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The comparison of images of a patient to a reference standard may enable the identification of structural brain changes. These comparisons may involve the use of vector or tensor images (i.e., 3-D images for which each voxel can be represented as an [R.sup.N] vector) such as diffusion tensor images (DTI) or transformations. The recent introduction of the Log-Euclidean framework for diffeomorphisms and tensors has greatly simplified the use of these images by allowing all the computations to be performed on a vector-space. However, many sources can result in a bias in the images, including disease or imaging artifacts. In order to estimate and compensate for these sources of variability, we developed a new algorithm, called continuous STAPLE, that estimates the reference standard underlying a set of vector images. This method, based on an expectation-maximization method similar in principle to the validation method STAPLE, also estimates for each image a set of parameters characterizing their bias and variance with respect to the reference standard. We demonstrate how to use these parameters for the detection of atypical images or outliers in the population under study. We identified significant differences between the tensors of diffusion images of multiple sclerosis patients and those of control subjects in the vicinity of lesions. Index Terms--Atlas, diffusion tensor image (DTI), expectation-maximization (EM), ground truth, Kullback-Leibler divergence (KLD), STAPLE, transformations, validation.

In this paper, a novel scheme for obtaining the fundamental-frequency positive-sequence grid voltage is proposed. The method is based on four simple mathematical transformations; two of them are in the stationary reference frame, which are able to eliminate odd harmonics from the original signals. The other two transformations are implemented in a synchronously rotating reference frame in order to eliminate even harmonics. The output of the last transformation block is the input to a synchronous reference-frame phase-locked loop for detecting the frequency and position of the positive-sequence voltage vector. The proposed algorithm was verified through simulations and experiments by applying distorted and unbalanced signals, containing positive and negative-sequence components. The results are in agreement with those theoretically predicted and indicate that the proposed scheme has a great potential for use in grid-connected converter synchronization algorithms. Index Terms--Converters, interconnected power systems, power quality.

The modified discrete cosine transform (MDCT) and inverse MDCT (IMDCT) are two of the most computationally intensive operations in MPEG audio coding standards. A new mixed-radix algorithm for efficiently computing the MDCT/IMDCT is presented. The proposed mixed-radix MDCT algorithm is composed of two recursive algorithms. The first algorithm, called the radix-2 decimation-in-frequency algorithm, is obtained by decomposing an N-point MDCT into two MDCTs with the length N/2. The second algorithm, called the radix-3 decimation-in-time algorithm, is obtained by decomposing an N-point MDCT into three MDCTs with the length N/3. Since the proposed MDCT algorithm is also expressed in the form of a simple sparse matrix factorization, the corresponding IMDCT algorithm can be easily derived by simply transposing the matrix factorization. Comparison of the proposed algorithm with some existing ones shows that our proposed algorithm is more suitable for parallel implementation and particularly suitable for the layer HI of MPEG-1 and MPEG-2 audio encoding and decoding. Moreover, the proposed algorithm can be easily extended to the multidimensional case by using the vector-radix method. Index Terms--Fast algorithm, mixed radix, modified discrete cosine transform (MDCT), MPEG audio coding.

In this paper, the technique of McClellan transformation is applied to design variable 2-D FIR digital filters. Compared with the conventional transformation, the 2-D transformation subfilter and the 1-D prototype filter are designed such that their frequency characteristics are adjustable. Moreover, they are tunable by the same variable parameter, so the variable characteristics of 1-D prototype filters are coincident with those of 2-D subfilters. Several examples, including variable fan filters, variable circularly symmetric filters, and variable elliptically symmetric filters with arbitrary orientation, are presented to demonstrate the effectiveness and the flexibility of the presented method. Index Terms--Circularly symmetric filter, elliptically symmetric filter, fan filter, least squares approach, McClellan transformation, two-dimensional (2-D) filter, variable digital filter.

Interest points are widely used as point-features for image matching. This paper describes robust and efficient algorithms to extract multiscale interest points in hyperspectral images in which structural information is distributed across several spectral bands. The formulation is based on a Gaussian scale-space representation of the hyperspectral data cube, and the use of a principal components decomposition to combine information efficiently across spectral bands. A spectral distance measure is used to characterize spatial relations between neighboring hyperspectral pixels. In addition, we describe methods for preprocessing a pair of hyperspectral images, clustering the spectral signatures of interest points, and using the resulting data for matching points under simple geometric transformations. The stability of the resulting interest points in time-lapse satellite images was determined to be in the range of 52% to 75% in the testing data set that were acquired from variety of landforms like coastal islands of La Parguera, Chesapeake Bay, the Cuprite Mining District of Nevada, and agricultural field images of Kansas and Oklahoma, and thus, they can be used as a foundation for image matching and related image analysis tasks. Index Terms--Clustering, difference of Gaussian (DOG), hyperspectral image, interest points, key points, principal components analysis (PCA), scale-invariant feature transform (SIFT).

We study the relationship between the Walsh transform and the algebraic normal form (ANF) of a Boolean function. In the first part of the paper, we obtain a formula for the Walsh transform at a certain point in terms of parameters derived from the algebraic normal form. We use previous results by Carlet and Guillot to obtain an explicit expression for the Walsh transform at a point in terms of parameters derived from the ANF. The second part of the paper is devoted to simplify this formula and develop an algorithm to evaluate it. This algorithm can be applied in situations where it is practically impossible to use the fast Walsh transform algorithm. Experimental results show that under certain conditions it is possible to execute our algorithm to evaluate the Walsh transform (at a small set of points) of functions on a few scores of variables having a few hundred terms in the algebraic normal form. Index Terms--Algebraic normal form, Boolean function, Walsh transform.

