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High efficiency video coding (HEVC) fractional interpolation algorithm has very high computational complexity. In this paper, two approximate HEVC fractional interpolation filters are proposed. They significantly reduce computational complexity of HEVC fractional interpolation with a negligible PSNR loss and bit rate increase. In addition, two approximate HEVC fractional interpolation hardware are proposed. They, in the worst case, can process 45 quad full HD (${3840\times 2160}$) fps. They consume up to 67.1% less energy than original HEVC fractional interpolation hardware. Therefore, they can be used in consumer electronics products that require a low energy HEVC encoder. [ABSTRACT FROM AUTHOR]

Random switching of magnetization is studied using a continuous master equation derived for magnetization dynamics driven by a jump-noise process. This paper is concerned with numerical analysis of the Kramers-Brown approximation as well as with low temperature random magnetization switching where the so-called phenomena of macroscopic quantum tunneling of magnetization has been experimentally observed and theoretically predicted. [ABSTRACT FROM AUTHOR]

Light-fidelity (LiFi) is a networked optical wireless communication (OWC) solution for high-speed indoor connectivity for fixed and mobile optical communications. Unlike conventional radio frequency wireless systems, the OWC channel is not isotropic, meaning that the device orientation affects the channel gain significantly, particularly for mobile users. However, due to the lack of a proper model for device orientation, many studies have assumed that the receiver is vertically upward and fixed. In this paper, a novel model for device orientation based on experimental measurements of 40 participants has been proposed. It is shown that the probability density function (PDF) of the polar angle can be modeled either based on a Laplace (for static users) or a Gaussian (for mobile users) distribution. In addition, a closed-form expression is obtained for the PDF of the cosine of the incidence angle based on which the line-of-sight (LOS) channel gain is described in OWC channels. An approximation of this PDF based on the truncated Laplace is proposed and the accuracy of this approximation is confirmed by the Kolmogorov–Smirnov distance. Moreover, the statistics of the LOS channel gain are calculated and the random orientation of a user equipment (UE) is modeled as a random process. The influence of the random orientation on signal-to-noise-ratio performance of OWC systems has been evaluated. Finally, an orientation-based random waypoint (ORWP) mobility model is proposed by considering the random orientation of the UE during the user’s movement. The performance of ORWP is assessed on the handover rate and it is shown that it is important to take the random orientation into account. [ABSTRACT FROM AUTHOR]

The conventional channel resolvability problem refers to the determination of the minimum rate required for an input process so that the output distribution approximates a target distribution in either the total variation distance or the relative entropy. In contrast to previous works, in this paper, we use the (normalized or unnormalized) Rényi divergence (with the Rényi parameter in $[{0,2}]\cup \{\infty \}$) to measure the level of approximation. We also provide asymptotic expressions for normalized Rényi divergence when the Rényi parameter is larger than or equal to 1 as well as (lower and upper) bounds for the case when the same parameter is smaller than 1. We characterize the Rényi resolvability, which is defined as the minimum rate required to ensure that the Rényi divergence vanishes asymptotically. The Rényi resolvabilities are the same for both the normalized and unnormalized divergence cases. In addition, when the Rényi parameter smaller than 1, consistent with the traditional case where the Rényi parameter is equal to 1, the Rényi resolvability equals the minimum mutual information over all input distributions that induce the target output distribution. When the Rényi parameter is larger than 1 the Rényi resolvability is, in general, larger than the mutual information. The optimal Rényi divergence is proven to vanish at least exponentially fast for both of these two cases, as long as the code rate is larger than the Rényi resolvability. The optimal exponential rate of decay for i.i.d. random codes is also characterized exactly. We apply these results to the wiretap channel, and completely characterize the optimal tradeoff between the rates of the secret and non-secret messages when the leakage measure is given by the (unnormalized) Rényi divergence. This tradeoff differs from the conventional setting when the leakage is measured by the traditional mutual information. [ABSTRACT FROM AUTHOR]

We present a novel distributed Gauss–Newton method for the non-linear state estimation (SE) model based on a probabilistic inference method called belief propagation (BP). The main novelty of our work comes from applying BP sequentially over a sequence of linear approximations of the SE model, akin to what is done by the Gauss–Newton method. The resulting iterative Gauss–Newton belief propagation (GN-BP) algorithm can be interpreted as a distributed Gauss–Newton method with the same accuracy as the centralized SE, however, introducing a number of advantages of the BP framework. The paper provides extensive numerical study of the GN-BP algorithm, provides details on its convergence behavior, and gives a number of useful insights for its implementation. [ABSTRACT FROM AUTHOR]

Coprime arrays can achieve an increased number of degrees of freedom by deriving the equivalent signals of a virtual array. However, most existing methods fail to utilize all information received by the coprime array due to the non-uniformity of the derived virtual array, resulting in an inevitable estimation performance loss. To address this issue, we propose a novel virtual array interpolation-based algorithm for coprime array direction-of-arrival (DOA) estimation in this paper. The idea of array interpolation is employed to construct a virtual uniform linear array such that all virtual sensors in the non-uniform virtual array can be utilized, based on which the atomic norm of the second-order virtual array signals is defined. By investigating the properties of virtual domain atomic norm, it is proved that the covariance matrix of the interpolated virtual array is related to the virtual measurements under the Hermitian positive semi-definite Toeplitz condition. Accordingly, an atomic norm minimization problem with respect to the equivalent virtual measurement vector is formulated to reconstruct the interpolated virtual array covariance matrix in a gridless manner, where the reconstructed covariance matrix enables off-grid DOA estimation. Simulation results demonstrate the performance advantages of the proposed DOA estimation algorithm for coprime arrays. [ABSTRACT FROM AUTHOR]

