Search

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]

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]

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]

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]

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]

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]

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]

This paper presents an algorithmic scan-chain-fault diagnosis procedure. The diagnosis for a single scan-chain fault is performed in three steps. The first step uses special chain test patterns to determine both the faulty chain and the fault type in the faulty chain. The second step uses a novel procedure to identify the suspect scan cell within a range of scan cells. The final step further improves the diagnostic resolution by ranking the suspect scan cells inside this range. The proposed technique handles both stuck-at and timing failures (transition faults and hold-time faults). The application of the procedure in a production test flow is discussed. Simulation and silicon results from several products show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Computation of grasps with form/force closure is one of the fundamental problems in the study of multifingered grasping and dextrous manipulation. Based on the geometric condition of the closure property, this paper presents a numerical test to quantify how far a grasp is from losing form/force closure. With the polyhedral approximation of the friction cone, the proposed numerical test can be formulated as a single linear program. An iterative algorithm for computing optimal force-closure grasps, which is implemented by minimizing the proposed numerical test in the grasp configuration space, is also developed. The algorithm is computationally efficient and generally applicable. tt can be used for computing form/force-closure grasps on 3-D objects with curved surfaces, and with any number of contact points. Simulation examples are given to show the effectiveness and computational efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm to design jointly interpolation filters and decision feedback equalizers in the sense of minimum mean-square error such that the joint capacity which is neglected in conventional design is explored to improve the receiver performance. The algorithm comprises an iteration of two alternating simple quadratic minimizing operations and ensures convergence. A simulation example for the raised-cosine channel demonstrates that via this approach an improvement over the conventional design can be achieved. [ABSTRACT FROM AUTHOR]

In this paper, a rational interpolation approach is used to approximate the transfer function of passive systems characterized by sampled data. Orthogonal polynomials are used to improve the numerical stability of the ill-conditioned Vandermonde-like interpolation matrix associated with the ordinary power series. First, the poles of the system are obtained by efficiently and accurately transforming the coefficients of the orthogonal polynomials to the ordinary power series using Clenshaw's recurrence algorithm. Then, the residues are solved in real or in complex conjugate pairs to insure a physically realizable system. Finally, the passivity of the system is enforced by applying certain constraints on the poles and residues of the system. The performances of the three most common orthogonal polynomials, Legends and Chebyshev of the first and second kinds, are also compared to that of the power series. [ABSTRACT FROM AUTHOR]

This paper demonstrates the use of asynchronous maximum-likelihood (ML) detection to improve the detection performance of coded servo repeatable run out data. A suboptimal ML algorithm based on an absolute value metric is presented. This paper compares the performance of the ML algorithms with an asynchronous bit by bit (BBB) detection algorithm. Simulation results quantify the performance improvement over the BBB algorithm. A gain correction algorithm is also proposed to allow the asynchronous ML detection performance to be less sensitive to gain errors. The efficacy of the gain correction algorithm is quantified via simulations. [ABSTRACT FROM AUTHOR]

In this paper, a motion-compensated de-interlacing algorithm using the Markov random field (MRF) model is proposed. The de-interlacing problem is formulated as a maximum a posteriori (MAP) MRF problem. The MAP solution is the one that minimizes an energy function, which imposes discontinuity-adaptive smoothness (DAS) spatial constraint on the de-interlaced frame. The edge direction information, which is used to formulate the DAS constraint, is implicitly indicated by weight vectors (weights for 16 digitized directions). Generally, large weights are assigned to along-edge directions and relatively small weights are assigned to across-edge directions. As a local statistical-based method, the proposed weighting method should be more robust than traditional edge-directed interpolation methods in deciding local edge directions. The proposed algorithm is implemented by an iterative optimization process, which guarantees convergence. However, a global optimal solution is not guaranteed due to computational complexity concern. Simulation results compare the proposed algorithm to other motion compensated de-interlacing algorithms. Significant improvements of de-interlaced edges are observed. [ABSTRACT FROM AUTHOR]

