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Carolina Abulafia,1,2 María F Vidal,3 Natividad Olivar,4 Andrea Odzak,5 Ignacio Brusco,4– 6 Salvador M Guinjoan,7 Daniel P Cardinali,8 Daniel E Vigo1,9 1Laboratory of Chronophysiology, Institute for Biomedical Research (BIOMED), Pontifical Catholic University of Argentina (UCA) and CONICET, Buenos Aires, Argentina; 2Facultad de Psicología, Universidad de Buenos Aires, Buenos Aires, Argentina; 3Servicio de Psiquiatría, Departamento de Neurología, Fleni, Buenos Aires, Argentina; 4Hospital de Clínicas “José de San Martín”, Universidad de Buenos Aires, Buenos Aires, Argentina; 5Servicio de Clínica Médica, Hospital Argerich, Buenos Aires, Argentina; 6CONICET, Buenos Aires, Argentina; 7Laureate Institute for Brain Research, Tulsa, OK, USA; 8Facultad de Ciencias Médicas, Universidad Católica Argentina, Buenos Aires, Argentina; 9Faculty of Psychology and Educational Sciences, Katholieke Universiteit Leuven, Leuven, BelgiumCorrespondence: Daniel E Vigo, Instituto de Investigaciones Biomédicas, Pontificia Universidad Católica Argentina, Alicia Moreau de Justo 1500, 4° piso, Buenos Aires, C1107AAZ, Argentina, Tel +54 0810-2200-822 ext 1152, Email dvigo@conicet.gov.ar; danielvigo@uca.edu.arPurpose: The objective of the present study was to assess sleep-wake differences of autonomic activity in patients with mild cognitive impairment (MCI) compared to control subjects. As a post-hoc objective, we sought to evaluate the mediating effect of melatonin on this association.Patients and Methods: A total of 22 MCI patients (13 under melatonin treatment) and 12 control subjects were included in this study. Sleep-wake periods were identified by actigraphy and 24hr-heart rate variability measures were obtained to study sleep-wake autonomic activity.Results: MCI patients did not show any significant differences in sleep-wake autonomic activity when compared to control subjects. Post-hoc analyses revealed that MCI patients not taking melatonin displayed lower parasympathetic sleep-wake amplitude than controls not taking melatonin (RMSSD − 7 ± 1 vs 4 ± 4, p = 0.004). In addition, we observed that melatonin treatment was associated with greater parasympathetic activity during sleep (VLF 15.5 ± 0.1 vs 15.1 ± 0.1, p = 0.010) and in sleep-wake differences in MCI patients (VLF 0.5 ± 0.1 vs 0.2 ± 0.0, p = 0.004).Conclusion: These preliminary findings hint at a possible sleep-related parasympathetic vulnerability in patients at prodromal stages of dementia as well as a potential protective effect of exogenous melatonin in this population.Keywords: heart rate variability, actigraphy, circadian rhythms, wavelets

The control of underactuated mechanical systems (UMS) remains an attracting field where researchers can develop their control algorithms. To this date, various linear and nonlinear control techniques using classical and intelligent methods have been published in literature. In this work, an adaptive controller using sliding mode control (SMC) and wavelets network (WN) is proposed for a class of second-order UMS with two degrees of freedom (DOF). This adaptive control strategy takes advantage of both sliding mode control and wavelet properties. In the main result, we consider the case of un-modeled dynamics of the above-mentioned UMS, and we introduce a wavelets network to design an adaptive controller based on the SMC. The update algorithms are directly extracted by using the gradient descent method and conditions are then settled to achieve the required convergence performance. The efficacy of the proposed adaptive approach is demonstrated through an application to the pendubot.