This paper proposes an improved extended finite element method for modeling electromagnetic devices with multiple nearby geometrical interfaces. In regions near these interfaces, the magnetic vector potential approximation is enriched by incorporating multiple derivative discontinuous fields based on the partition of unity method such that the interfaces can be represented independent of the mesh. The support of a node or an element can be cut by several interfaces. This method results in the high accuracy in the approximation field and derivative field. Numerical examples applied to the iron core in 1-D eddy current field involving level set-based parts, error analysis, and electromagnetic field computations are provided to demonstrate the utility of the proposed approach. [ABSTRACT FROM PUBLISHER]

This paper examines the applicability of hierarchical-matrices (H-matrices) to a computation of the demagnetizing field, which is the most time-consuming part in the micromagnetic simulation of spin torque oscillators (STO). Given that the kernel function of the convolution integral operator for the demagnetizing field has a second-order singularity, efficient approximation cannot be expected using conventional H-matrices employing adaptive cross approximation as the low-rank approximation. We introduce improved H-matrices to overcome this challenge. Furthermore, matrix sizes appearing in STO simulations are relatively small compared with the usual sizes of H-matrices. Through numerical experiments, we confirm the size conditions for memory usage and the computational time of H-matrix-vector products to demonstrate the advantages of using H-matrices. [ABSTRACT FROM AUTHOR]

In this paper, we study the magnetoquasistatic problem with uncertainties in the nonlinear magnetic material characteristic. In the case of small input uncertainties, adjoint techniques can be used to efficiently approximate the statistics of the quantities of interest. We carry out the corresponding sensitivity analysis and investigate the method's approximation properties. Numerical results discussing the approximation error are given for an electrical transformer. [ABSTRACT FROM AUTHOR]

This paper is the second part of a work which aims at proposing a global approach for the numerical modeling of parasitic capacitances in high-frequency multiwinding transformers. In this part, we focus on the numerical identification using the finite-element method (FEM) of the capacitive circuits which have been introduced in a companion paper in the same issue. An original procedure based on the FEM in 2-D electrostatics is first presented. The validity of the 2-D approximation is thereafter discussed, and a new method which consists in solving two successive 3-D models (an electrokinetic problem in the windings and an electrostatic one in the dielectrics) is then exposed. The two methods are illustrated and experimentally validated on a three-winding transformer. [ABSTRACT FROM AUTHOR]

A concave finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) is presented for scattering by a large body with nonuniform deep cavities. Different from the conventional FE-BI-MLFMA, the boundary integral equation in this concave FE-BI-MLFMA is established on a concave surface to reduce the region of the finite element method (FEM), which can significantly reduce the dispersion error from the FEM and improve the efficiency of FE-BI-MLFMA especially for nonuniform cavities. To eliminate the problem of slow convergence caused by concave surface, an efficient preconditioner based on the sparse approximate inverse (SAI) is constructed in this paper. Numerical performance of the constructed preconditioner based on the SAI is investigated in detail. Numerical experiments demonstrate the accuracy and efficiency of this SAI preconditioned concave FE-BI-MLFMA for nonuniform deep and large cavites. This SAI preconditioned concave FE-BI-MLFMA is parallelized to further improve its capability in this paper. An extremely big and deep nonuniform cavity has been calculated, demonstrating the great capability of this parallel concave FE-BI-MLFMA. [ABSTRACT FROM PUBLISHER]

Oscillators have been a research focus for decades in many disciplines such as electronics and biology. The time keeping capability of oscillators is best described by the scalar quantity phase. Phase computations and equations describing phase dynamics have been useful in understanding oscillator behavior and designing oscillators least affected by disturbances such as noise. In this paper, we present a unified theory of phase equations assimilating the work that has been done in electronics and biology for the last seven decades. We first provide a review of isochrons, which forms the basis of a generalized phase notion for oscillators. We present a general framework for phase equations and derive an exact phase equation that is practically unusable but facilitates the derivation of usable ones based on linear (already known) and quadratic (new and more accurate) approximations for isochrons. We discuss the utility of these phase equations in performing (semi) analytical phase computations and also describe simpler and more accurate phase computation schemes. Numerical experiments on several examples are presented comparing the accuracy of the various phase equations and computation schemes described in this paper. [ABSTRACT FROM AUTHOR]

Accurate numerical simulation of Eddy-Current Testing (ECT) experiments usually requires large computational efforts. So, a natural idea is to build a cheap approximation of the expensive-to-run simulator. This paper presents an approximation method based on functional kriging. Kriging is widely used in other domains, but is still unused in the ECT community. Its main idea is to build a random process model of the simulator. The extension of kriging to the case of functional output data (which is the typical case in ECT) is a recent development of mathematics. The paper introduces functional kriging and illustrates its performance via numerical examples using an ECT simulator based on a surface integral method. A comparison with other classical data interpolation methods is also carried out. [ABSTRACT FROM AUTHOR]