The proper choice of mapping used in space-mapping optimization algorithms is typically problem dependent. The number of parameters of the space-mapping surrogate model must be adjusted so that the model is flexible enough to reflect the features of the fine model, but at the same time is not over flexible. Its extrapolation capability should allow the prediction of the fine model response in the neighborhood of the current iteration point. A wrong choice of space-mapping type may lead to poor performance of the space-mapping optimization algorithm. In this paper, we consider a space-mapping optimization algorithm with an adaptive surrogate model. This allows us to adjust the type of space-mapping surrogate model used in a given iteration based on the approximation/extrapolation capability of the model. The technique does not require any additional fine model evaluations. [ABSTRACT FROM AUTHOR]

In this paper, we prove the following two results that expose some combinatorial limitations to list decoding Given n distinct elements α1,…,αn, from a field F, and n subsets S1,…Sn of F each of size at most l, the list decoding algorithm of Guruswami and Sudan can in polynomial time output all polynomials p of degree at most k that satisfy p(αi] ϵ Si for every i, as long as l ≤ [n⁄k]. We show that the performance of this algorithm is the best possible in a strong sense; specifically, when l = [n⁄k], the list of output polynomials can be superpolynomially large in n. For Reed-Solomon codes of block length n and dimension k + 1 where k = nδ for small enough δ, we exhibit an explicit received word with a superpolynomial number of Reed-Solomon codewords that agree with it on (2 - ϵ)k locations, for any desired ϵ ≥ 0 (agreement of k is trivial to achieve). Such a bound was known earlier only for a nonexplicit center. Finding explicit bad list decoding configurations is of significant interest—for example, the best known rate versus distance tradeoff, due to Xing, is based on a bad list decoding configuration for algebraic-geometric codes, which is unfortunately not explicitly known. [ABSTRACT FROM AUTHOR]

In this paper, a novel technique for the approximation of three-dimensional (3-D) antenna radiation patterns is presented. The proposed method combines the two principal cuts in order to acquire an adequate estimate of the 3-D antenna radiation solid. The absolute error from the theoretical solution is analyzed along with other statistical measures for various types of antenna structures, namely omni-directional and directive arrays. The performance of the method is compared against other existing extrapolation algorithms. The proposed technique exhibits low approximation errors and is easily integrated into 3-D radio propagation planning tools (such as ray-tracing algorithms). [ABSTRACT FROM AUTHOR]

We consider the optimal control of mechanical systems on Lie groups and develop numerical methods that exploit the structure of the state space and preserve the system motion invariants. Our approach is based on a coordinate-free variational discretization of the dynamics that leads to structure-preserving discrete equations of motion. We construct necessary conditions for optimal trajectories that correspond to discrete geodesics of a higher order system and develop numerical methods for their computation. The resulting algorithms are simple to implement and converge to a solution in very few iterations. A general software implementation is provided and applied to two example systems: an underactuated boat and a satellite with thrusters. [ABSTRACT FROM AUTHOR]

A computationally efficient algorithm, which combines the characteristic basis function method (CBFM), the physical optics (PO) approach (when applicable) with the forward backward method (FBM), is applied for the investigation of electromagnetic scattering from--and propagation over--large-scale rough terrain problems. The algorithm utilizes high-level basis functions defined on macro-domains (blocks), called the characteristic basis functions (CBFs) that are constructed by aggregating low-level basis functions (i.e., conventional sub-domain basis functions). The FBM as well as the PO approach (when applicable) are used to construct the aforementioned CBFs. The conventional CBFM is slightly modified to handle large-terrain problems, and is further embellished by accelerating it, as well as reducing its storage requirements, via the use of an extrapolation procedure. Numerical results for the total fields, as well as for the path loss are presented and compared with either measured or previously published reference solutions to assess the efficiency and accuracy of the algorithm. [ABSTRACT FROM AUTHOR]