The Brazilian energetic matrix is predominantly based on hydroelectric plants and its planning is very sensitive to climate variability in different time scales. Natural Affluent Energy (NAE) is an established planning tool to project different scenarios of possible energy production, especially in an integrated system. This work aims to fill a gap between short-term (seasonal/ interannual) and long-term (climate change) planning scales by realizing NAE medium-term projections for the Brazilian National Interconnected System basins. The historical NAE series provided by the National System Operator was used for the years 1931 to 2014. The series was divided into two periods: from 1931 to 2003 for verification, and from 2004 to 2014 for calibration. The Wavelets Auto-Regressive (WAR) model was applied from low- and medium-frequency bands. The band signal was analyzed and the NAE was projected for the years 2014 to 2024. A relationship of the NAE variability with the Pacific Decadal Oscillation (PDO) climate index and the Atlantic Multidecadal Oscillation (AMO) was verified.

The perfect achievements have been made for Lp(1 ≤ p < +∞) risk estimation, when a density function has compact support. However, there does not exist L1 risk estimation for uncompactly supported densities in general. Motivated by the work of Juditsky & Lambert-Lacroix (A. Juditsky and S. Lambert-Lacroix, On minimax density estimation on RR, Bernoulli, 10(2004), 187-220) and Goldenshluger & Lepski (A. Goldenshluger and O. Lepski, On adaptive minimax density estimation on Rd, Probab. Theory Relat. Fields., 159(2014), 479-543), we provide an adaptive estimate for a family of density functions not necessarily having compact supports in this paper. [ABSTRACT FROM AUTHOR]

Using a wavelet basis, Chesneau and Shirazi study the estimation of one-dimensional regression functions in a biased non parametric model overL2risk (see Chesneau, C and Shirazi, E. Non parametric wavelet regression based on biased data, Communication in Statistics – Theory and Methods, 43: 2642–2658, 2014). This article considersd-dimensional regression function estimation overLp (1 ⩽p< ∞) risk. It turns out that our results reduce to the corresponding theorems of Chesneau and Shirazi’s theorems, whend= 1 andp= 2. [ABSTRACT FROM AUTHOR]

We consider the GARCH-type modelS= σ2Zwhere σ2andZare independent random variables. We assume that the densityof σ2is unknown with support [0, 1] but differentiable whereas the densityfSofSis bounded. We will also assume that the probability density function of the random variableZis known and has the same distribution as the ν-fold product of independent random variables uniformly distributed on the interval [0, 1]. We want to estimate the derivative of the density of σ2fromnindependent and identically distributed observations ofS. We will construct adaptive and non adaptive wavelet estimators for the derivative of the density and obtain sharp upper bounds on their mean integrated squared errors. [ABSTRACT FROM AUTHOR]

The materials of the structures in use are always subjected to degradation in its characteristics over the period of time. The reduction in stiffness is always associated with such degradation. The analysis of vibration response of such materials with appropriate signal processing techniques has always led to the solution of damage identification exercises. The aim of the paper is to evaluate the performance of mode shape based technique along with wavelet transform through simulated model of structure- a cantilever, in damage identification exercise. A small transverse cut of wire thickness is introduced in cantilever beam. Depth of wire cut is varied to intensify the damage at various locations. Number of flexural modes are extracted from finite element modal analysis. Spatial continuous wavelet analysis is carried on number of modes. Effectiveness of different biorthogonal and reverse biorthogonal mother wavelets is studied to investigate the efficacy of the method. The proper selection of analysing mother wavelet influences the desired information extraction and its amplification process. The most suitable mother wavelet is recommended considering the nature of variation of wavelet coefficients. [ABSTRACT FROM AUTHOR]

Recently, wavelet has been used for copula density estimation. A known characteristic of wavelet functions is that they cannot be symmetric, orthogonal, and compact support at the same time while multiwavelets overcome this disadvantage. This article highlights the usefulness of the multiwavelet in order to approximate copula density functions. Possessing three appropriate properties at the same time, high smoothness, and high approximation order properties, multiwavelet can be more precise in copula density approximation. We make this approximation method more accurate by using multiresolution analysis. Finally, we apply our proposed method to approximate the copula density in actuarial data. [ABSTRACT FROM AUTHOR]

We investigate the ability of artificial neural networks to reconstruct discrete chaotic maps with singular points. We use as a simple test model the Cusp map. We compare the traditional Multilayer Perceptron, the Chebyshev Neural Network and the Wavelet Neural Network. The numerical scheme for the accurate determination of a singular point is also developed. We show that combining a neural network with the numerical algorithm for the determination of the singular point we are able to accurately approximate discrete chaotic maps with singularities.