An algorithm that is capable not only of tracking multiple targets but also of "track management"-meaning that it does not need to know the number of targets as a user input-is of considerable interest. In this paper we devise a recursive track-managed filter via a quantized state-space ("bin") model. In the limit, as the discretization implied by the bins becomes as refined as possible (infinitesimal bins) we find that the filter equations are identical to Mahier's probability hypothesis density (PHD) filter, a novel trackmanaged filtering scheme that is attracting increasing attention. Thus, one contribution of this paper is an interpretation of, if not the PHD itself, at least what the PHD is doing. This does offer some intuitive appeal, but has some practical use as well: with this model it is possible to identify the PHD's "target-death" problem, and also the statistical inference structures of the PHD filters. To obviate the target death problem, PHD originator Mahler developed a new "cardinalized" version of PHD (CPHD). The second contribution of this paper is to extend the "bin-occupancy" model such that the resulting recursive filter is identical to the cardinalized PHD filter. [ABSTRACT FROM AUTHOR]

In order to find sparse approximations of signals, an appropriate generative model for the signal class has to be known. If the model is unknown, it can be adapted using a set of training samples. This paper presents a novel method for dictionary learning and extends the learning problem by introducing different constraints on the dictionary. The convergence of the proposed method to a fixed point is guaranteed, unless the accumulation points form a continuum. This holds for different sparsity measures. The majorization method is an optimization method that substitutes the original objective function with a surrogate function that is updated in each optimization step. This method has been used successfully in sparse approximation and statistical estimation [e.g., expectation-maximization (EM)] problems. This paper shows that the majorization method can be used for the dictionary learning problem too. The proposed method is compared with other methods on both synthetic and real data and different constraints on the dictionary are compared. Simulations show the advantages of the proposed method over other currently available dictionary learning methods not only in terms of average performance but also in terms of computation time. [ABSTRACT FROM AUTHOR]

Except some extremely special cases, signal resampling was generally considered to be irreversible because of strong attenuation of high frequencies after interpolation. In this paper, we prove that signal resampling based on polynomial interpolation can be reversible even for integer signals, i.e., the original signal can be reconstructed losslessly from the resampled data. By using matrix factorization, we also propose a reversible method for uniform shifted resampling and uniform scaled and shifted resampling. The new factorization yields three elementary integer-reversible matrices. The method is actually a new way to compute linear transforms and a lossless integer implementation of linear transforms with the factor matrices. It can be applied to integer signals by in-place integer-reversible computation, which needs no auxiliary memory to keep the original sample data for the transformation during the process or for "undo" recovery after the process. Some examples of low-order resampling solutions are also presented in this paper and our experiments show that the resampling error relative to the original signal is comparable to that of the traditional irreversible resampling. [ABSTRACT FROM AUTHOR]

In this paper, a modified approach for noise estimation in optical remotely sensed images is developed under the framework of semivariogram (SV) technique in geostatistics, which is a fundamental and important task for on-ground quantitative application. In comparison with the original method, which involves the extrapolation of modeled SV to the ordinate, in the modified approach, the relationship between two different SVs of true objects at different lags is established. Simulation results show that the latter is more accurate and stable in estimating noise, particularly in the conditions of usual subimage sizes (i.e., 16 × 16 and 32 × 32) as well as in lower noise level. Moreover, the potential negative values in the original method no longer exist in the modified one. Additionally, after the removal of the analog-to-digital conversion noise effects, detection sensitivity evaluations and long-term surveillances for on-orbit optical remotely sensed instrument, for example FY-2 visible infrared spin-scan radiometer, are performed successfully, and the absolute error for noise-equivalent delta temperature estimation is within 0.05 K at 300 K. A common and feasible way for estimating nugget variance of SV in geostatistics is proposed in this paper with the assumption of stationary for both objects and noise process. [ABSTRACT FROM AUTHOR]

This paper is concerned with approximation of Wonham filters. A focal point is that the underlying hidden Markov chain has a large state space. To reduce computational complexity, a two-time-scale approach is developed. Under time scale separation, the state space of the underlying Markov chain is divided into a number of groups such that the chain jumps rapidly within each group and switches occasionally from one group to another. Such structure gives rise to a limit Wonham filter that preserves the main features of the filtering process, but has a much smaller dimension and therefore is easier to compute. Using the limit filter enables us to develop efficient approximations and useful filters for hidden Markov chains. The main advantage of our approach is the reduction of dimensionality. [ABSTRACT FROM AUTHOR]

This paper tightens previous information combining bounds on the performance of iterative decoding of binary low-density parity-check (LDPC) codes over binary-input symmetric-output channels by tracking the probability of erroneous bit in conjunction with mutual information. Evaluation of the new bounds as well as of other known bounds on different LDPC ensembles demonstrates sensitivity of the finite dimensional iterative bounds to λ2, the fraction of edges connected to degree 2 variable nodes. [ABSTRACT FROM AUTHOR]