Finding sparse approximate solutions to large under-determined linear systems of equations is a common problem in signal/image processing and statistics. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), wavelet-based deconvolution and reconstruction, and compressed sensing (CS) are a few well-known areas in which problems of this type appear. One standard approach is to minimize an objective function that includes a quadratic (ℓ2) error term added to a sparsity-inducing (usually ℓ1) regularizater. We present an algorithmic framework for the more general problem of minimizing the sum of a smooth convex function and a nonsmooth, possibly nonconvex regularizer. We propose iterative methods in which each step is obtained by solving an optimization subproblem involving a quadratic term with diagonal Hessian (i.e., separable in the unknowns) plus the original sparsity-inducing regularizer; our approach is suitable for cases in which this subproblem can be solved much more rapidly than the original problem. Under mild conditions (namely convexity of the regularizer), we prove convergence of the proposed iterative algorithm to a minimum of the objective function. In addition to solving the standard ℓ2 - ℓ1 case, our framework yields efficient solution techniques for other regularizers, such as an ℓ∞ norm and group-separable regularizers. It also generalizes immediately to the case in which the data is complex rather than real. Experiments with CS problems show that our approach is competitive with the fastest known methods for the standard ℓ2 - ℓ1 problem, as well as being efficient on problems with other separable regularization terms. [ABSTRACT FROM AUTHOR]

A reconstruction algorithm is detailed for three-dimensional full-vectorial microwave imaging based on Newton-type optimization. The goal is to reconstruct the three-dimensional complex pemittivity of a scatterer in a homogeneous background from a number of time-harmonic scattered field measurements. The algorithm combines a modified Gauss—Newton optimization method with a computationally efficient forward solver, based on the fast Fourier transform method and the marching-on-in-source-position extrapolation procedure. A regularized cost function is proposed by applying a multiplicative-additive regularization to the least squares datafit. This approach mitigates the effect of measurement noise on the reconstruction and effectively deals with the non-linearity of the optimization problem. It is furthermore shown that the modified Gauss—Newton method converges much faster than the Broyden—Fletcher—Goldfarb—Shanno quasi-Newton method. Promising quantitative reconstructions from both simulated and experimental data are presented. The latter data are bi-static polarimetric free-space measurements provided by Institut Fresnel, Marseille, France. [ABSTRACT FROM AUTHOR]

Two novel block-based algorithms are presented for the reconstruction of uniform samples given the nonuniform samples. The first algorithm uses a sinc interpolator whereas the second one uses a DFT-based interpolator. It is shown that the proposed algorithms are stable and the error due to noise and sampling jitter is bounded by the corresponding error norms of noise and jitter, respectively. We show that both of the block-based algorithms provide nearly perfect reconstruction for a class of practically time and bandlimited signals. Boundary effects are considered and single and multiblock processing is discussed. A modified block-based algorithm is developed by using the windowing technique in order to improve the mean-squared error (MSE) performance for nonbandlimited signals. It is shown that this algorithm performs better than a group of alternative algorithms, including Yen's third algorithm, for a variety of signal, noise, and sampling grids. [ABSTRACT FROM AUTHOR]

In medical helical cone-beam CT, it is common that the region-of-interest (ROI) is contained inside the helix cylinder, while the complete object is long and extends outside the top and the bottom of the cylinder. This is the Long Object Problem. Analytical reconstruction methods for helical cone-beam CT have been designed to handle this problem. It has been shown that a moderate amount of over-scanning is sufficient for reconstruction of a certain ROI. The over-scanning projection rays travel both through the ROI, as well as outside the ROI. This is unfortunate for iterative methods since it seems impossible to compute accurate values for the projection rays which travel partly inside and partly outside the ROI. Therefore, it seems that the useful ROI will diminish for every iteration step. We propose the following solution to the problem. First, we reconstruct volume regions also outside the ROI. These volume regions will certainly be incompletely reconstructed, but our experimental results show that they serve well for projection generation. This is rather counter-intuitive and contradictory to our initial assumptions. Second, we use careful extrapolation and masking of projection data. This is not a general necessity, but needed for the chosen iterative algorithm, which includes rebinning and iterative filtered backprojection. Our idea here was to use an approximate reconstruction method which gives cone-beam artifacts and then improve the reconstructed result by iterative filtered backprojection. The experimental results seem very encouraging. The cone-beam artifacts can indeed be removed. Even voxels close to the boundary of the ROI are as well enhanced by the iterative loop as those in the middle of the ROI. [ABSTRACT FROM AUTHOR]