The pupil shows a fast dynamical adaptation to external light changes, in order to potentiate visual perception. It contracts in high luminosity environments, so as to limit the quantity of photons that reach the retina (miosis) and dilates in environments with little luminosity, thus increasing the number of photons in the retina (mydriasis). Hence, the pupil acts as a normalizer of the quantity of light that enters the optical system. These pupillary movements are controlled by the action of smooth muscles, which are associated with the sympathetic (SNS) and parasympathetic autonomous nervous systems (PsNS). Therefore, the study of the pupillary dynamics can lead to inferences on the functioning of those two antagonist systems and their involvement in pupillary control. In addition, our study may prove clinically helpful in determining a patient's level of consciousness, as well as identifying certain diseases, such as sleep disorders, photophobia, schizophrenia, Adie syndrome, Alzheimer's and Parkinson's disease. With a clear goal in its clinical applications, we focus our research in the identification of the frequency intervals pertaining to the action of the autonomous nervous system, as well as their individual sympathetic and parasympathetic roles. We analyze high-resolution, non-invasive pupillometric signals, both in a basal condition and as a response to visual flashes or to the application of a cold stimulus. We use Singular Spectrum Analysis (SSA) to identify the frequencies of interest related to the actions of the SNS and PsNS. In addition, and as a complementary means of frequency analysis, we also use the more classical wavelets analysis. We find out that SSA is an ideal tool for the identification of the desired frequencies in stake. The agreement between the outcomes of both analyses supports our conclusions regarding the autonomous nervous system. [ABSTRACT FROM AUTHOR]

The estimation of the regression function in the biased nonparametric regression model is investigated. We propose and develop a new wavelet-based methodology for this problem. In particular, an adaptive hard thresholding wavelet estimator is constructed. Under mild assumptions on the model, we prove that it enjoys powerful mean integrated squared error properties over Besov balls. [ABSTRACT FROM AUTHOR]

This paper presents a novel multiscale shape representation and segmentation algorithm based on the spherical wavelet transform. This work is motivated by the need to compactly and accurately encode variations at multiple scales in the shape representation in order to drive the segmentation and shape analysis of deep brain structures, such as the caudate nucleus or the hippocampus. Our proposed shape representation can be optimized to compactly encode shape variations in a population at the needed scale and spatial locations, enabling the construction of more descriptive, nonglobal, nonuniform shape probability priors to be included in the segmentation and shape analysis framework. In particular, this representation addresses the shortcomings of techniques that learn a global shape prior at a single scale of analysis and cannot represent fine, local variations in a population of shapes in the presence of a limited dataset. Specifically, our technique defines a multiscale parametric model of surfaces belonging to the same population using a compact set of spherical wavelets targeted to that population. We further refine the shape representation by separating into groups wavelet coefficients that describe independent global and/or local biological variations in the population, using spectral graph partitioning. We then learn a prior probability distribution induced over each group to explicitly encode these variations at different scales and spatial locations. Based on this representation, we derive a parametric active surface evolution using the multiscale prior coefficients as parameters for our optimization procedure to naturally include the prior for segmentation. Additionally, the optimization method can be applied in a coarse-to-fine manner. We apply our algorithm to two different brain structures, the caudate nucleus and the hippocampus, of interest in the study of schizophrenia. We show: 1) a reconstruction task of a test set to validate the expressiveness of our multiscale prior and 2) a segmentation task. In the reconstruction task, our results show that for a given training set size, our algorithm significantly improves the approximation of shapes in a testing set over the Point Distribution Model, which tends to oversmooth data. In the segmentation task, our validation shows our algorithm is computationally efficient and outperforms the Active Shape Model algorithm, by capturing finer shape details. [ABSTRACT FROM AUTHOR]