This paper presents a computationally simple and accurate method to compute the error probabilities in decentralized detection in sensor networks. The cost of the direct computation of these probabilities—e.g., the probability of false alarm, the probability of a miss, or the average error probability—is combinatorial in the number of sensors and becomes infeasible even with small size networks. The method is based on the theory of large deviations, in particular, the saddlepoint approximation and applies to generic parallel fusion sensor networks, including networks with nonidentical sensors, nonidentical observations, and unreliable communication links. The paper demonstrates with parallel fusion sensor network problems the accuracy of the saddlepoint methodology: 1) computing the detection performance for a variety of small and large sensor network scenarios; and 2) designing the local detection thresholds. Elsewhere, we have used the saddlepoint approximation to study tradeoffs among parameters for networks of arbitrary size. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of multidimensional signal reconstruction from nonuniform or generalized samples. Typical solutions in the literature for this problem utilize continuous filtering. The key result of the current paper is a multidimensional "interpolation" identity, which establishes the equivalence of two multidimensional processing operations. One of these uses continuous domain filters, whereas the other uses discrete processing. This result has obvious benefits in the context of the afore mentioned problem. The results here expand and generalize earlier work by other authors on the one-dimensional (1-D) case. Potential applications include two-dimensional (2-D) images and video signals. [ABSTRACT FROM AUTHOR]

The concept of fuzzy rule interpolation in sparse rule bases was introduced in 1993. It has become a widely researched topic in recent years because of its unique merits in the topic of fuzzy rule base complexity reduction. The first implemented technique of fuzzy rule interpolation was termed as α-cut distance based fuzzy rule base interpolation. Despite its advantageous properties in various approximation aspects and in complexity reduction, it was shown that it has some essential deficiencies, for instance, it does not always result in immediately interpretable fuzzy membership functions. This fact inspired researchers to develop various kinds of fuzzy rule interpolation techniques in order to alleviate these deficiencies. This paper is an attempt into this direction. It proposes an interpolation methodology, whose key idea is based on the interpolation of relations instead of interpolating α-cut distances, and which offers a way to derive a family of interpolation methods capable of eliminating some typical deficiencies of fuzzy rule interpolation techniques. The proposed concept of interpolating relations is elaborated here using fuzzy- and semantic-relations. This paper presents numerical examples, in comparison with former approaches, to show the effectiveness of the proposed interpolation methodology. [ABSTRACT FROM AUTHOR]

This paper introduces a simple method for calculating the times at which any signal crosses a prespecified threshold voltage (e.g., 10%, 20%, 50%, etc) directly from the moments. The method can use higher order moments to asymptotically improve the accuracy of the estimated crossing limes. This technique bypasses the steps involved in calculating poles and residues to obtain time-domain information. Once q moments are calculated, only 2q multiplications and (q - 1) additions are required to determine any threshold-crossing time at a certain node. Moreover, this technique avoids other problems such as pole Instability. The final outcome of this paper is a set of empirical expressions relating the moments to different threshold-crossing times in analogy to the td = -0.693m1 formula. The presented methodology can also be used with other user defined forms of empirical expressions relating the moments to different threshold-crossing limes. Several orders of approximations are presented for different threshold-crossing times, depending on the number of moments involved. For example, the worst-case error of a first- to seventh-order (single to seven moments) approximation of 50% RC delay is 1650%, 192.26%, 1131%, 3.37%, 2.57% 2.56%, and 143%, respectively. This technique is very useful to obtain information about certain signal metrics, such as delay and rise time directly without having to compute the whole time domain waveform. In addition, if the whole waveform is required It can be easily determined by interpolation between different threshold-crossing points. The presented technique works for both step and nonstep inputs, including piecewise-linear waveforms. [ABSTRACT FROM AUTHOR]

A common practice for computing an elementary transcendental function in an libm implementation nowadays has two phases: reductions of input arguments to fall into a tiny interval and polynomial approximations for the function within the interval. Typically, the interval is made tiny enough so that polynomials of very high degree aren't required for accurate approximations. Often, approximating polynomials as such are taken to be the best polynomials or any others such as the Chebyshev interpolating polynomials. The best polynomial of degree n has the property that the biggest difference between it and the function is smallest among alt possible polynomials of degrees no higher than n. Thus, it is natural to choose the best polynomials over others. In this paper, it is proven that the best polynomial can only be more accurate by at most a fractional bit than the Chebyshev interpolating polynomial of the same degree in computing elementary functions or, in other words, the Chebyshev interpolating polynomials wilt do just as well as the best polynomials. Similar results were obtained in 1967 by Powell who, however, did not target elementary function computations in particular and placed no assumption on the function and, remarkably, whose results imply accuracy differences of no more than 2 to 3 bits in the context of this paper. [ABSTRACT FROM AUTHOR]

This paper discusses Krylov subspace methods to solve a linear system whose coefficient matrix is represented by a hierarchical matrix. We propose a preconditioning technique using a part of the original hierarchical matrix to accelerate the convergence of the Krylov subspace methods. The proposed preconditioning technique is based on the assumption that the submatrices on the original hierarchical matrix are approximated using the adaptive cross approximation or variants thereof. The performance of Krylov subspace methods with the proposed preconditioning technique is examined through numerical experiments on an electrostatic field analysis. [ABSTRACT FROM AUTHOR]