In the incoming amendment of H.264/AVC for scalable video coding (SVC), down and up-samplings in a spatial domain are incorporated for spatial scalability. A new two-fold up-sampling method is proposed for SVC. The proposed up-sampling method is based on a combination of the forward and backward type-II discrete cosine transform (DCT). As the proposed up-sampling kernel has various symmetries for efficient computation, a fast algorithm of type-II DCT-based up-sampling method is also proposed. For further improvement of the up-sampling performance, an adaptive filtering method in the type-II DCT up-sampling is introduced, which applies different weighting parameters to DCT coefficients. Even as this adaptive method is applied, the up-sampling operation in the decoder has the same computational complexity as the fixed weighting method. The proposed adaptive up-sampling method shows a much improved PSNR in comparison with the recent H.264 SVC up-sampling method. Index Terms--Adaptive up-sampling, down-sampling, H.264, scalable video coding (SVC), type-II DCT, up-sampling.

Coherency between generators is tracked, by examining the instantaneous phase differences among interarea oscillations and swing curves in disturbed multiarea power systems. Huang's empirical mode decomposition is applied to extract dominant oscillatory modes from interarea oscillations/swing curves. Hilbert transform on these modes yields their instantaneous phase. The coherency is thus revealed by the temporal evolution of the phase difference among interarea oscillations/generator swing curves. The technique is illustrated using simulations on a test system, as well as actual wide-area measurements. Index Terms--Empirical mode decomposition, generator coherency, Hilbert-Huang transform, intrinsic mode function, proper orthogonal decomposition, wide-area measurement system.

This paper proposes a one-to-one mapping between the coefficients of continuous-time (s-domain) and discrete-time (z-domain) IIR transfer functions such that the s-domain numerator/denominator coefficients can be uniquely mapped to the z-domain numerator/denominator coefficients. The one-to-one mapping provides a firm basis for proving the inverses of the so-called generalized Pascal matrices from various first-order s-z transformations. We also derive recurrence formulas for recursively determining the inner elements of the generalized Pascal matrices from their boundary ones. Consequently, all the elements of the whole generalized Pascal matrix can be easily generated through utilizing their neighbourhood, which can be exploited for further simplifying the Pascal matrix generations. Finally, we reveal and prove some interesting properties of the generalized Pascal matrices. Index Terms--Generalized Pascal matrix, inverse Pascal matrix, continuous-time (CT) filter, discrete-time (DT) filter, first-order s-z transformation, one-to-one coefficient mapping.

A comparison between two well-known near field to far field (NF-FF) transformation methods is presented: the spherical wave expansion (SWE) and the sources reconstruction method (SRM). The goal of this paper is to show the methods performance for NF-FF transformation pointing out the advantages and limitations of each one. First, the computational cost is studied, showing its dependence with the antenna under test (AUT) electric size. Second, the NF-FF transformation accuracy of each method is compared for a fixed AUT electric size, analyzing also the influence of the main parameters that affect the SRM and SWE accuracy. Third, the SRM capabilities are presented, with focus on the NF-NF transformation inside the minimum sphere. Practical applications of the SWE and SRM are illustrated by means of an example of NF-FF transformation and antenna diagnostics problem using measured NF data. Index Terms--Antenna diagnostics, antenna measurement, near field to far field (NF-FF) transformation, sources reconstruction, spherical wave expansion (SWE).

Let a biorthogonal Reed-Muller code RM (1, m) of length n = [2.sup.m] be used on a memoryless channel with an input alphabet [+ or -] 1 and a real-valued output R. Given any nonzero received vector y in the Euclidean space [R.sup.n] and some parameter [epsilon] [member of] (0, 1), our goal is to perform list decoding of the code RM (1, m) and retrieve all codewords located within the angle arccos [member of] from y. For an arbitrarily small [epsilon], we design an algorithm that outputs this list of codewords with the linear complexity order of n [[ln.sup.2] [epsilon]] bit operations. Without loss of generality, let vector y be also scaled to the Euclidean length [square root of n] of the transmitted vectors. Then an equivalent task is to retrieve all coefficients of the Hadamard transform of vector y whose absolute values exceed n[epsilon]. Thus, this decoding algorithm retrieves all n[epsilon]-significant coefficients of the Hadamard transform with the linear complexity n [[ln.sup.2] [epsilon]] instead of the complexity n [ln.sup.2] n of the full Hadamard transform. Index Terms--Biorthogonal codes, Hadamard transform, soft-decision list decoding.

We employ the Mellin transform to facilitate the bit error ratio (BER) analysis of a fast frequency hopping (FFH)-assisted, M-ary frequency-shift keying (MFSK) using product combining (PC) when the transmitted signal is subjected to both Rayleigh fading and partial-band noise jamming. Exploiting the fact that the Mellin transform of the product of independent random variables is the product of their Mellin transforms, we derive the probability density function (PDF) of the PC's output. The derivation of the PDF then allows the computation of the system's BER. It is shown that the Mellin transform substantially simplifies the analysis of the PC receiver and hence facilitates, for the first time, the analysis of the FFH-MFSK PC receiver for modulation orders of M > 2. Index Terms--Fast frequency hopping (FFH), Mellin transform, partial-band noise jamming (PBNJ), probability density function (PDF), product combining (PC), Rayleigh fading, residues.

Power system oscillatory behavior can be analyzed in terms of modes, expressed as exponentially modulated sinusoids, exhibited in signals measured on the system. These signals are driven by the behavior of a large, nonlinear, time-variant system. In this paper, two modal identification methods are examined comparatively: Prony analysis and a method based on the Hilbert transform. Considerable structural differences exist between the two methods. Prony analysis yields modes which are directly expressed as exponentially modulated sinusoids, whereas the Hilbert method provides a more general solution. Synthetic and measured signals are used in the comparison. Some general conclusions are drawn from the analysis of several signals, including two sets of measured field data. Index Terms--Dynamics, empirical mode decomposition (EMD), Hilbert transforms, Hilbert-Huang method, interarea oscillations, power system dynamic stability, power system measurements, power systems, prony analysis.