Using a stochastic framework, we propose two algo- rithms for the problem of obtaining a single high-resolution image from multiple noisy, blurred, and undersampled images. The first is based on a Bayesian formulation that is implemented via the ex- pectation maximization algorithm. The second is based on a max- imum a posteriori formulation. In both of oUr formulations, the registration, noise, and image statistics tire treated as unknown parameters. These unknown parameters and the high-resolution image are estimated jointly based on the available observations. We present an efficient implementation of these algorithms in the fre- quency domain that allows their application to large images. Sim- ulations are presented that test and compare the proposed algo- rithms. [ABSTRACT FROM AUTHOR]

We propose a mixed “skeleton” and “equivalence” nested approximation method to compress the impedance matrix of the method of moments for the wideband multiscale simulations. We first introduce a nested skeleton approximation, where the impedance matrix is expressed recursively by sampling the dominant basis functions (e. g., skeletons) with a fully algebraic implementation from the original basis functions. The idea is to introduce the automatically constructed test surface around the interface between near- and far-field regions, for each group the dominant RWGs are sampled recursively with the adaptive cross approximation to compress the matrix against the test surface. Second, we introduce a mixed-form algorithm of “skeleton” and “equivalence” nested approximation method, at low levels, the nested skeleton approximation is employed, and it is smoothly transferred to standard wideband nested equivalence approximation (WNESA) at high levels. An accurate number of skeletons can be always found with a predetermined threshold at a low level, which will improve computation efficiency, with respect to WNESA. The computational complexity of the proposed algorithm is $\mathcal {O}(N\log {N})$ , $N$ is the number of unknowns. Numerical wideband multiscale simulations demonstrate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The demand of performance robustness against the uncertainty in design variables is required during the optimization process. From the viewpoint of fast robustness evaluation for the electromagnetic problem, based on the worst case scenario approximation and design sensitivity analysis, a new robust optimization algorithm, the sensitivity-assisted worst case optimization (SA-WCO), is developed. In order to keep higher accuracy of the robustness prediction, the second-order sensitivity implemented by the hybrid direct differentiation-adjoint variable method is introduced into the robustness assessment. The performance and robustness of the proposed SA-WCO algorithms are investigated through a numerical experiment with the TEAM Problem 22. [ABSTRACT FROM AUTHOR]

Consider the discrete wavelet transform (DWT) of a time series X=\Xt,t\in\BBZ\ with weakly stationary Kth differences. Such time series are encountered in many situations, including unit root or long memory processes. If the wavelet has at least K vanishing moments, the DWT is jointly stationary across scales provided that small scales coefficients are reshaped in appropriate blocks to cope with the downsampling embedded in the DWT. Our goal is to compute the covariance matrix or the joint spectral density of the DWT, given the autocovariance of the Kth differences. We assume that the DWT corresponds to a multiresolution analysis (MRA), which allows us to compute wavelet coefficients iteratively through a succession of finite impulse response (FIR) filters and downsampling. This iterative scheme, however, is not suitable for our purpose in the case where the process X itself is not stationary. Hence, we first derive an iterative algorithm with the same DWT output but with input the Kth differences of the time series. An iterative low complexity scheme is then deduced to compute the exact covariance matrix and spectral density of the DWT. This new algorithm is an opportunity to investigate how using exact DWT covariance computations improves previously proposed statistical methods that rely on approximated computations. Numerical experiments are used for comparisons. Two cases are examined: 1) a local semi-parametric likelihood estimation of long memory processes in the wavelet domain and 2) the computation of a test statistic for detecting change points in the wavelet domain for long memory processes. A real data set analysis is also presented. Namely, economic structural changes are investigated by looking for change points in the daily S&P 500 absolute log returns. [ABSTRACT FROM AUTHOR]