Fast and accurate simulation of the electromagnetic field around frequency selective surfaces (FSSs) are needed for the design and optimization of devices based on the use of FSSs. The authors recently published a computationally efficient calculation method for the analysis of FSSs where the current distribution in the conducting parts are locally approximated by currents associated to electromagnetic waves propagating perpendicularly to the surface of the FSS. In this paper, an improved version of this method is presented. Here, in addition to the described assumption, local plane wave distribution of the current density is imposed also with respect to that surfaces being perpendicular to the surface of the FSS. By this modification, the error of the described calculations becomes very small in a very broad frequency range while the computational burden remains low, consequently the method can be advantageously applied for the solution of design and optimization problems. [ABSTRACT FROM PUBLISHER]

In this paper, we extend an existing universal variational framework for image inpainting with new numerical algorithms. Given certain regularization operator \(\Phi \) and denoting \(u\) the latent image, the basic model is to minimize the \(\ell _{p},(p=0,1)\) norm of \(\Phi u\) preserving the pixel values outside the inpainting region. Utilizing the operator splitting technique, the original problem can be approximated by a new problem with extra variable. With the alternating minimization method, the new problem can be decomposed as two subproblems with exact solutions. There are many choices for \(\Phi \) in our approach such as gradient operator, wavelet transform, framelet transform, or other tight frames. Moreover, with slight modification, we can decouple our framework into two relatively independent parts: 1) denoising and 2) linear combination. Therefore, we can take any denoising method, including BM3D filter in the denoising step. The numerical experiments on various image inpainting tasks, such as scratch and text removal, randomly missing pixel filling, and block completion, clearly demonstrate the super performance of the proposed methods. Furthermore, the theoretical convergence of the proposed algorithms is proved. [ABSTRACT FROM AUTHOR]

Although meshless methods, in particularly those with scalar radial basis functions (RBFs), have been applied effectively to solve electromagnetic problems, their solutions may not be always divergence free in source-free regions, resulting in possibly large errors. In this paper, a new vector RBF based meshless method, which is divergence free, is proposed for solving transient electromagnetic problems. Its divergence properties are investigated and compared with those of scalar RBFs; and they are further verified with numerical examples that present good accuracy. [ABSTRACT FROM PUBLISHER]

Single sensor digital cameras use color filter arrays to capture a subset of the color data at each pixel coordinate. Demosaicing or color filter array (CFA) interpolation is the process of estimating the missing color samples to reconstruct a full color image. In this paper, we propose a demosaicing method that uses multiscale color gradients to adaptively combine color difference estimates from different directions. The proposed solution does not require any thresholds since it does not make any hard decisions, and it is noniterative. Although most suitable for the Bayer CFA pattern, the method can be extended to other mosaic patterns. To demonstrate this, we describe its application to the Lukac CFA pattern. Experimental results show that it outperforms other available demosaicing methods by a clear margin in terms of CPSNR and S-CIELAB measures for both mosaic patterns. [ABSTRACT FROM AUTHOR]

In performance modeling of parallel synchronous iterative applications, the longest individual execution time among parallel processors determines the iteration time and often must be estimated for performance analysis. This involves the mean maximum calculation which has been a challenge in computer modeling for a long time. For large systems, numerical methods are not suitable because of heavy computation requirements and inaccuracy caused by rounding. On the other hand, previous approximation methods face challenges of accuracy and generality, especially for heterogeneous computing environments. This paper presents an interesting property of extreme values to enable Effective Mean Maximum Approximation (EMMA). Compared to previous mean maximum execution time approximation methods, this method is more accurate and general to different computational environments. [ABSTRACT FROM AUTHOR]

A Fresnel double scattering (FDS) method is presented in this paper to accurately and efficiently calculate the scattering cross section from two tree branches not necessarily in the far field of each other at L-band frequencies. The branches, modeled as dielectric cylinders, are assumed to have lengths comparable to one or more wavelengths. It is demonstrated that the FDS method provides a good approximation to the exact solutions of two branches modeled as one scatterer. The FDS method can be employed to study the double scattering effects between tree branches in microwave forest scattering models and accurately model a tree where single scatter and double scatter are the only important scattering mechanisms. [ABSTRACT FROM PUBLISHER]

Implementation of adaptive backstepping controllers requires analytic calculation of the partial derivatives of certain stabilizing functions. It is well documented that, as the order of a nonlinear system increases, analytic calculation of these derivatives becomes prohibitive. Therefore, in practice, either alternative control approaches are used or the derivatives are neglected in the implementation. Neglecting the derivatives results in the loss of all guarantees proven by Lyapunov methods for the adaptive backstepping approach and may result in instability. This paper presents a new implementation approach for adaptive backstepping control. The main objectives are to facilitate the derivation and implementation of the adaptive backstepping approach, with performance guarantees proven by Lyapunov methods, for applications that were prohibitively difficult using the standard analytic implementation approach. The new approach uses filtering methods to produce certain command signals and their derivatives which eliminates the requirement of analytic differentiation. The approach also introduces filters to generate certain compensating signals necessary to compute compensated tracking errors suitable for adaptive parameter estimation. We present a set of Lemmas and Theorems to analyze the performance both during the initialization and the operating phases. We show that the initialization phase is of finite duration that can be controlled by selection of a design parameter. We also show that all signals within the system are bounded during this short initialization phase. During the operating phase, we show that the command filtered implementation approach has theoretical properties identical to those of the conventional approach. The general approach is presented and analyzed for systems in generalized parameter strict feedback form. Extensions of the approach are presented to demonstrate the application of the method to a land vehicle trajectory following application. Application and effectiveness of the proposed method is shown by simulation results. [ABSTRACT FROM PUBLISHER]