We propose a two-dimensional generalization to the 1W-band case of the dual-tree decomposition structure (initially proposed by Kingsbury and further investigated by Selesnick) based on a Hilbert pair of wavelets. We particularly address: 1) the construction of the dual basis and 2) the resulting directional analysis. We also revisit the necessary pre-processing stage in the LW-band case. While several reconstructions are possible because of the redundancy of the representation, we propose a new optimal signal reconstruction technique, which minimizes potential estimation errors. The effectiveness of the proposed M-band decomposition is demonstrated via denoising comparisons on several image types (natural, texture, seismics), with various 1W-band wavelets and thresholding strategies. Significant improvements in terms of both overall noise reduction and direction preservation are observed. [ABSTRACT FROM AUTHOR]

We develop three novel wavelet domain denoising methods for subband-adaptive, spatially-adaptive and multivalued image denoising. The core of our approach is the estimation of the probability that a given coefficient contains a significant noise-free component, which we call "signal of interest." In this respect, we analyze cases where the probability of signal presence is 1) fixed per subband, 2) conditioned on a local spatial context, and 3) conditioned on information from multiple image bands. All the probabilities are estimated assuming a generalized Laplacian prior for noise-free subband data and additive white Gaussian noise. The results demonstrate that the new subband-adaptive shrinkage function outperforms Bayesian thresholding approaches in terms of mean-squared error. The spatially adaptive version of the proposed method yields better results than the existing spatially adaptive ones of similar and higher complexity. The performance on color and on multispectral images is superior with respect to recent multiband wavelet thresholding. [ABSTRACT FROM AUTHOR]

Wave let bases are mainly used in the methods of moments (MoM) to render the system matrix sparse; clipping entries below a given threshold is an essential operation to obtain the desired sparse matrix. In this paper, we present a novel a priori way to estimate the clipping threshold that can be used if one wants an error on the solution below a desired accuracy. The procedure has a very low computational complexity, typically of O(N). [ABSTRACT FROM AUTHOR]

The evaluation of uncertainty is a task usually neglected by people performing wavelet-based measurements. In this paper, the wavelet analysis aimed at gauging the synthesis of transient disturbances is considered, and a general expression of the uncertainty affecting this synthesis is provided. Simulations have been performed to validate the above expression, which holds no matter which mother wavelet is used and the kind of disturbance. Results of experiments on actual signals are also reported and discussed. [ABSTRACT FROM AUTHOR]

This paper presents the construction, use, and properties of a multiresolution (wavelet) basis for the method of moments (MoM) analysis of metal antennas, scatterers, and microwave circuits discretized by triangular meshes. Several application examples show fast convergence of iterative solvers and accurate solutions with highly sparse MoM matrices. The proposed basis is organized in hierarchical levels, and keeps the different scales of the problem directly into the basis functions representation; the current is divided into a solenoidal and a quasi-irrotational part, which allows mapping these two vector parts onto fully scalar quantities, where the wavelets are defined. As a byproduct, this paper also presents a way to construct hierarchical sets of Rao-Wilton-Glisson (RWG) functions on a family of meshes obtained by subsequent refinement, i.e., with the RWG of coarser meshes expressed as linear combinations of those of finer meshes. [ABSTRACT FROM AUTHOR]

A novel controller based on multiresolution decomposition using wavelets is presented. The controller is similar to a proportional-integral-derivative (PlD) controller in principle and application. The output from a motion control system represents the cumulative effect of uncertainties such as measurement noise, frictional variation, and external torque disturbances, which manifest at different scales. The wavelet is used to decompose the error signal into signals at different scales. These signals are then used to compensate for the uncertainties in the plant. This approach provides greater expanse over the degree of control applied to the system. Through hardware and simulation results on motion control systems, this controller is shown to perform better than a PID in terms of its ability to provide smooth control signal, better disturbance, and noise rejection. [ABSTRACT FROM AUTHOR]

