optimization technique to solve the original downlink problem. For the first group of problems, we have established symbol-wise and user-wise WSMSE downlink-interference duality. These duality are established by formulating the noise covariance matrices of the interference channels as fixed point functions. On the other hand, for the second group of problems, we have established symbol-wise and user-wise MSE downlink-interference duality. These duality are established by formulating the noise covariance matrices of the interference channels as marginally stable (convergent) discrete-time-switched systems. The proposed duality based iterative solutions can be extended straightforwardly to solve many other linear transceiver design problems. We also show that our MSE downlink-interference duality unify all existing MSE duality. In our simulation results, we have observed that the proposed duality based iterative algorithms utilize less total BS power than that of the existing algorithms.

MIMO Two-Way Compress-and-Forward Relaying with Approximate Joint Eigen-Decomposition

While compress-and-forward (CF) is one of the basic relay protocols in cooperative transmission, little is known about the optimal design of CF in multiple-input multiple-output (MIMO) two-way relay channels (TWRC). An intuitive method is to compress each element of the superimposed signal vector during the multiple-access (MAC) phase independently and with identical compression noise variance. In this paper, we introduce an improved compression method. The key idea is to apply approximate joint diagonalization (AJD) to realize simultaneous eigen-decomposition of the two channel matrices in the MAC phase of two-way relaying in an approximate manner. After that, a novel covariance matrix design of the compression noise vector is derived for sum-rate maximization. Numerical results show that the proposed CF design can improve the spectral efficiency, especially when the relay node is close to any of the two source nodes instead of in the midpoint.

Combined Signal and Model-Based Sensor Fault Diagnosis for a Doubly Fed Induction Generator

The problem of multiplicative and/or additive fault detection and isolation (FDI) in the current sensors of a doubly fed induction generator (DFIG) is considered in the presence of model uncertainty. A residual generator based on the DFIG model is proposed using the structure of the classical generalized observer scheme. However, each observer in this scheme is replaced by a robust H_/H∞ fault detection filter followed by a Kalman-like observer. The latter further attenuates the effect of the modeling uncertainties on the residuals. It exploits the specific pattern induced by the balanced three-phase nature of all the electric signals. It turns out that the FDI problem then amounts to detecting an abrupt change in the mean of the residual vector in the additive fault case, or the appearance of sine waves superimposed on a white noise vector in the multiplicative fault case. A decision algorithm made of a combination of generalized likelihood ratio algorithms allows us to detect and isolate the additive and multiplicative sensor faults. The complete FDI system is tested through simulations on a controlled DFIG.

An Affine Projection Algorithm With Update-Interval Selection

This paper presents a mean-square deviation (MSD) analysis of the periodic affine projection algorithm (P-APA) and two update-interval selection methods to achieve improved performance in terms of the convergence and the steady-state error. The MSD analysis of the P-APA considers the correlation between the weight error vector and the measurement noise vector. Using this analysis, it is verified that the update interval governs the trade-off between the convergence rate and the steady-state errors in the P-APA. To overcome this drawback, the proposed APAs increase the update interval when the adaptive filter reaches the steady state. Consequently, these algorithms can reduce the overall computational complexity. The simulation results show that the proposed APAs perform better than the previous algorithms.

Secure Beamforming with Artificial Noise for Two-way Relay Networks

This paper studies the problem of secure information exchange between two sources via multiple relays in the presence of an eavesdropper. To this end, we propose a relay beamforming scheme, i.e., relay beamforming with artificial noise (RBwA), where the relay beamforming vector and the artificial noise vector are jointly designed to maintain the received signal-to-interference-ratio (SINR) at the two sources over a predefined Quality of Service (QoS) threshold while limiting the received SINR at the eavesdropper under a predefined secure threshold. For comparsion, the relay beamforming without artificial noise (RBoA) is also considered. We formulate two optimization problems for the two schemes, where our goal is to seek the optimal beamforming vector to minimize the total power consumed by relay nodes such that the secrecy of the information exchange between the two sources can be protected. Since both optimization problems are nonconvex, we solve them by semidefinite program (SDP) relaxation theory. Simulation results show that, via beamforming design, physical layer secrecy of two-way relay networks can be greatly improved and our proposed RBwA outperforms the RBoA in terms of both low power consumption and low infeasibility rate.