The consistent and computationally economical analysis of demanding amplification and filtering structures is introduced in this paper via a new spectrally-precise finite-volume time-domain algorithm. Combining a family of spatial derivative approximators with controllable accuracy in general curvilinear coordinates, the proposed method employs a fully conservative field flux formulation to derive electromagnetic quantities in areas with fine structural details. Moreover, the resulting 3-D operators assign the appropriate weight to each spatial stencil at arbitrary media interfaces, while for periodic components the domain is systematically divided to a number of nonoverlapping subdomains. Numerical results from various real-world configurations verify our technique and reveal its universality. [ABSTRACT FROM PUBLISHER]

The electromagnetic fields generated by a vertical electric dipole, expressed in the form of the Sommerfeld integral, are important in the study of lightning. In this paper, an algorithm, which can analytically approximate the Sommerfeld tail integral, is proposed. Due to the fact that the tail integral is expressed by a sum of several error functions, the tail integral of a vertical electric dipole can be evaluated without the truncation of the infinite upper limit. The comparison indicates that the results calculated by the proposed algorithm are accurate, and the computational time, compared to the one using direct numerical quadrature method, is much shorter. [ABSTRACT FROM AUTHOR]

In this contribution, an algorithm for evaluating the capacity-achieving input covariance matrices for frequency selective Rayleigh MIMO channels is proposed. In contrast with the flat fading Rayleigh case, no closed-form expressions for the eigenvectors of the optimum input covariance matrix are available. Classically, both the eigenvectors and eigenvalues are computed numerically and the corresponding optimization algorithms remain computationally very demanding. In this paper, it is proposed to optimize (w.r.t. the input covariance matrix) a large system approximation of the average mutual information derived by Moustakas and Simon. The validity of this asymptotic approximation is clarified thanks to Gaussian large random matrices methods. It is shown that the approximation is a strictly concave function of the input covariance matrix and that the average mutual information evaluated at the argmax of the approximation is equal to the capacity of the channel up to a \cal O\left(1\over t\right) term, where t is the number of transmit antennas. An algorithm based on an iterative waterfilling scheme is proposed to maximize the average mutual information approximation, and its convergence studied. Numerical simulation results show that, even for a moderate number of transmit and receive antennas, the new approach provides the same results as direct maximization approaches of the average mutual information. [ABSTRACT FROM AUTHOR]

This paper presents a hybrid time–frequency domain methodology to calculate midfrequency transients of an electrical network that includes transmission lines (TLs) and considering that the simulation is carried out on a partitioned-time basis. Basically, the line is modeled as a two-port element and the network simulation is performed in the frequency domain for each time subinterval. The transition between subintervals is made by calculating an equivalent current source for each end of the line. These sources represent the initial conditions for a subsequent subinterval, and their calculation is based on a rational approximation of the two-port line parameters. The conversion of frequency-domain variables to the time domain is efficiently performed through numerical Laplace transform operations. A sequential closure of a three-phase TL is presented for illustration of the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of H\infty model approximation for discrete-time Takagi–Sugeno (T–S) fuzzy time-delay systems. For a given stable T– S fuzzy system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well in an H\infty performance but is also translated into a linear lower dimensional system. By applying the delay partitioning approach, a delay-dependent sufficient condition is proposed for the asymptotic stability with an H\infty error performance for the error system. Then, the H\infty model approximation problem is solved by using the projection approach, which casts the model approximation into a sequential minimization problem subject to linear matrix inequality (LMI) constraints by employing the cone complementary linearization algorithm. Moreover, by further extending the results, H\infty model approximation with special structures is obtained, i.e., delay-free model and zero-order model. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly nonsmooth) regularizer is minimized under the constraint that the solution explains the observations sufficiently well. Although the regularizer and constraint are usually convex, several particular features of these problems (huge dimensionality, nonsmoothness) preclude the use of off-the-shelf optimization tools and have stimulated a considerable amount of research. In this paper, we propose a new efficient algorithm to handle one class of constrained problems (often known as basis pursuit denoising) tailored to image recovery applications. The proposed algorithm, which belongs to the family of augmented Lagrangian methods, can be used to deal with a variety of imaging IPLIP, including deconvolution and reconstruction from compressive observations (such as MRI), using either total-variation or wavelet-based (or, more generally, frame-based) regularization. The proposed algorithm is an instance of the so-called alternating direction method of multipliers, for which convergence sufficient conditions are known; we show that these conditions are satisfied by the proposed algorithm. Experiments on a set of image restoration and reconstruction benchmark problems show that the proposed algorithm is a strong contender for the state-of-the-art. [ABSTRACT FROM AUTHOR]