In recent years, new remote sensing techniques have been developed to measure two-dimensional (2-D) sea surface elevation fields. The availability of these data has led to the necessity to extend the classical analysis methods for one-dimensional (1-D) buoy lime series to two dimensions. This paper is concerned with the derivation of group parameters from 2-D sea surface elevation fields using a wavelet-based technique. Wave grouping is known to be an important factor in ship and offshore safety, as it plays a role in dangerous resonance phenomenons and the generation of extreme waves. Synthetic aperture radar (SAR) data are used for the analysis. The wavelet technique is introduced using synthetic ocean surfaces and simulated SAR data. It is shown that the group structure of the ocean wave field can be recovered from the SAR image if the nonlinear imaging effects are moderate. The method is applied to a global dataset of European Remote Sensing satellite (ERS-2) wave mode data. Different group parameters including the area covered by the largest group and the number of groups in a given area are calculated for over 33000 SAR images. Global maps of the parameters are presented. For comparison, classical 1-D grouping parameters are calculated from colocated wave model data showing good overall agreement with the wavelet- derived parameters. ERS-2 image mode data are used to study wave fields in coastal areas. Waves approaching the island of Sylt in the North Sea are investigated, showing the potential of the wavelet technique to analyze the spatial wave dynamics associated with the bottom topography. Observations concerning changes of waves length and group parameters are compared to linear wave theory. [ABSTRACT FROM AUTHOR]

Slow motion replay is a special effect used in the video entertainment field. It consists in a presentation of a video scene at a rate display lower than the original. Already consolidated as a commercial feature of analog video players, today slow motion is likely to be extended to the digital environment. Purpose of this paper is to present a technique combining fractals (I.F.S.) and wavelets to obtain a subjectively pleasant zoom and slow motion of digital video sequences. Active scene detection and post processing techniques are used to reduce computational cost and improve visual quality respectively. This study shows that the proposed technique produces better results than the state of the art techniques based either on data replication or classical interpolation. [ABSTRACT FROM AUTHOR]

With the aim of designing signal processing tools that act locally in space upon specific features of a signal, we compare two algorithms to remove or isolate individual anomalies in potential field profiles. The first method, based on multiscale edge analysis, leaves other features in the signal relatively untouched. A second method, based on iterative lateral continuation and subtraction of anomalies, accounts for the influence of adjacent anomalies on one another. This allows a potential field profile to be transformed into a number of single anomaly signals. Each single anomaly can then be individually processed, which considerably simplifies applications such as inversion and signal processing. [ABSTRACT FROM AUTHOR]

The Coifman wavelets are employed to perform Galerkin's procedure in the method of moments (MoM). The Coiflets are continuous, smooth, overlapping, yet orthogonal, which permit significant reduction of the sampling rate and dramatic compression of the matrix size with respect to the pulse based MoM. In addition, the wavelet based impedance matrix is sparse. More importantly, the vanishing moments of the Coiflets of order L = 4 provide us with high precision 0(h5) one-point quadrature, which knocks down the computational effort in filling the matrix entries from O(n²) to O(n). Our approach is different from the conventional wavelet technique, which employs wavelets to sparsify an existing impedance matrix under similarity transformation with computational cost in O(n²). Excellent agreement between this Coifman wavelet method and the previous publications is observed. [ABSTRACT FROM AUTHOR]

A new algorithm is introduced for motor current signature analysis of induction machines operating during transients. The algorithm is able to extract the amplitude, phase and frequency of a single sinusoid embedded in a nonstationary wave- form. The algorithm is applied to the detection of broken rotor bars in induction machines during startup transients. The fundamental component of current, which varies in amplitude, phase, and frequency, is extracted using the algorithm. The residual current is then analyzed using wavelets for the detection of broken rotor bars. This method of condition monitoring does not require parameters such as speed or number of rotor bars, is not load dependent and can be applied to motors that operate continuously in the transient mode, e.g., wind generators or motor-operated valves. [ABSTRACT FROM AUTHOR]