In this brief, we consider extracting generalized eigenvectors in parallel for the generalized eigendecomposition problem. The problem is formulated as an optimization problem of minimizing an unconstrained quartic cost function based on the weighted rule. It is shown that the proposed weighted cost function has a unique global minimum, which corresponds to the principal generalized eigenvectors. In order to estimate the principal generalized eigenvector matrix efficiently, we simplify the quartic cost function as a quadric one by making an appropriate approximation, and then derive a fast algorithm for extracting the principal generalized eigenvector in parallel. We also show the application of the proposed algorithm in blind source separation. Numerical simulations are performed, and the results demonstrate the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

We have developed a new full-waveform groundpenetrating radar (GPR) multicomponent inversion scheme for imaging the shallow subsurface using arbitrary recording configurations. It yields significantly higher resolution images than conventional tomographic techniques based on first-arrival times and pulse amplitudes. The inversion is formulated as a nonlinear least squares problem in which the misfit between observed and modeled data is minimized. The full-waveform modeling is implemented by means of a finite-difference time-domain solution of Maxwell's equations. We derive here an iterative gradient method in which the steepest descent direction, used to update iteratively the permittivity and conductivity distributions in an optimal way, is found by cross-correlating the forward vector wavefield and the backward-propagated vectorial residual wavefield. The formulation of the solution is given in a very general, albeit compact and elegant, fashion. Each iteration step of our inversion scheme requires several calculations of propagating wavefields. Novel features of the scheme compared to previous full-waveform GPR inversions are as follows: 1) The permittivity and conductivity distributions are updated simultaneously (rather than consecutively) at each iterative step using improved gradient and step length formulations; 2) the scheme is able to exploit the full vector wavefield; and 3) various data sets/survey types (e.g., crosshole and borehole-to-surface) can be individually or jointly inverted. Several synthetic examples involving both homogeneous and layered stochastic background models with embedded anomalous inclusions demonstrate the superiority of the new scheme over previous approaches. [ABSTRACT FROM AUTHOR]

In applications of tomographic imaging, insufficient data problems can take various forms, such as few-view projection imaging which enables rapid scanning with lower X-ray dose. In this work, an iterative reconstruction-reprojection (IRR) algorithm with total variation (TV) constraint is developed for few-view projections. The IRR algorithm is used to estimate the missing projection data by iterative extrapolation between projection and image space. TV minimization is a popular image restoration method with edge preserving. In recent studies, it has been successfully used for reconstructing images from sparse samplings, such as few-view projections. Our method is derived from this work. The combination of IRR and TV achieves both estimation in projection space and regularization in image space, which accelerates the convergence of the iterations. To improve the quality of the image reconstructed from few-view fan-beam projections, a short-scan type IRR is also approached to reduce the redundancy of projection data. An improved weighting function is proposed for few-view short-scan projection reconstruction by the filtered backprojection (FBP) algorithm. Numerical simulations show that the IRR-TV algorithm is effective for the few-view problem of reconstructing sparse-gradient images. [ABSTRACT FROM AUTHOR]

Two modified blind equalization algorithms are analyzed for performance. These algorithms add a constellation-matched error term to the cost functions of the generalized Sato and multimodulus algorithms. The dynamic convergence behavior and steady-state performance of these algorithms, and of a related version of the constant modulus algorithm, are characterized; The analysis establishes the improved performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

To improve numerical dispersion and second-order convergence behavior of the traditional Yee finite-difference time-domain (FDTD) algorithm, various higher order finite difference implementations have been proposed. Many have difficulty handling interfaces between distinct dielectric media or metallic sheets, because the high-order Taylor expansions on which these codes are based are invalidated by field or derivative discontinuities. One-sided extensions/extrapolations are a common approach to remedy interface discontinuities. Here, another approach based upon Whitney form, mass lumped finite elements is pursued to develop the "Lobatto Cell," a high-order replacement for the Yee cell with appropriate continuity behavior at contrasting media interfaces. The Lobatto Cell retains many robust features of the Yee method (discrete conservation laws, a guarantee of conditional stability and straightforward explicit updating), but provides higher order interpolation and dispersion error convergence. A notable drawback of the method is larger modeling granularity (staircasing), which is managed here by combining the Lobatto Cell method with preexisting, robust subgridding techniques. [ABSTRACT FROM AUTHOR]