This paper deals with crosstalk estimation in a set of individually insulated wires laced together to form a bundle, and running above a ground plane. A simplified and numerically efficient multiconductor transmission line model is developed, involving a single reference cross section with pseudocircular shape and staircase approximation for the wire trajectories. The presence of lacing cords along the bundle is modeled as a sinusoidal modulation of the reference cross-section dimension. It is shown that crosstalk in wire bundles is mainly affected by the relative positions of the generator and receptor wires, whose paths are to be accurately represented as smooth curved trajectories, whereas it results to be substantially insensitive to rough modeling of the paths of the remaining wires. The weak random nonuniformity of the generator and receptor wires proves to be the fundamental property to be reproduced in order to obtain physically sound crosstalk predictions. This is enforced by deducing the staircase approximation of the generator and receptor wires from a preliminary representation of only that wire pair in terms of splines with a very small number of nodes. Differently, the staircase trajectories of the remaining wires are obtained by direct mapping onto the reference cross section. Model performance is assessed by comparing crosstalk predictions versus measurement data and theoretical results available in the technical literature. Predictions compare appreciably well with measurements, also in the most critical case of high-impedance loads. The coupling distribution shows nonsymmetrical structure and a long tail to the right, as several other crosstalk analyses have shown. [ABSTRACT FROM AUTHOR]

This paper introduces a new discretization technique that retains the basic structure of the failure rate function of the original life distribution. Earlier approaches for discretizing a continuous random variable, reported in the literature so far, are moment equalization, and discrete concentration techniques. This proposed approach has been used for approximating the reliability of complex systems where exact determination of survival probability is analytically intractable. These applications show a reasonable degree of closeness between this new method and the simulated results. Admissibility of the proposed method over the methods of discrete concentration and numerical integration has also been established. [ABSTRACT FROM AUTHOR]

Medical ultrasound imaging instrumentation typically performs image interpolation using the signals acquired after envelope extraction, i.e., noncoherent signals. This operation is completely satisfying when the Nyquist condition for spatial sampling is fulfilled. However, the maximum spatial frequency of a signal increases as a consequence of the envelope extraction, making it more difficult to fulfill the Nyquist condition. For this reason, this paper suggests the interpolation of signals before envelope extraction, i.e., the use of coherent data, and discusses the applicability of this procedure to actual ultrasound scanners. Emphasis is given to the linear-array imaging technique, and the adoption of windowed sinc functions as interpolation kernels with limited support is assessed. Moreover, the authors investigated the situation in which coherent signals are also undersampled, and perfect reconstruction is not at all possible. The investigation was carried out using a numerical study and a simulated imaging test, and it was supported by subjective and objective evaluations. It is concluded that, at a moderate undersampling level, the interpolation of coherent signals allows significantly better performance than the interpolation of noncoherent signals. [ABSTRACT FROM AUTHOR]

The paper introduces DILOC, a distributed, iterative algorithm to locate M sensors (with unknown locations) in Rm, m ⩾ 1, with respect to a minimal number of m + 1 anchors with known locations. The sensors and anchors, nodes in the network, exchange data with their neighbors only; no centralized data processing or communication occurs, nor is there a centralized fusion center to compute the sensors' locations. DILOC uses the barycentric coordinates of a node with respect to its neighbors; these coordinates are computed using the Cayley-Menger determinants, i.e., the determinants of matrices of internode distances. We show convergence of DILOC by associating with it an absorbing Markov chain whose absorbing states are the states of the anchors. We introduce a stochastic approximation version extending DILOC to random environments, i.e., when the communications among nodes is noisy, the communication links among neighbors may fail at random times, and the internodes distances are subject to errors. We show a.s. convergence of the modified DILOC and characterize the error between the true values of the sensors' locations and their final estimates given by DILOC. Numerical studies illustrate DILOC under a variety of deterministic and random operating conditions. [ABSTRACT FROM AUTHOR]

Multiple building diffraction loss calculation is often based on the assumption that their dimensions are infinite in the direction perpendicular to the propagation path, even though in reality this assumption is not valid. In this paper, a modified diffraction coefficient model for the calculation of a more realistic diffraction loss caused by a single building with finite dimensions is proposed. The overall diffraction loss is calculated for a group of buildings in a row by using the proposed model. In addition, after carrying out the field measurements, it is shown that for some particular cases where the transmitter and diffracting obstacles are not far away from each other (i.e., microcells or picocells), spherical-wave modeling produces a better accuracy than the plane-wave approximation. It is also demonstrated that the theoretical results can further be improved by considering the higher order terms in the calculation of diffraction coefficients. Lastly, excess path loss obtained for a row of buildings with spherical-wave assumption is compared with our measurement data. This comparison shows reasonable correspondence between our theoretical model and measurements. Therefore, our proposed model can successfully be used for improving the theoretical methods for predicting path loss in urban environments, where diffraction from a number of buildings has to be considered. [ABSTRACT FROM AUTHOR]

