Showing papers on "Multiresolution analysis published in 2006"

Estimating the probability of the presence of a signal of interest in multiresolution single- and multiband image denoising

Abstract: 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.

Directionlets: anisotropic multidirectional representation with separable filtering

Abstract: In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensional (1-D) discontinuities in images (edges and contours) that are very important elements in visual perception, intersect too many wavelet basis functions and lead to a nonsparse representation. To efficiently capture these anisotropic geometrical structures characterized by many more than the horizontal and vertical directions, a more complex multidirectional (M-DIR) and anisotropic transform is required. We present a new lattice-based perfect reconstruction and critically sampled anisotropic M-DIR WT. The transform retains the separable filtering and subsampling and the simplicity of computations and filter design from the standard two-dimensional WT, unlike in the case of some other directional transform constructions (e.g., curvelets, contourlets, or edgelets). The corresponding anisotropic basis functions (directionlets) have directional vanishing moments along any two directions with rational slopes. Furthermore, we show that this novel transform provides an efficient tool for nonlinear approximation of images, achieving the approximation power O(N/sup -1.55/), which, while slower than the optimal rate O(N/sup -2/), is much better than O(N/sup -1/) achieved with wavelets, but at similar complexity.

A self-organizing learning array system for power quality classification based on wavelet transform

Abstract: This paper proposed a novel approach for the Power Quality (PQ) disturbances classification based on the wavelet transform and self organizing learning array (SOLAR) system. Wavelet transform is utilized to extract feature vectors for various PQ disturbances based on the multiresolution analysis (MRA). These feature vectors then are applied to a SOLAR system for training and testing. SOLAR has three advantageous over a typical neural network: data driven learning, local interconnections and entropy based self-organization. Several typical PQ disturbances are taken into consideration in this paper. Comparison research between the proposed method, the support vector machine (SVM) method and existing literature reports show that the proposed method can provide accurate classification results. By the hypothesis test of the averages, it is shown that there is no statistically significant difference in performance of the proposed method for PQ classification when different wavelets are chosen. This means one can choose the wavelet with short wavelet filter length to achieve good classification results as well as small computational cost. Gaussian white noise is considered and the Monte Carlo method is used to simulate the performance of the proposed method in different noise conditions.

Multiresolution MAP Despeckling of SAR Images Based on Locally Adaptive Generalized Gaussian pdf Modeling

Abstract: In this paper, a new despeckling method based on undecimated wavelet decomposition and maximum a posteriori (MAP) estimation is proposed. Such a method relies on the assumption that the probability density function (pdf) of each wavelet coefficient is generalized Gaussian (GG). The major novelty of the proposed approach is that the parameters of the GG pdf are taken to be space-varying within each wavelet frame. Thus, they may be adjusted to spatial image context, not only to scale and orientation. Since the MAP equation to be solved is a function of the parameters of the assumed pdf model, the variance and shape factor of the GG function are derived from the theoretical moments, which depend on the moments and joint moments of the observed noisy signal and on the statistics of speckle. The solution of the MAP equation yields the MAP estimate of the wavelet coefficients of the noise-free image. The restored SAR image is synthesized from such coefficients. Experimental results, carried out on both synthetic speckled images and true SAR images, demonstrate that MAP filtering can be successfully applied to SAR images represented in the shift-invariant wavelet domain, without resorting to a logarithmic transformation

Multiresolution FIR neural-network-based learning algorithm applied to network traffic prediction

Abstract: In this paper, a multiresolution finite-impulse-response (FIR) neural-network-based learning algorithm using the maximal overlap discrete wavelet transform (MODWT) is proposed. The multiresolution learning algorithm employs the analysis framework of wavelet theory, which decomposes a signal into wavelet coefficients and scaling coefficients. The translation-invariant property of the MODWT allows alignment of events in a multiresolution analysis with respect to the original time series and, therefore, preserving the integrity of some transient events. A learning algorithm is also derived for adapting the gain of the activation functions at each level of resolution. The proposed multiresolution FIR neural-network-based learning algorithm is applied to network traffic prediction (real-world aggregate Ethernet traffic data) with comparable results. These results indicate that the generalization ability of the FIR neural network is improved by the proposed multiresolution learning algorithm.

A Lagrangian Particle‐Wavelet Method

Abstract: This paper presents a novel, multiresolution Lagrangian particle method with enhanced, wavelet‐based adaptivity. The method is formulated for transport problems and combines the efficiency of wavelet collocation with the inherent numerical stability of particle methods. The accuracy and efficiency of the present method is assessed on a number of benchmark problems pertaining to interface capturing and transport. The method is compared with existing techniques demonstrating its advantages and limitations. The present approach leads to a new generation of particle methods with multiresolution capabilities.

Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing

Abstract: An advanced continuous wavelet transform algorithm for digital interferogram analysis and processing is proposed. The algorithm is an extension of the traditional wavelet transform; the mother wavelet and normalization parameter are selected based on the characteristics of optical interferograms. To reduce the processing time, a fast Fourier transform scheme is employed to implement the wavelet transform calculation. The algorithm is simple and is a robust tool for interferogram filtering and for whole-field fringe and phase information detection. The concept is verified by computer simulation and actual experimental interferogram analysis.

The multiscale Hermite transform for local orientation analysis

Abstract: The efficient representation of local differential structure at various resolutions has been a matter of great interest for adaptive image processing and computer vision tasks. In this paper, we derive a multiscale model to represent natural images based on the scale-space representation: a model that has an inspiration in the human visual system. We first derive the one-dimensional case and then extend the results to two and three dimensions. The operators obtained for analysis and synthesis stages are derivatives of the Gaussian smoothing kernel, so that, for the two-dimensional case, we can represent them either in a rotated coordinate system or in terms of directional derivatives. The method to perform the rotation is efficient because it is implemented by means of the application of the so-called generalized binomial filters. Such a family of discrete sequences fulfills a number of properties that allows estimating the local orientation for several image structures. We also define the discrete counterpart in which the coordinate normalization of the continuous case is approximated as a subsampling of the discrete domain.

Wavelets with Short Support

Abstract: This paper is to construct Riesz wavelets with short support. Riesz wavelets with short support are the objective of interest in both theory and application. In theory, it is known that a B-spline of order m has the shortest support among all compactly supported refinable functions with the same regularity. However, it remained open whether a Riesz wavelet with the shortest support and m vanishing moments can be constructed from the multiresolution analysis generated by the B-spline of order m. In various applications, a Riesz wavelet with a short support, a high order of regularity, and vanishing moments is often desirable in signal and image processing, since they have a good time frequency localization and approximation property, as well as fast algorithms. This paper presents a theory for the construction of Riesz wavelets with short support and gives various examples. In particular, from the multiresolution analysis whose underlying refinable function is the B-spline of order m, we are able to constr...

A spline wavelet finite‐element method in structural mechanics

Abstract: The wavelet-based methods are powerful to analyse the field problems with changes in gradients and singularities due to the excellent multi-resolution properties of wavelet functions. Wavelet-based finite elements are often constructed in the wavelet space where field displacements are expressed as a product of wavelet functions and wavelet coefficients. When a complex structural problem is analysed, the interface between different elements and boundary conditions cannot be easily treated as in the case of conventional finite-element methods (FEMs). A new wavelet-based FEM in structural mechanics is proposed in the paper by using the spline wavelets, in which the formulation is developed in a similar way of conventional displacement-based FEM. The spline wavelet functions are used as the element displacement interpolation functions and the shape functions are expressed by wavelets. The detailed formulations of typical spline wavelet elements such as plane beam element, in-plane triangular element, in-plane rectangular element, tetrahedral solid element, and hexahedral solid element are derived. The numerical examples have illustrated that the proposed spline wavelet finite-element formulation achieves a high numerical accuracy and fast convergence rate. Copyright © 2005 John Wiley & Sons, Ltd.

From differential equations to the construction of new wavelet-like bases

Abstract: In this paper, an approach is introduced based on differential operators to construct wavelet-like basis functions. Given a differential operator L with rational transfer function, elementary building blocks are obtained that are shifted replicates of the Green's function of L. It is shown that these can be used to specify a sequence of embedded spline spaces that admit a hierarchical exponential B-spline representation. The corresponding B-splines are entirely specified by their poles and zeros; they are compactly supported, have an explicit analytical form, and generate multiresolution Riesz bases. Moreover, they satisfy generalized refinement equations with a scale-dependent filter and lead to a representation that is dense in L/sub 2/. This allows us to specify a corresponding family of semi-orthogonal exponential spline wavelets, which provides a major extension of earlier polynomial spline constructions. These wavelets are completely characterized, and it is proven that they satisfy the following remarkable properties: 1) they are orthogonal across scales and generate Riesz bases at each resolution level; 2) they yield unconditional bases of L/sub 2/-either compactly supported (B-spline-type) or with exponential decay (orthogonal or dual-type); 3) they have N vanishing exponential moments, where N is the order of the differential operator; 4) they behave like multiresolution versions of the operator L from which they are derived; and 5) their order of approximation is (N-M), where N and M give the number of poles and zeros, respectively. Last but not least, the new wavelet-like decompositions are as computationally efficient as the classical ones. They are computed using an adapted version of Mallat's filter bank algorithm, where the filters depend on the decomposition level.