Nonorthogonal problem in iterated unscented Kalman filter for passive tracking

AbstractThe iterated unscented Kalman filter (IUKF) is a promising nonlinear tracking algorithm. However, we find that the IUKF has poor performance in tracking accuracy and will diverge easily when the variance of observation noise is large, because the iterated state prediction is nonorthogonal to the current observation after the first iteration. This will increase the proportion of current observation in state estimate and lead to the tendency for the final iteration result to be closer to the observation compared with the optimal solution, which is a phenomenon termed the nonorthogonal problem here. We solve this problem by augmenting the state vector with the process and observation noise vectors and slightly reconstructing the IUKF formula. Simulation results show that the proposed algorithm has better tracking performance than IUKF. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley &amp; Sons, Inc.

Fingerprinting With Equiangular Tight Frames

Digital fingerprinting is a framework for marking media files, such as images, music, or movies, with user-specific signatures to deter illegal distribution. Multiple users can collude to produce a forgery that can potentially overcome a fingerprinting system. This paper proposes an equiangular tight frame fingerprint design which is robust to such collusion attacks. We motivate this design by considering digital fingerprinting in terms of compressed sensing. The attack is modeled as linear averaging of multiple marked copies before adding a Gaussian noise vector. The content owner can then determine guilt by exploiting correlation between each user's fingerprint and the forged copy. The worst case error probability of this detection scheme is analyzed and bounded. Simulation results demonstrate that the average-case performance is similar to the performance of orthogonal and simplex fingerprint designs, while accommodating several times as many users.

Optimal Two-Dimensional Lattices for Precoding of Linear Channels

Consider the communication system model y = HFx + n, where H and F are the channel and precoder matrices, x is a vector of data symbols drawn from some lattice-type constellation, such as M-QAM, n is an additive white Gaussian noise vector and y is the received vector. It is assumed that both the transmitter and the receiver have perfect knowledge of the channel matrix H and that the transmitted signal Fx is subject to an average energy constraint. The columns of the matrix HF can be viewed as the basis vectors that span a lattice, and we are interested in the precoder F that maximizes the minimum distance of this lattice. This particular problem remains open within the theory of lattices and the communication theory. This paper provides the complete solution for any nonsingular M × 2 channel matrix H. For real-valued matrices and vectors, the solution is that HF spans the hexagonal lattice. For complex-valued matrices and vectors, the solution is that HF, when viewed in four-dimensional real-valued space, spans the Schlafli lattice D4.

Robust Recursive Beamforming in the Presence of Impulsive Noise and Steering Vector Mismatch

This paper proposes a new method for robust beamforming in the presence of impulsive noise as well as steering vector mismatch. In our proposed method, the idea of M-estimation is firstly incorporated into the traditional orthonormal PAST (OPAST) algorithm for subspace tracking to combat the hostile effect of impulsive noise. Taking advantage of the subspace principle, we show that the steering vector mismatch can be recursively and robustly estimated in closed form. Then, by making use of the estimated steering vector, the problem of robust beamforming in the presence of impulsive noise is formulated. The solution of this problem is analytically derived and the resultant robust beamformer is shown to have a similar form to the Capon beamformer, whereas the array covariance matrix and the steering vector are robustly estimated. Different from conventional methods, the impulsive noise and the steering vector mismatch are simultaneously handled by extending the traditional OPAST algorithm, and hence the proposed method has low complexity and it is feasible to nonstationary scenarios with moving sources. Simulation results demonstrate the validity and superiority of the proposed method over conventional methods in impulsive noise environment with steering vector mismatch.