Ultrawideband radar is commonly used in the frequency range of 50-500 MHz to detect buried pipes at a depth of about 1-2 m depending on the soil characteristics. The typical feature used to locate the pipes is the hyperbolic pattern of the time of flight generated by a linear scan of the antenna above the surface. When the pipes are close together, the hyperbolas overlap, anda straightforward least squares fit is not possible. The Hough transform provides one possible solution. This paper extends the Hough transform by introducing a weighting factor depending on the differentials of the unknown parameters with respect to the experimental errors, namely, the probe position error and the time-of-flight error. This enables optimally placed sets of data pairs to be given greater weight than 'ill-conditioned' sets, as for example when all data pairs lie near one end of the arc. The result is a decrease in the background amplitude with respect to the maximum of the peaks in the Hough accumulator space. It is shown that this improvement persists even when many arcs are present. A mathematical analysis with analytical results is given for the case of four unknowns: pipe radius R, pipe center position (Y, Z), and soil propagation velocity V. The results are presented through simulations introducing controlled uncertainties in the probe position, the time of flight, and its bin size. The simulations demonstrate the correlations that occur between the radius, depth, and velocity for given experimental uncertainties. Index Terms--Algorithms, buried objects, equations, ground-penetrating radar (GPR), Hough transforms, radar data processing, radar measurements.

In the paper, an extension of LaSalle's Invariance Principle to a class of switched linear systems is studied. One of the motivations is the consensus problem in multi-agent systems. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, this paper allows that the switching modes are only Lyapunov stable. Under certain ergodicity assumptions, an extension of LaSalle's Invariance Principle for global asymptotic stability is obtained. Then it is used to solve the consensus reaching problem of certain multi-agent systems in which each agent is modeled by a double integrator, and the associated interaction graph is switching and is assumed to be only jointly connected. Index Terms--LaSalle's invariance principle, multi-agent consensus, switched linear systems, weak common quadratic Lyapunov function.

The Fiat--Shamir paradigm for transforming identification schemes into signature schemes has been popular since its introduction because it yields efficient signature schemes, and has been receiving renewed interest of late as the main tool in deriving forward-secure signature schemes. In this paper, minimal (meaning necessary and sufficient) conditions on the identification scheme to ensure security of the signature scheme in the random oracle model are determined, both in the usual and in the forward-secure cases. Specifically, it is shown that the signature scheme is secure (respectively, forward-secure) against chosen-message attacks in the random oracle model if and only if the underlying identification scheme is secure (respectively, forward-secure) against impersonation under passive (i.e., eavesdropping only) attacks, and has its commitments drawn at random from a large space. An extension is proven incorporating a random seed into the Fiat--Shamir transform so that the commitment space assumption may be removed. Index Terms--Fiat-Shamir transform, forward security, identification schemes, random oracle model, security proofs, signature schemes.

This paper presents a new deformable modeling strategy that is aimed at integrating shape and appearance in a unified space. If we think of traditional deformable models as "active contours" or "evolving curve fronts," the new deformable shape and appearance models that we propose are "deforming disks or volumes." Each model not only has boundary shape but also interior appearance. The model shape is implicitly embedded in a higher dimensional space of distance transforms and is thus represented by a distance map "image." This way, both the shape and the appearance of the model are defined in the pixel space. A common deformation scheme, that is, the Free-Form Deformations (FFDs), parameterizes warping deformations of the volumetric space in which the model is embedded, hence simultaneously deforming both model boundary and interior. When applied to segmentation, a Metamorphs model can be initialized by covering a seed region far from the object boundary, and then the model efficiently evolves and converges to an optimal solution. The model dynamics are derived in a unified variational framework that consists of edge-based and region-based energy terms, both of which are differentiable with respect to the common set of FFD parameters. As the model deforms, its interior appearance statistics are adaptively learned and, then, toward the next-step deformation, the model examines not only edge information but also its exterior region statistics to ensure that it only expands to new territory with consistent appearance statistics. The Metamorphs formulation also allows natural merging and competition of multiple models. We demonstrate the robustness of Metamorphs by using both natural and medical images that have high noise levels, intensity inhomogeneity, and complex texture. Index Terms--Segmentation, deformable models, shape, appearance, region, edge, boundary, implicit shape representation, free-form deformations, nonparametric intensity statistics, distance transform, level set.

Mixture of Gaussians (MoG) model is a useful tool in statistical learning. In many learning processes that are based on mixture models, computational requirements are very demanding due to the large number of components involved in the model. We propose a novel algorithm for learning a simplified representation of a Gaussian mixture that is based on the Unscented Transform, which was introduced for filtering nonlinear dynamical systems. The superiority of the proposed method is validated on both simulation experiments and categorization of a real image database. The proposed categorization methodology is based on modeling each image using a Gaussian mixture model. A category model is obtained by learning a simplified mixture model from all the images in the category. Index Terms--Mixture of Gaussians, reduced model, Unscented Transform, weighted likelihood, clustering.

Jacket matrices motivated by the center weight Hadamard matrices have played important roles in signal processing, communication, image compression, cryptography, etc. In this paper we propose a notation called block Jacket matrix which substitutes elements of the matrix into common matrices or even block matrices. Employing the well-known Pauli matrices which are very important in many subjects, block Jacket matrices with any size are investigated in detail, and some recursive relations for fast construction of the block Jacket matrices are obtained. Based on the general recursive relations, several special block Jacket matrices are constructed. To decompose high order block Jacket matrices, a fast decomposition algorithm for the factorable block Jacket matrices is suggested. After that some properties of the block Jacket matrices are investigated. Finally, several remarks are presented. These remarks are associated with comparisons between the Clifford algebra and the block Jacket matrices, generations of orthogonal and quasi-orthogonal sequences, and relations of the block Jacket matrices to the orthogonal transforms for signal processing. Since the Pauli matrices are actually infinitesimal generators of SU(2) group, the proposed construction and decomposition algorithms for the block Jacket matrices are available in the signal processing, communication, quantum signal processing and information theory. Index Terms--Block Jacket transform, fast matrices construction and decomposition, Pauli matrices, signal sequence transforms.