Adaptive scale fixing for multiscale texture segmentation

Abstract: This paper addresses two challenging issues in unsupervised multiscale texture segmentation: determining adequate spatial and feature resolutions for different regions of the image, and utilizing information across different scales/resolutions. The center of a homogeneous texture is analyzed using coarse spatial resolution, and its border is detected using fine spatial resolution so as to locate the boundary accurately. The extraction of texture features is achieved via a multiresolution pyramid. The feature values are integrated across scales/resolutions adaptively. The number of textures is determined automatically using the variance ratio criterion. Experimental results on synthetic and real images demonstrate the improvement in performance of the proposed multiscale scheme over single scale approaches.

Low-Complexity Multiresolution Image Compression Using Wavelet Lower Trees

Abstract: In this paper, a new image compression algorithm is proposed based on the efficient construction of wavelet coefficient lower trees. The main contribution of the proposed lower-tree wavelet (LTW) encoder is the utilization of coefficient trees, not only as an efficient method of grouping coefficients, but also as a fast way of coding them. Thus, it presents state-of-the-art compression performance, whereas its complexity is lower than the one presented in other wavelet coders, like SPIHT and JPEG 2000. Fast execution is achieved by means of a simple two-pass coding and one-pass decoding algorithm. Moreover, its computation does not require additional lists or complex data structures, so there is no memory overhead. A formal description of the algorithm is provided, while reference software is also given. Numerical results show that our codec works faster than SPIHT and JPEG 2000 (up to three times faster than SPIHT and fifteen times faster than JPEG 2000), with similar coding efficiency

Fusion of Panchromatic and Multispectral Images by Genetic Algorithms

Abstract: Pan-sharpened MS is a fusion product in which the multispectral (MS) bands are spatially enhanced by the higher-resolution panchromatic (Pan) image. Most effective algo- rithms for pan-sharpening are based on multiresolution analysis (MRA), e.g., wavelets, Laplacian pyramids, wavelet frames, or curvelets. MRA approaches present one main critical point: filtering operations may produce ringing artifacts when high frequency details are extracted from the panchromatic image. In this paper, a pan-sharpening algorithm for 4-band MS data is proposed, which is not based on MRA, but it applies a Generalized Intensity-Hue-Saturation (GIHS) transformation to the MS bands. A genetic algorithm is adopted to define the injection model which establishes how the missing highpass information is extracted from the Pan image. The fitness function of the genetic algorithm which provides the algorithm parameters driving the fusion process is based on a quality index specifically designed for quality assessment of 4-band MS images. Both visual and objective comparisons with advanced fusion methods are presented on QuickBird image data. I. INTRODUCTION Multispectral (MS) observations from spaceborne imaging sensors exhibit ground resolutions that may be inadequate to specific identification tasks, especially when urban areas are concerned. Data merge methods, based on injecting spatial details taken from a panchromatic image (Pan) into resampled versions of the MS data, have demonstrated superior performances. In the last years, multiresolution analysis (MRA), based on wavelets, Laplacian pyramids, wavelet frames, curvelets, etc., has been applied to produce effective tools to help carry out data fusion/merge tasks. However, MRA approaches present one main critical point: filtering operations may produce ringing artifacts, e.g. when high frequency details are extracted from the panchromatic image. This problem does not decrease significantly any global quality index, but it may locally reduce the visual quality of the fused product in a considerable way. To avoid this problem, we propose a pan-sharpening algorithm which is not based on MRA, but it applies a Generalized Intensity-Hue-Saturation (GIHS) transformation to the MS bands and makes use of optimal parameters which are computed by a genetic algorithm. Similarly to other pan-sharpening methods based on the injection of spatial details, the proposed algorithm assumes an injection model. To overcome instability and data-dependent results which are typical of space-varying models, we propose a simple injection model in which the coefficients that equalize the Pan image before detail injection into the MS image are derived globally - one for each band - from coarser scales, similarly to previous schemes such as SDM (1), CBD (2) and RWM (3) techniques, but not a-priori defined on image statistics, e.g., variance, mean, correlation coefficient, etc. The coefficients are computed by a genetic algorithm (GA) together with the weights which define the generalized intensity of the original MS bands. The genetic algorithm adopts the Q4 quality index defined in (4) as the fitness function to be maximized for optimal fusion parameter estimation.