A new convolution-based image interpolation method is presented, whose kernel function is designed via blending some well-known kernels. The new kernel is a better approximation to sinc function both in the space domain and the frequency domain. Comparative experiments with several polynomial spline type algorithms indicate that our approach exhibits a significant improvement in image quality. [ABSTRACT FROM AUTHOR]

In this letter, we show that with high probability, the thresholding algorithm can recover signals that are sparse in a redundant dictionary as long as the 2-Babel function is growing slowly. This implies that it can succeed for sparsity levels up to the order of the ambient dimension. The theoretical bounds are illustrated with numerical simulations. As an application of the theory, sensing dictionaries for optimal average performance are characterized, and their performance is tested numerically. [ABSTRACT FROM AUTHOR]

A new spatial interpolation scheme is proposed to reduce the matrix fill time in the method of moments implementation of planar microstrip structures. The approach is based on the division of the distance between the basis and the testing functions into three, namely near, intermediate and far regions. The matrix entries in the near region are computed directly. The entries corresponding to both intermediate and far regions are evaluated in two steps: 1) choosing an adequate number of sampling points in these regions and computing the associated entries directly and 2) interpolating the remaining entries by using cubic spline or bicubic spline algorithms. To demonstrate the efficiency and accuracy, the technique is applied to a planar microstrip low-pass filter and a microstrip-line fed patch antenna problems. It is shown that the interpolation scheme can result in significant savings with high accuracy. [ABSTRACT FROM AUTHOR]

We propose a robust interpolation algorithm for model-based spectral analysis. Instead of estimating the spectral model directly, the so-called ha If spectrum, which has a one-to-one relationship with the spectrum through standard spectral decomposition, is estimated using an interpolation approach. The interpolation data consists of the values and the derivatives of the half spectrum function at a set of user-specified points, and can be easily estimated using an input-to-state filter. Our algorithm allows a large number of noisy interpolation data to be used to optimally fit a half spectrum function of a fixed order. The capability of handling large number of interpolation data makes our algorithm robust to the inherent finite sample noise in the interpolation data. The algorithm involves solving some least-squares problems and semidefinite programming problems, and is thus numerically efficient. Numerical tests show that our algorithm gives very reliable spectral estimates. [ABSTRACT FROM AUTHOR]

In this letter, we apply the Kikuchi approximation method to the problem of joint decoding of a low-density parity-check code and a partial-response channel. The Kikuchi method is, in general, more powerful than the conventional loopy belief propagation (BP) algorithm, and can produce better approximations to an underlying inference problem. We will first review the Kikuchi approximation method and the generalized BP algorithm, which is an iterative message-passing algorithm based on this method. We will then report simulation results which show that the Kikuchi method outperforms the best conventional iterative method. [ABSTRACT FROM AUTHOR]

Various log-likelihood-ratio-based belief-propagation (LLR-BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representations of the decoding computations are shown to achieve a reduction in complexity by simplifying the check-node update, or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from performance, latency, computational-complexity, and memory-requirement perspectives. [ABSTRACT FROM AUTHOR]

This article focuses on the book "Numerical Recipes in C++: The Art of Scientific Computing," by William H. Press, Saul A. Teukoisky, William T. Vetterling, and Brian P. Flannery. The book's chapters detail linear algebraic equation solutions, interpolation and extrapolation, and functions' evaluation and minimization. They also cover Monte Carlo methods, root finding, Eigensystems, the Fourier transform and its applications, data modeling, boundary value problems, ordinary and partial differential equations, and integral equations. The book also contains other algorithms that scientists might find useful, such as those dealing with the statistical description of data, random numbers, compression, coding, and arbitrary--precision arithmetic. The book's range of topics is extremely wide; hopefully, the next edition's minimization techniques discussion will include additional stochastic methods apart from simulated annealing, such as genetic algorithms and tabu search techniques. Anyone performing calculations more complex than integer addition and subtraction is likely to benefit from this book's sometimes wry guidelines.