Krylov subspace methods for computing hydrodynamic interactions in Brownian dynamics simulations

Hydrodynamic interactions play an important role in the dynamics of macromolecules. The most common way to take into account hydrodynamic effects in molecular simulations is in the context of a brownian dynamics simulation. However, the calculation of correlated brownian noise vectors in these simulations is computationally very demanding and alternative methods are desirable. This paper studies methods based on Krylov subspaces for computing brownian noise vectors. These methods are related to Chebyshev polynomial approximations, but do not require eigenvalue estimates. We show that only low accuracy is required in the brownian noise vectors to accurately compute values of dynamic and static properties of polymer and monodisperse suspension models. With this level of accuracy, the computational time of Krylov subspace methods scales very nearly as O(N(2)) for the number of particles N up to 10 000, which was the limit tested. The performance of the Krylov subspace methods, especially the "block" version, is slightly better than that of the Chebyshev method, even without taking into account the additional cost of eigenvalue estimates required by the latter. Furthermore, at N = 10,000, the Krylov subspace method is 13 times faster than the exact Cholesky method. Thus, Krylov subspace methods are recommended for performing large-scale brownian dynamics simulations with hydrodynamic interactions.

Time-domain noise reduction based on an orthogonal decomposition for desired signal extraction

This paper addresses the problem of noise reduction in the time domain where the clean speech sample at every time instant is estimated by filtering a vector of the noisy speech signal. Such a clean speech estimate consists of both the filtered speech and residual noise (filtered noise) as the noisy vector is the sum of the clean speech and noise vectors. Traditionally, the filtered speech is treated as the desired signal after noise reduction. This paper proposes to decompose the clean speech vector into two orthogonal components: one is correlated and the other is uncorrelated with the current clean speech sample. While the correlated component helps estimate the clean speech, it is shown that the uncorrelated component interferes with the estimation, just as the additive noise. Based on this orthogonal decomposition, the paper presents a way to define the error signal and cost functions and addresses the issue of how to design different optimal noise reduction filters by optimizing these cost functions. Specifically, it discusses how to design the maximum SNR filter, the Wiener filter, the minimum variance distortionless response (MVDR) filter, the tradeoff filter, and the linearly constrained minimum variance (LCMV) filter. It demonstrates that the maximum SNR, Wiener, MVDR, and tradeoff filters are identical up to a scaling factor. It also shows from the orthogonal decomposition that many performance measures can be defined, which seem to be more appropriate than the traditional ones for the evaluation of the noise reduction filters.

Active Brownian particles with velocity-alignment and active fluctuations

We consider a model of active Brownian particles (ABPs) with velocity alignment in two spatial dimensions with passive and active fluctuations. Here, active fluctuations refers to purely non-equilibrium stochastic forces correlated with the heading of an individual active particle. In the simplest case studied here, they are assumed to be independent stochastic forces parallel (speed noise) and perpendicular (angular noise) to the velocity of the particle. On the other hand, passive fluctuations are defined by a noise vector independent of the direction of motion of a particle, and may account, for example, for thermal fluctuations. We derive a macroscopic description of the ABP gas with velocity-alignment interaction. Here, we start from the individual-based description in terms of stochastic differential equations (Langevin equations) and derive equations of motion for the coarse-grained kinetic variables (density, velocity and temperature) via a moment expansion of the corresponding probability density function. We focus here on the different impact of active and passive fluctuations on onset of collective motion and show how active fluctuations in the active Brownian dynamics can change the phase-transition behaviour of the system. In particular, we show that active angular fluctuations lead to an earlier breakdown of collective motion and to the emergence of a new bistable regime in the mean-field case.

A FAST LAGRANGE METHOD FOR LARGE-SCALE IMAGE RESTORATION PROBLEMS WITH REFLECTIVE BOUNDARY CONDITION

The goal of the image restoration is to find a good approximation of the original image for the degraded image, the blurring matrix, and the statistics of the noise vector given. Fast truncated Lagrange (FTL) method has been proposed by G. Landi as a image restoration method for large-scale ill-conditioned BTTB linear systems([3]). We implemented FTL method for the image restoration problem with reflective boundary condition which gives better reconstructions of the unknown, the true image.