The maximum-likelihood detection (MLD) algorithm is the optimal detection scheme for vertical Bell Laboratories layered space-time (V-BLAST) systems. However, it is generally infeasible to implement the MLD algorithm in practical systems because of its high computational complexity. In this paper, we used two parallel interference cancellation techniques, including precancellation and postcancellation, to simplify the MLD algorithm into a class of computationally efficient suboptimal detection algorithms, herein called the generalized parallel interference cancellation (GPIC) algorithm. Numerical analysis shows that the GPIC algorithm can approximately achieve the MLD performance with considerably low and stable computational complexity. Furthermore, it can be significantly accelerated via parallel processing methods. With near-optimal performance, low and stable complexity, and high running speed, the GPIC algorithm is very suitable for real-time communication systems. [ABSTRACT FROM AUTHOR]

Finding a good preconditioner to solve a given sparse linear system is often considered a difficult but important task. One of the simplest ways of defining a preconditioner is to perform an incomplete LU decomposition (ILU) of the original matrix. The ILU factorization is considered to be an easy and inexpensive preconditioner to use. However, it fails to provide a solution of a sparse linear system generated from general three-dimensional problems with three unknowns. In this paper, a modified ILU preconditioner is proposed to provide an efficient preconditioner for highly sparse matrices, especially for matrices constructed using the Finite-Difference Frequency-Domain (FDFD) method for three-dimensional applications. It has been proven that the proposed LU preconditioner provides a valid solution when the classical ILU preconditiorier fails. The efficiency of the proposed ILU preconditioner is also demonstrated by the small memory requirements relative to traditional ILU preconditioners. [ABSTRACT FROM AUTHOR]

This paper presents a multidimensional extension of the Schur-Cohn algorithm for testing BIBO stability in N variables. This new method only needs a unique condition to be checked, as an alternative to the set of N conditions of the well-known Huang-Jury-Anderson stability test. The proposed algorithm is based on a generalization of the Schur coefficients recently obtained by the authors. In the two-variable case a simplification to the Sturm algorithm is presented, which can also be used in the case of a polynomial with complex coefficients. This approach is illustrated on several numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents a new algorithm based on the Mumford-Shah model for simultaneously detecting the edge features of two images and jointly estimating a consistent set of transformations to match them. Compared to the current asymmetric methods in the literature, this fully symmetric method allows one to determine one-to-one correspondences between the edge features of two images. The entire variational model is realized in a multiscale framework of the finite element approximation. The optimization process is guided by an estimation minimization-type algorithm and an adaptive generalized gradient flow to guarantee a fast and smooth relaxation. The algorithm is tested on Ti and T2 magnetic resonance image data to study the parameter setting. We also present promising results of four applications of the proposed algorithm: interobject monomodal registration, retinal image registration, matching digital photographs of neurosurgery with its volume data, and motion estimation for frame interpolation. [ABSTRACT FROM AUTHOR]

This paper deals with the views synthesis problem and proposes an automatic method for specifying the virtual camera position and orientation in an uncalibrated setting, based on the interpolation and extrapolation of the motion among the reference views. Novel images can be rendered from virtual cameras moving on parametric trajectories. Synthetic and real experiments illustrate the approach. [ABSTRACT FROM AUTHOR]

Character skeleton plays a significant role in character recognition. The strokes of a character may consist of two regions, i.e., singular and regular regions. The intersections and junctions of the strokes belong to singular region, while the straight and smooth parts of the strokes are categorized to regular region. Therefore, a skeletonization method requires two different processes to treat the skeletons in theses two different regions. All traditional skeletonization algorithms are based on the symmetry analysis technique. The major problems of these methods are as follows. 1) The computation of the primary skeleton in the regular region is indirect, so that its implementation is sophisticated and costly. 2) The extracted skeleton cannot be exactly located on the central line of the stroke. 3) The captured skeleton in the singular region may be distorted by artifacts and branches. To overcome these problems, a novel scheme of extracting the skeleton of character based on wavelet transform is presented in this paper. This scheme consists of two main steps, namely: a) extraction of primary skeleton in the regular region and b) amendment processing of the primary skeletons and connection of them in the singular region. A direct technique is used in the first step, where a new wavelet-based symmetry analysis is developed for finding the central line of the stroke directly. A novel method called smooth interpolation is designed in the second step, where a smooth operation is applied to the primary skeleton, and, thereafter, the interpolation compensation technique is proposed to link the primary skeleton, so that the skeleton in the singular region can be produced. Experiments are conducted and positive results are achieved, which show that the proposed skeletonization scheme is applicable to not only binary image but also gray-level image, and the skeleton is robust against noise and affine transform. [ABSTRACT FROM AUTHOR]

In this paper, a regularized spectral estimation formula and a regularized iterative algorithm for band-limited extrapolation are presented. The ill-posedness is taken into account. First the Fredholm equation is regularized. Then it is transformed to a differential equation in the case where the time interval is R. A fast algorithm to solve the differential equation is given by the finite difference and a regularized spectral estimation formula is obtained. Then a regularized iterative extrapolation algorithm is introduced and compared with the Papoulis and Gerchberg algorithm. [ABSTRACT FROM AUTHOR]