Inadequate &fracIO; performance remains a major challenge in using high-end computing systems effectively. To address this problem, the paper presents TsModeler, an automatic time series modeling and prediction framework for adaptive &fracIO; prefetching that uses ARIMA time series models to predict the temporal patterns of &fracIO; requests. These online pattern analysis techniques and cutoff indicators for autocorrelation patterns enable multistep online predictions suitable for multiblock prefetching. This work also combines time series predictions with spatial Markov model predictions to determine when, what, and how many blocks to prefetch. Experimental results show reductions in execution time compared to the standard Linux file system across various hardware configurations. [ABSTRACT FROM AUTHOR]

A new approach to image retrieval is presented in the domain of museum and gallery image collections. Specialist algorithms, developed to address specific retrieval tasks, are combined with more conventional content and metadata retrieval approaches, and implemented within a distributed architecture to provide cross-collection searching and navigation in a seamless way. External systems can access the different collections using interoperability protocols and open standards, which were extended to accommodate content based as well as text based retrieval paradigms. After a brief overview of the complete system, we describe the novel design and evaluation of some of the specialist image analysis algorithms including a method for image retrieval based on sub-image queries, retrievals based on very low quality images and retrieval using canvas crack patterns. We show how effective retrieval results can be achieved by real end-users consisting of major museums and galleries, accessing the distributed but integrated digital collections. [ABSTRACT FROM AUTHOR]

The objective assessment of image quality is essential for design of imaging systems. Barrett and Gifford [1] introduced the Fourier crosstalk matrix and use it to analyze cone-beam tomography. Fourier crosstalk matrix is a powerful technique for discrete imaging systems that are close to shift invariant because it is diagonal for continuous linear shift-invariant imaging systems. However, for a system that is intrinsically shift-variant, Fourier techniques are not particularly effective. Since Fourier bases have no spatial localization property, the shift-variance of the imaging system cannot be shown by the response of individual Fourier bases; rather, it is shown in the correlation between the Fourier coefficients. This makes the analysis and optimization quite difficult. In this paper, we introduce a wavelet crosstalk matrix based on wavelet series expansions. The wavelet crosstalk matrix allows simultaneous study of the imaging system in both the frequency and spatial domains. Hence, it is well suited for shift-variant systems. We compared the wavelet crosstalk matrix with the Fourier crosstalk matrix for several simulated imaging systems, namely the interior and exterior tomography problems, a dual-planar positron emission tomograph, and a rectangular geometry positron emission tomograph. The results demonstrate the advantages of the wavelet crosstalk matrix in analyzing shift-variant imaging systems. [ABSTRACT FROM AUTHOR]

We propose an efficient, hybrid Fourier-wavelet regularized deconvolution (ForWaRD) algorithm that performs noise regularization via scalar shrinkage in both the Fourier and wavelet domains. The Fourier shrinkage exploits the Fourier transform's economical representation of the colored noise inherent in deconvolution, whereas the wavelet shrinkage exploits the wavelet domain's economical representation of piecewise smooth signals and images. We derive the optimal balance between the amount of Fourier and wavelet regularization by optimizing an approximate mean-squared error (MSE) metric and find that signals with more economical wavelet representations require less Fourier shrinkage. ForWaRD is applicable to all ill-conditioned deconvolution problems, unlike the purely wavelet-based wavelet-vaguelette deconvolution (WVD); moreover, its estimate features minimal ringing, unlike the purely Fourier-based Wiener deconvolution. Even in problems for which the WVD was designed, we prove that ForWaRD's MSE decays with the optimal WVD rate as the number of samples increases. Further, we demonstrate that over a wide range of practical sample-lengths, ForWaRD improves on WVD's performance. [ABSTRACT FROM AUTHOR]