A novel method is presented that is based on the use of the Kontorovich--Lebedev integral transform and the semi-inversion technique, developed for building the efficient and accurate numerical solutions to the boundary-value problems of electromagnetic wave scattering by the 3D coaxial slotted cones. A generic structure under consideration consists of two semi-infinite coaxial circular perfectly electrical conducting and zero-thickness cones with periodic longitudinal slots excited by a radial dipole. The considered problem is reduced to an infinite set of linear algebraic equations of the Fredholm second kind that is truncated and solved numerically. A detail analysis of the accuracy and convergence of the method is presented. The basic electromagnetic characteristics such as the field behavior near the structure singularities, field patterns in the wave zone, and field polarization for various problem parameters are investigated for the cones excited by on-axis elementary dipoles. The slotted cones allow obtaining more directional patterns in wider band than the solid ones. Index Terms--Coaxial cones, Kontorovich-Lebedev integral transform, semi-inversion method, tip behavior.

Pulsed arrays are becoming popular in new ultrawideband applications to enhance the robustness of transmitted and received signals in complex environments and to identify the angle of arrival of multiple echoes. A global synthesis technique is here proposed to shape the array field in accordance to given angle-time constraints. The synthesis problem is cast as the inverse Radon transform of a desired array mask, applying the alternate projections method to include constraints over the input signals' waveform and to improve the synthesis robustness. The unknown array currents are generated as linear combinations of Hermite--Rodriguez functions in order to achieve a simple and realizable beamforming network. The effectiveness of the method is demonstrated by many examples. Index Terms--Alternate projections, array synthesis, pulsed arrays, Radon transform, space-time beamforming, ultrawideband (UWB) antennas.

With power electronics entering the saturation side of the technology's S-curve, we cannot expect too many new topologies or circuits. The future development should come mostly from application of new power semiconductor devices or from identification of new application fields. The only way to disrupt the contemporary incremental development consists in analyzing and branching out of the original theories that founded power electronics discipline. This paper develops the mathematical theory of a generalized vector transform able to smooth the progress of new research directions in power electronics by considering any three-phase set of nonsinusoidal waveforms instead of the conventional sinusoidal waveforms. Immediate applications are demonstrated. Index Terms--Motor drive, power converter, vector space.

Fundamental phasors are used to monitor and control power systems. The conventional method of calculating the phasors is using a Fourier transform, which introduces a delay of at least one fundamental cycle. This paper examines the feasibility of exploiting an alternative using a direct-quadrature (DQ) transformation to calculate the phasors by extracting the fundamental component from a three-phase voltage or current in the DQ reference frame, which may be distorted by unbalanced components and harmonics. The proposed method allows obtaining a clean fundamental component of three-phase quantity with a minor delay less than one third of a fundamental cycle. Index Terms--Blondel-Park transformation, fundamental component, harmonic trapping, negative sequence, phasor, positive sequence.

In this correspondence, we propose a vector-radix algorithm for the fast computation of a 2-D discrete Hartley transform (DHT). For data sequences whose length is a power of three, a radix-3 x 3 decimation in frequency algorithm is developed. It decomposes a length-N x N DHT into nine length-(N/3) x (N/3) DHTs. Comparison of the computational complexity with known algorithms shows that the proposed algorithm, in some cases, reduces significantly the number of arithmetic operations. Index Terms--2-D discrete Hartley transform (DHT), 2-D radix-3 x 3, vector-radix algorithm.

The learning capability of neural networks is equivalent to modeling physical events that occur in the real environment. Several early works have demonstrated that neural networks belonging to some classes are universal approximators of input-output deterministic functions. Recent works extend the ability of neural networks in approximating random functions using a class of networks named stochastic neural networks (SNN). In the language of system theory, the approximation of both deterministic and stochastic functions falls within the identification of nonlinear no-memory systems. However, all the results presented so far are restricted to the case of Gaussian stochastic processes (SPs) only, or to linear transformations that guarantee this property. This paper aims at investigating the ability of stochastic neural networks to approximate nonlinear input-output random transformations, thus widening the range of applicability of these networks to nonlinear systems with memory. In particular, this study shows that networks belonging to a class named non-Gaussian stochastic approximate identity neural networks (SAINNs) are capable of approximating the solutions of large classes of nonlinear random ordinary differential transformations. The effectiveness of this approach is demonstrated and discussed by some application examples. Index Terms--Approximation, Lee-Schetzen method, neural computation, neural networks, nonlinear systems, stochastic processes (SPs).

Granular damping results from a combination of energy dissipation mechanisms including the impact and the friction between the vibrating structure and granules and among the granules. Although simple in concept, granular damping is very complicated and its performance depends on a number of factors, such as vibration level, granular material properties, packing ratio, etc. In this study, free vibration experiments are conducted on a cantilevered beam incorporated with granular damping. A signal analysis approach based on the Hilbert transform (HT) is then employed to identify the nonlinear damping characteristics from the acquired responses, such as the dependency of the natural frequency and damping ratio on the vibration level. This HT based analysis can produce an effective temporal-frequency amplitude/energy analysis, which provides us with physical insights of the nonlinear transient response. A direct comparison between the granular damping and the impact damping (with single impactor to dissipate vibratory energy) is performed to highlight the difference between these two and the advantages of granular damping. Finally, the validity of the proposed approach is also examined by the successful prediction of vibration response using the extracted granular damping characteristics.

We explore predictive coding for the JPEG baseline sequential algorithm in this article. Our objective is to reduce inter-block redundancy of discrete cosine transform (DCT) blocks. We first present an implementation of image interpolation approach and develop a method for predicting ac coefficients of a block in terms of sum of pixels (or dc coefficients) of some surrounding patches. If we use 2-D quadratic polynomials for interpolation over 24 x 24 pixel area, our method derives the same equations, which JPEG developed for reducing blocking artifacts. Next, we show that nonpolynomial functions such as arctan perform better for ac prediction. We develop additional prediction equations considering different configurations of the interpolation area. Finally, we present performance results, which show that for images compressed at the default quality factor of 75, our equations reduce the ac energy of DCT blocks by about 22% and the final code bit size by about 5.5% over the JPEG sequential algorithm. At the quality factor of 90, the code size reduction is 10.8%. We also present an adaptive dc coding method by considering the prediction algorithm of JPEG-LS. It reduces the average JPEG dc residual by over 20% and the dc code bits by 7.75%. Index Terms--AC coefficient estimation, discrete cosine transform (DCT), DCT prediction coding, image interpolation.

Irreversible video coding like MPEG-2 may cause deterioration in picture quality depending on the properties of the source images and coding type. A monitoring technology to assess picture quality with fluctuations is needed for digital video services. We previously proposed a method to estimate the peak signal-to-noise-ratio (PSNR) of MPEG-2 coded video by using bit stream information. The method is categorized as a nonreference measurement that does not use source signals. It estimates the amount of distortion in each frame by analyzing the information in the decoded DCT coefficients. This paper describes a way to improve the accuracy of the PSNR estimation of our previous method, especially for the not coded blocks. The proposed method utilizes the temporal fluctuations of ac energy and estimates the PSNR of not-coded blocks from the inter-frame correlation of the decoded pictures. Experimental results show that the determination coefficient [R.sup.2] between estimated and actual PSNRs is above 0.95 for every type of picture frame. Index Terms--AC energy, discrete cosine transform (DCT) information, MPEG-2, nonreference method, not-coded blocks, peak signal-to-noise ratio (PSNR).

Edge is an important feature in video classification which finds applications in video representation and coding. In H.264/AVC, intra-prediction mode decision (a computationally intensive process) is based on the orientation of the edges in the macroblock. In this paper, we first investigate the difference properties derived from three coefficients in the non-normalized Haar transform (NHT) domain and present a fast and efficient method to classify block edge using these properties. The proposed method significantly reduces the number of computational operations in the edge models determination with no multiplications and less addition operations. The use of edge classification for fast intra-prediction mode decision in H.264/AVC video coding is then presented. The experimental results show the effectiveness of the proposed method. Index Terms--AVC, block edge, edge detection, H.264, intra-prediction, non-normalized Haar transform (NHT), video coding.

In this paper, we propose a fast full-pel variable block size motion estimation algorithm called fast walsh search in variable block size (FWS-VBS). FWS-VBS employs a new error measurement defined in Walsh-Hadamard domain, which is called partial sum-of-absolute difference, to identify likely mismatches. Mismatches are rejected by thresholding method and the thresholds are determined adaptively to cater for different activity levels in each block. Early termination techniques are employed to further reduce the number of candidates and modes to be searched of each block. Experimental results show that FWS-VBS performs equally well to the exhaustive full search algorithm and requires only about 10% of the computation time. Index Terms--H.264, motion estimation, Walsh-Hadamard transform (WHT).

We examine the problem of efficient distance-based similarity search over high-dimensional data. We show that a promising approach to this problem is to reduce dimensions and allow fast approximation. Conventional reduction approaches, however, entail a significant shortcoming: The approximation volume extends across the dataspace, which causes overestimation of retrieval sets and impairs performance. This paper focuses on a new criterion for dimensionality reduction methods: bounded approximation. We show that this requirement can be accomplished by a novel nonlinear transformation scheme that extracts two important parameters from the data. We devise two approximation formulations, namely, rectangular and spherical range search, each corresponding to a closed volume around the original search sphere. We discuss in detail how we can derive tight bounds for the parameters and prove further results, as well as highlight insights into the problems and our proposed solutions. To demonstrate the benefits of the new criterion, we study the effects of (un)boundedness on approximation performance, including selectivity, error toleration, and efficiency. Extensive experiments confirm the superiority of this technique over recent state-of-the- art schemes. Index Terms--Similarity search, spherical range search, dimensionality reduction, nonlinear transformation, bounded approximation.

A method is presented that can often reduce the number of scheduling parameters for gain-scheduled controller implementation by transformation of the system representation using parameter-dependent dimensional transformations. In some cases, the reduction in parameter dependence is so significant that a linear parameter-varying system can be transformed to an equivalent linear time invariant (LTI) system, and a simple example of this is given. A general analysis of the parameter-dependent dimensional transformation using a matrix-based approach is then presented. It is shown that, while some transformations simplify gain scheduling, others may increase the number of scheduling parameters. This work explores the mathematical conditions causing an increase or decrease in varying parameters resulting from a given transformation, thereby allowing one to seek transformations that most reduce the number of gain-scheduled parameters in the controller synthesis step. Keywords: gain scheduling, pi theorem, dimensionless parameters, dimensional transformation

The Hough transformation employing a normal line-to-point parameterization is widely applied in digital image processing for feature detection. In this paper, we demonstrate how this same transformation can be adapted to classify defect signatures on semiconductor wafers as an aid to visual defect metrology. Given a rectilinear grid of die centers on a wafer, we demonstrate an efficient and effective procedure for classifying defect clusters composed of lines at angles of 0[degrees], 45[degrees], 90[degrees], and 135[degrees] from the horizontal, as well as adjacent compositions of such lines. Included are defect clusters representing stripes, scratches at arbitrary angles, and center and edge defects. The principle advantage of the procedure over current industrial practice is that it can be fully automated to screen wafers for further engineering analysis. Index Terms--Defect metrology, Hough transformation, image processing, process control, spatial defect analysis and classification, wafer maps.