A novel embedded wavelet coding scheme is proposed for the transmission of images over unreliable channels. The proposed scheme is based on the partitioning of information into a number of layers which can be decoded independently provided that some important and highly protected information is initially errorlessly transmitted to the decoder. Forward error correction is used in conjunction with the error-resilient source coder for the protection of the compressed stream. Unlike many other robust coding schemes presented to date, the proposed scheme is able to decode portions of the bit stream even after the occurrence of uncorrectable errors. This coding strategy is very suitable for application with block coding schemes such as defined by the JPEG2000 standard. The proposed scheme is compared with other robust image coders and is shown to be very suitable for transmission of images over memoryless channels. [ABSTRACT FROM AUTHOR]

We present a supervised classification model based on a variational approach. This model is specifically devoted to textured images. We want to get a partition of an image, composed of texture regions separated by regular interfaces. Each kind of texture defines a class. We use a wavelet packet transform to analyze the textures, characterized by their energy distribution in each sub-band. In order to have an image segmentation according to the classes, we model the regions and their interfaces by level set functions. We define a functional on these level sets whose minimizers define the optimal classification according to textures. A system of coupled PDE's is deduced from the functional. By solving this system, each region evolves according to its wavelet coefficients and interacts with the neighbor regions in order to obtain a partition with regular contours. Experiments are shown on synthetic and real images. [ABSTRACT FROM AUTHOR]

Images registration is the process by which we determine a transformation that provides the most accurate match between two images. The search for the matching transformation can be automated with the use of a suitable metric, but it can be very time-consuming and tedious. In this paper, we introduce a registration algorithm that combines a simple yet powerful search strategy based on a stochastic gradient with two similarity measures, correlation and mutual information, together with a wavelet-based multiresolution pyramid. We limit our study to pairs of images, which are misaligned by rotation and/or translation and present two main results. First, we demonstrate that in our application mutual information may be better suited for sub-pixel registration as it produces consistently sharper optimum peaks than correlation . Then, we show that the stochastic gradient search combined with either measure produces accurate results when applied to synthetic, as well as multitemporal or multisensor collections of satellite data. Mutual information is generally found to optimize with one-third the number of iterations required by correlation. Results also show that a multiresolution implementation of the algorithm yields significant improvements in terms of both speed and robustness over a single-resolution implementation. [ABSTRACT FROM AUTHOR]

Recently, we have developed a new framework to study error-control coding using finite-fleld wavelets and filter-banks (FBs). This framework reveals a rich set of signal processing techniques that can be exploited to investigate new error correcting codes and to simplify encoding and decoding techniques for some existing ones. This paper introduces the theory of wavelet decompositions of signals in vector spaces defined over Galois fields. To avoid the limitations of the number theoretic Fourier transform, our wavelet transform relies on a basis decomposition in the time rather than the frequency domain. First, by employing a symmetric, nondegenerate canonical bilinear form, we obtain a necessary and sufficient condition that the basis functions defined over finite fields must satisfy in order to construct an orthogonal wavelet transform. Then, we present a design methodology to generate the mother wavelet and scaling function over finite fields by relating the wavelet transform to two-channel paraunitary (PU) FBs. Finally, we describe the application of this transform to the construction of error correcting codes. In particular, we give examples of double circulant codes that are generated by wavelets. [ABSTRACT FROM AUTHOR]

Most model selection procedure use a fixed penalty penalizing an increase in the size of a model. These nonadaptive selection procedure perform well only in one type of situation. For instance, Bayesian information criterion (BIC) with a large penalty performs well for "small" models and poorly for "large" models, and Akaike's information criterion (AIC) does just the opposite. This article proposes an adaptive model selection procedure that uses a data-adaptive complexity penalty based on a concept of generalized degree of freedom. The proposed procedure, combining the benefit of a class of nonadaptive procedure, approximates the best performance of this class of procedures across a variety of different situations. This class includes many well-known procedures, such as AIC, BIC, Mallows's Cp, and risk inflation criterion (RIC). The proposed procedure is applied to wavelet thresholding in nonparametric regression and variables selection in least squares regression. Simulation results and an asymptotic analysis support the effectiveness of the proposed procedure. [ABSTRACT FROM AUTHOR]