The angular radial transform (ART) is the region-based shape descriptor for MPEG-7. It is a compact descriptor that presents invariance to simple transformations, while presenting very low information redundancy. However, limited effort has been spent on the fast computation of ART, which is of the essence, especially in systems with sparse computational resources. In this paper, we present an efficient implementation of the descriptor, relating it to accumulation moments. The approximations used are shown not to affect the final 140-bit descriptor, and the architecture is capable of processing images up to one order of magnitude faster than the conventional method. Index Terms--Angular radial transform (ART), MPEG-7, realtime.

Modeling background and segmenting moving objects are significant techniques for video surveillance and other video processing applications. Most existing methods of modeling background and segmenting moving objects mainly operate in the spatial domain at pixel level. In this paper, we present three new algorithms (running average, median, mixture of Gaussians) modeling background directly from compressed video, and a two-stage segmentation approach based on the proposed background models. The proposed methods utilize discrete cosine transform (DCT) coefficients (including ac coefficients) at block level to represent background, and adapt the background by updating DCT coefficients. The proposed segmentation approach can extract foreground objects with pixel accuracy through a two-stage process. First a new background subtraction technique in the DCT domain is exploited to identify the block regions fully or partially occupied by foreground objects, and then pixels from these foreground blocks are further classified in the spatial domain. The experimental results show the proposed background modeling algorithms can achieve comparable accuracy to their counterparts in the spatial domain, and the associated segmentation scheme can visually generate good segmentation results with efficient computation. For instance, the computational cost of the proposed median and MoG algorithms are only 40.4% and 20.6% of their counterparts in the spatial domain for background construction. Index Terms--Background models, discrete cosine transform (DCT), moving object segmentation, video surveillance.

The present work focuses on the dynamic characterization of oil-free wire mesh dampers. The research was aimed at determining nonlinear stiffness and damping coefficients while varying the excitation amplitude, excitation frequency, and static eccentricity. Force coefficients were extracted using a forced response method and also a transient vibration method. Due to the nonlinearity of the dampers, controlled amplitude single frequency excitation tests were required for the forced excitation method, whereas the transient response was analyzed using a Hilbert transform procedure. The experimental results showed that eccentricity has minimal influence on force coefficients, whereas increasing excitation amplitude and frequency yields decreasing stiffness and damping trends. In addition to the parameter identification tests, a rotating test was performed demonstrating high-speed damping capability of the oil-free wire mesh dampers to 40,000 rpm, which was also simulated using a nonlinear rotordynamic response to imbalance analysis.

We present a novel approach to the problem of the indoor localization in wireless environments. The main contribution of this paper is fourfold: 1) we show that by projecting the measured signal into a decorrelated signal space, the positioning accuracy is improved, since the cross correlation between each AP is reduced, 2) we demonstrate that this novel approach achieves a more efficient information compaction and provides a better scheme to reduce online computation (the drawback of AP selection techniques is overcome, since we reduce the dimensionality by combing features, and each component in the decorrelated space is the linear combination of all APs; therefore, a more efficient mechanism is provided to utilize information of all APs while reducing the computational complexity), 3) experimental results show that the size of training samples can be greatly reduced in the decorrelated space; that is, fewer human efforts are required for developing the system, and 4) we carry out comparisons between RSS and three classical decorrelated spaces, including Discrete Cosine Transform (DCT), Principal Component Analysis (PCA), and Independent Component Analysis (ICA) in this paper. Two AP selection criteria proposed in the literature, MaxMean and InfoGain are also compared. Testing on a realistic WLAN environment, we find that PCA achieves the best performance on the location fingerprinting task. Index Terms--WLAN, location fingerprinting, decorrelated transformation, PCA.

The warped discrete cosine transform (WDCT) has been shown to improve the compression performance compared to standard DCT for image compression at high bit rates. In the proposed approach, the WDCT parameters are embedded into the transform coefficients for low bit rates in the form of a watermark to avoid the WDCT parameter side information overhead, improving the compression performance for low bit rates. Furthermore, optimal postprocess filtering, with filter coefficients being determined at the encoder and multiplexed into the bit stream, is proposed to improve the quality of the decoded image through postprocess filtering at the decoder. It is shown that a significant gain in quality can be achieved by the postprocess filtering. As optimal postprocess filtering is utilized, the need of a deblocking filter for low bit rates is finally evaluated to improve the statistical quality and visual appearance. Index Terms--Embedded warping parameter, optimal filtering, warped discrete cosine transform (WDCT).

This paper presents an efficient approach for detecting zero quantized discrete cosine transform (ZQDCT) coefficients using the sum of absolute transformed difference (SATD). Previously, all the ZQDCT prediction approaches employ the sum of absolute difference (SAD) available ahead of DCT and quantization (Q) for early detection. However, when the Hadamard transform is enabled for H.264/AVC encoding, only the SATD instead of SAD is available before DCT and Q, and all the prediction approaches can not be directly applied. To solve this problem, the Gaussian distribution is applied to study the integer 4 x 4 DCT coefficients in H.264/AVC and hence an adaptive scheme with multiple thresholds against SATD is derived to realize different types of DCT and Q implementations. In addition, another two SATD based sufficient conditions are proposed for early detecting zero quantized DC coefficients for the luma components encoded with the intra16 x 16 mode and the chroma components. The experimental results demonstrate that the proposed approach can greatly reduce the DCT and Q computations and obtain almost the same rate-distortion performance as the original encoder. Index Terms--Discrete cosine transform (DCT), Gaussian distribution, Hadamard transform, H.264/AVC, quantization (Q).

Transform-domain (TD) receivers expand the received signal over a basis set, and then operate on the basis coefficients. An analog computation of the basis coefficients efficiently parallelizes the signal for digital processing, relaxing the sampling requirements and enabling parallel digital processing at a much lower rate. Frequency-domain (FD) sampling, as a special case of TD sampling, has been proposed to parallelize the sampling process in broad-band communication receivers. The flexibility and scalability of TD receivers allow for the design of receivers that can cope with a large range of narrow-band and broad-band communications standards. A theoretical TD receiver design example is provided which is capable of processing GSM, Bluetooth, IEEE802.11g, Wimax, and UWB in just one configurable front-end. An example of spectrum sensing in cognitive radio is also provided. Index Terms--Cognitive radio (CR), frequency-domain (FD) receiver, multistandard receiver, software-defined radio, transform-domain (TD) receiver.

This paper presents a new deformable model using both population-based and patient-specific shape statistics to segment lung fields from serial chest radiographs. There are two novelties in the proposed deformable model. First, a modified scale invariant feature transform (SIFT) local descriptor, which is more distinctive than the general intensity and gradient features, is used to characterize the image features in the vicinity of each pixel. Second, the deformable contour is constrained by both population-based and patient-specific shape statistics, and it yields more robust and accurate segmentation of lung fields for serial chest radiographs. In particular, for segmenting the initial time-point images, the population-based shape statistics is used to constrain the deformable contour; as more subsequent images of the same patient are acquired, the patient-specific shape statistics online collected from the previous segmentation results gradually takes more roles. Thus, this patient-specific shape statistics is updated each time when a new segmentation result is obtained, and it is further used to refine the segmentation results of all the available timepoint images. Experimental results show that the proposed method is more robust and accurate than other active shape models in segmenting the lung fields from serial chest radiographs. Index Terms--Deformable model, scale invariant feature transform (SIFT) local descriptor, segmentation, serial chest radiographs, shape statistics.

This note considers the application of the unscented transform to optimal smoothing of nonlinear state-space models. In this note, a new Rauch-Tung-Striebel type form of the fixed-interval unscented Kalman smoother is derived. The new smoother differs from the previously proposed two-filter-formulation-based unscented Kalman smoother in the sense that it is not based on running two independent filters forward and backward in time. Instead, a separate backward smoothing pass is used, which recursively computes corrections to the forward filtering result. The smoother equations are derived as approximations to the formal Bayesian optimal smoothing equations. The performance of the new smoother is demonstrated with a simulation. Index Terms--Rauch-Tung-Striebel (RTS) smoother, unscented Kalman smoother (UKS), unscented transform.

This paper presents efficient VLSI architectures of the shape-adaptive discrete cosine transform (SA-DCT) and its inverse transform (SA-IDCT) for MPEG-4. Two of the challenges encountered during the exploitation of more efficient architectures for the SA-DCT and SA-IDCT are addressed. One challenge is to handle the architectural irregularity due to the shape-adaptive nature. The other one is to provide acceptable throughput using minimal hardware. In the algorithm-level optimization, this work exploits the numerical properties found in the transform matrices of various lengths, and derives a fine-grained zero-skipping scheme for the IDCT which can perform 22.6% more zero-skipping than the common vector-based coarse-grained zero-skipping scheme does. In the architecture-level design, the 1-D variable-length DCT/IDCT architectures designed on the basis of the numerical properties are proposed. An auto-aligned transpose memory that aligns the data of different lengths is also incorporated. In addition, a zero-index table is also included in the transpose memory to support the fine-grained zero-skipping in the SA-IDCT. The synthesized designs of the SA-DCT and SA-IDCT are implemented using UMC 0.18-[micro]m technology. The SA-DCT architecture has 26 635 gates, and its average cycle-throughput is 0.66 pixels/cycle, which is comparable to other proposed architectures. On the other hand, the SA-IDCT architecture has 29 960 gates, and its cycle-throughput is 6.42 pixels/cycle. While decoding for CIF@30FPS, the SA-IDCT is clocked at 0.7 MHz, and the power consumption is 0.14 mW. Both the throughput and power consumption of the proposed SA-IDCT architecture are an order better than those of the existing SA-IDCT architectures. Index Terms--Discrete cosine transform (DCT), MPEG-4, video coding, VLSI.

The existing methods to perform motion compensation (MC) in discrete cosine transform (DCT) treat each 8 x 8 block as a fundamental unit and, therefore, involve the high cost of reconstructing prediction frames, especially when the half-pixel motion vectors (MVs) are involved. The proposed method operates on a block of variable size 16[N.sub.y] x 16[N.sub.x], where [N.sub.x] and [N.sub.y] are the number of adjoining 16 x 16 macroblocks with common MV, along the horizontal and vertical directions, respectively. We demonstrate that a basic operation in reconstructing an 16[N.sub.y] x 16[N.sub.x] DCT-MC block, both with integer and half-pixel MV, can be represented as a multiplication by fixed matrices, and the computations can be greatly simplified through decomposition of DCT/ IDCT operations. Experimental results using cascaded DCT domain transcoder show substantial reduction in computations at quality close to pixel domain transcoding. Index Terms--Discrete cosine transform (DCT) domain processing, motion compensation, MPEG-2, video transcoding.

Nearly all block-based transform schemes for image and video coding developed so far choose the 2-D discrete cosine transform (DCT) of a square block shape. With almost no exception, this conventional DCT is implemented separately through two 1-D transforms, one along the vertical direction and another along the horizontal direction. In this paper, we develop a new block-based DCT framework in which the first transform may choose to follow a direction other than the vertical or horizontal one. The coefficients produced by all directional transforms in the first step are arranged appropriately so that the second transform can be applied to the coefficients that are best aligned with each other. Compared with the conventional DCT, the resulting directional DCT framework is able to provide a better coding performance for image blocks that contain directional edges--a popular scenario in many image signals. By choosing the best from all directional DCTs (including the conventional DCT as a special case) for each image block, we will demonstrate that the rate-distortion coding performance can be improved remarkably. Finally, a brief theoretical analysis is presented to justify why certain coding gain (over the conventional DCT) results from this directional framework. Index Terms--Directional discrete cosine transform, discrete cosine transform (DCT), image coding, video coding.