In this paper, we introduce nonlinear regularized wavelet estimators for estimating nonparametric regression functions when sampling points are not uniformly spaced. The approach can apply readily to many other statistical contexts. Various new penalty functions are proposed. The hard-thresholding and soft-thresholding estimators of Donoho and Johnstone are specific members of nonlinear regularized wavelet estimators. They correspond to the lower and upper envelopes of a class of the penalized least squares estimators. Necessary conditions for penalty functions are given for regularized estimators to possess thresholding properties. Oracle inequalities and universal thresholding parameters are obtained for a large class of penalty functions. The sampling properties of nonlinear regularized wavelet estimators are established and are shown to be adaptively minimax. To efficiently solve penalized least squares problems, nonlinear regularized Sobolev interpolators (NRSI) are proposed as initial estimators, which are shown to have good sampling properties. The NRSI is further ameliorated by regularized one-step estimators, which are the one-step estimators of the penalized least squares problems using the NRSI as initial estimators. The graduated nonconvexity algorithm is also introduced to handle penalized least squares problems. They newly introduced approaches are illustrated by a few numerical examples. [ABSTRACT FROM AUTHOR]

For the problem of variable selection for the normal linear model, selection criteria such as aic, Cp , bic and ric have fixed dimensionality penalties. Such criteria are shown to correspond to selection of maximum posterior models under implicit hyperparameter choices for a particular hierarchical Bayes formulation. Based on this calibration, we propose empirical Bayes selection criteria that use hyperparameter estimates instead of fixed choices. For obtaining these estimates, both marginal and conditional maximum likelihood methods are considered. As opposed to traditional fixed penalty criteria, these empirical Bayes criteria have dimensionality penalties that depend on the data. Their performance is seen to approximate adaptively the performance of the best fixed‐penalty criterion across a variety of orthogonal and nonorthogonal set‐ups, including wavelet regression. Empirical Bayes shrinkage estimators of the selected coefficients are also proposed. [ABSTRACT FROM PUBLISHER]

We develop new local versions of familiar smoothing methods, such as cross-validation and smoothed cross-validation, in the contexts of density estimation and regression. These new methods are locally adaptive in the sense that they capture smooth local fluctuations in the curve by using smoothly varying bandwidths that change as the character of the curve changes. Moreover, the new methods are accurate, easy to apply, and computationally expedient. [ABSTRACT FROM AUTHOR]

The condition on scaling filters of two orthogonal wavelet bases that render the corresponding wavetets as filbert transform pairs is re-examined in this note. Without making any pre-assumption on the relationship between the two scaling filters, the authors derive necessary and sufficient conditions for forming filbert transform pairs. They lead to new magnitude conditions and Selesnick's phase condition. Unique solutions to these conditions are concluded. It is shown that orthogonal wavelet bases form Hubert transform pairs if and only if the two scaling filters are offset from one another by half a sample. [ABSTRACT FROM AUTHOR]

Cardiovascular disease remains the leading cause of death otherwise healthy humans. In particular, most cases of sudden cardiac death occur as a result of failure of the mechanical function of the heart which is triggered by a turbulent pattern of electrical excitation of the heart e.g., ventricular fibrillation (VF). Although the exact mechanisms of VF remain unknown, increasing evidence indicates that it is organized by multiple reentrant sources (wavelets). [ABSTRACT FROM AUTHOR]

In this correspondence, the phase condition on the scaling filters of two wavelet bases that readers the corresponding wavelets as Hilbert transform pairs is studied. An alternative and equivalent phase condition is derived. With the equivalent condition and using Fourier series expansions, we show that the solution for which the corresponding scaling filters are offset from one another by a half sample is the only solution satisfying the phase condition. [ABSTRACT FROM AUTHOR]