Implementing MPEG-2 to H.264 transcoding schemes in the pixel domain introduces a high degree of computational complexity. In the transform domain, this transcoding is more computationally efficient, and several methods have been developed to address that approach. However, incompatibilities between the two standards, such as the mismatches between the MPEG-2 and H.264 motion compensation processes, cause several distortions that may affect the overall picture quality. In this study, we address the main distortions that result from requantization errors: luminance half-pixel and chrominance quarter/three-quarter interpolation errors. Then, we propose algorithms that compensate for these errors. The traditional requantization error compensation algorithm for DCT coefficients is updated so that it can be applied to the H.264 integer transform coefficients. Equations that compensate for the luminance half-pixel and chrominance quarter/three-quarter pixel interpolation errors are derived. To remove the interpolation errors, the previous H.264 frame is needed. Thus, the compensation scheme includes a closed-loop H.264 motion compensation process, which is implemented in the pixel domain. To evaluate the performance of the proposed compensation algorithms in terms of picture quality, our scheme is compared with two different cascaded pixel-domain transcoding structures. The first structure reuses the MPEG-2 motion vectors, and the other implements [+ or -]2 pixels motion vector refinement, but each one has an H.264 deblocking filter. The experimental results show that the proposed compensation algorithms achieve 5-dB quality improvement over the open-loop transform-domain-based transcoding and almost the same picture quality (0.3-0.6 dB) as the cascaded structures. An additional advantage is the reduction in computational complexity that ranges from 13% to 69% compared with the two cascaded methods. Index Terms--H.264/AVC, interpolation, MPEG-2, requantization, transcoding.

A novel statistic for local wave amplitude of the 500-hPa geopotential height field is introduced. The statistic uses a Hilbert transform to define a longitudinal wave envelope and dynamical latitude weighting to define the latitudes of interest. Here it is used to detect the existence, or otherwise, of multimodality in its distribution function. The empirical distribution function for the 1960-2000 period is close to a Weibull distribution with shape parameters between 2 and 3. There is substantial interdecadal variability but no apparent local multimodality or bimodality. The zonally averaged wave amplitude, akin to the more usual wave amplitude index, is close to being normally distributed. This is consistent with the central limit theorem, which applies to the construction of the wave amplitude index. For the period 1960-70 it is found that there is apparent bimodality in this index. However, the different amplitudes are realized at different longitudes, so there is no bimodality at any single longitude. As a corollary, it is found that many commonly used statistics to detect multimodality in atmospheric fields potentially satisfy the assumptions underlying the central limit theorem and therefore can only show approximately normal distributions. The author concludes that these techniques may therefore be suboptimal to detect any multimodality.

Near-field antenna measurements combined with a near-field far-field transformation are an established antenna characterization technique. The approach avoids far-field measurements and offers a wide area of post-processing possibilities including radiation pattern determination and diagnostic methods. In this paper, a near-field far-field transformation algorithm employing plane wave expansion is presented and applied to the case of spherical near-field measurements. Compared to existing algorithms, this approach exploits the benefits of diagonalized translation operators, known from fast multipole methods. Due to the plane wave based field representation, a probe correction, using directly the probe's far-field pattern can easily be integrated into the transformation. Hence, it is possible to perform a full probe correction for arbitrary field probes with almost no additional effort. In contrast to other plane wave techniques, like holographic projections, which are suitable for highly directive antennas, the presented approach is applicable for arbitrary radiating structures. Major advantages are low computational effort with respect to the coupling matrix elements owing to the use of diagonalized translation operators and the efficient correction of arbitrary field probes. Also, irregular measurement grids can be handled with little additional effort. Index Terms--Diagonal translation operators, fast multipole method (FMM), near-field far-field transformation, near-field measurements, plane wave expansion.

This paper introduces a simple algorithm for tomographic reconstruction based on the use of a complexity regularization term. The regularization is formulated in the discrete cosine transform (DCT) domain by promoting a low-noise reconstruction having a high sparsity in the frequency domain. The resulting algorithm simply alternates between a maximum-likelihood (ML) expectation-maximization (EM) update and a decreasing sparsity constraint in the DCT domain. Applications to SPECT reconstruction and comparisons with a classical estimator using the best available regularization terms are given in order to illustrate the potential of our reconstruction technique. Index Terms--Discrete cosine transform (DCT), expectation-maximization (EM), reconstruction, SPECT tomography.

Accurate QRS detection is an important first step for the analysis of heart rate variability. Algorithms based on the differentiated ECG are computationally efficient and hence ideal for real-time analysis of large datasets. Here, we analyze traditional first-derivative based squaring function (Hamilton-Tompkins) and Hilbert transform-based methods for QRS detection and their modifications with improved detection thresholds. On a standard ECG dataset, the Hamilton-Tompkins algorithm had the highest detection accuracy (99.68% sensitivity, 99.63% positive predictivity) but also the largest time error. The modified Hamilton-Tompkins algorithm as well as the Hilbert transform-based algorithms had comparable, though slightly lower, accuracy; yet these automated algorithms present an advantage for real-time applications by avoiding human intervention in threshold determination. The high accuracy of the Hilbert transform-based method compared to detection with the second derivative of the ECG is ascribable to its inherently uniform magnitude spectrum. For all algorithms, detection errors occurred mainly in beats with decreased signal slope, such as wide arrhythmic beats or attenuated beats. For best performance, a combination of the squaring function and Hilbert transform-based algorithms can be applied such that differences in detection will point to abnormalities in the signal that can be further analyzed. Index Terms--Electrocardiography, heart rate variability, Hilbert transform, peak detection.