Fast Analysis of Large Finite Arrays With a Combined Multiresolution—SM/AIM Approach

Abstract: We present a synthesis of the sparse matrix/adaptive integral method (SM/AIM) and the multiresolution (MR) approach for the analysis of electrically large finite arrays, with planar or 3-D radiating elements; the two methods were separately introduced previously. The use of the MR has the effect of a preconditioner and speeds up the convergence rate of the SM/AIM of almost two orders of magnitude, with a total reduction of the numerical complexity with respect to the standard MoM of almost three orders of magnitude

Multiresolution analysis of fluctuations in non-stationary time series through discrete wavelets

Abstract: We illustrate the efficacy of a discrete wavelet based approach to characterize fluctuations in non-stationary time series. The present approach complements the multi-fractal detrended fluctuation analysis (MF-DFA) method and is quite accurate for small size data sets. As compared to polynomial fits in the MF-DFA, a single Daubechies wavelet is used here for de-trending purposes. The natural, built-in variable window size in wavelet transforms makes this procedure well suited for non-stationary data. We illustrate the working of this method through the analysis of binomial multi-fractal model. For this model, our results compare well with those calculated analytically and obtained numerically through MF-DFA. To show the efficacy of this approach for finite data sets, we also do the above comparison for Gaussian white noise time series of different size. In addition, we analyze time series of three experimental data sets of tokamak plasma and also spin density fluctuations in 2D Ising model.

Wavelet based non-parametric NARX models for nonlinear input-output system identification

Abstract: Wavelet based non-parametric additive NARX models are proposed for nonlinear input-output system identification. By expanding each functional component of the non-parametric NARX model into wavelet multiresolution expansions, the non-parametric estimation problem becomes a linear-in-the-parameters problem, and least-squares-based methods such as the orthogonal forward regression (OFR) approach, coupled with model size determination criteria, can be used to select the model terms and estimate the parameters. Wavelet based additive models, combined with model order determination and variable selection approaches, are capable of handling problems of high dimensionality.

Complexity-based program phase analysis and classification

Abstract: Modeling and analysis of program behavior are at the foundation of computer system design and optimization. As computer systems become more adaptive, their efficiency increasinsgly depends on program dynamic characteristics. Previous studies have revealed that program runtime execution manifests phase behavior. Recently, methods and tools to analyze and classify program phases have also been developed. However, very few studies have been proposed so far to understand and evaluate program phases from their dynamics and complexity perspectives. In this work, we propose new methods, metrics and frameworks which aim to analyze, quantify, and classify the dynamics and complexity of program phases. Our methods use wavelet techniques to represent program phases at multiresolution scales. The cross-correlation coefficients between phase dynamics observed at different scales are then computed as metrics to quantify phase complexity. We propose to apply wavelet-based multiresolution analysis and data clustering to classify program execution into phases that exhibit similar degree of complexity. Experimental results on SPEC CPU 2000 benchmarks show that the proposed schemes classify complexity-based program phases better than currently used approaches.

Long term prediction of non-linear time series using multiresolution wavelet models

Abstract: The long term prediction of non-linear dynamical time series, based on identified multiresolution wavelet models, from historically observed data sets is investigated and a new direct prediction approach is introduced. Prediction results based on the new direct scheme are compared with those from iterative methods and it is shown that improved predictions can be obtained using the new approach.

Multiwavelet Constructions and Volterra Kernel Identification

Abstract: The Volterra series is commonly used for the modeling of nonlinear dynamical systems. In general, however, a large number of terms are needed to represent Volterra kernels, with the number of required terms increasing exponentially with the order of the kernel. Therefore, reduced-order kernel representations are needed in order to employ the Volterra series in engineering practice. This paper presents an approach whereby multiwavelets are used to obtain low-order estimates of first-, second-, and third-order Volterra kernels. A family of multiwavelets is constructed from the classical finite element basis functions using the technique of intertwining. The resulting multiwavelets are piecewise-polynomial, orthonormal, compactly-supported, and can be constructed with arbitrary approximation order. Furthermore, these multiwavelets are easily adapted to the domains of support of the Volterra kernels. In contrast, most wavelet families do not possess this characteristic. Higher-dimensional multiwavelets can easily be constructed by taking tensor products of the original one-dimensional functions. Therefore, it is straightforward to extend this approach to the representation of higher-order Volterra kernels. This kernel identification algorithm is demonstrated on a prototypical oscillator with a quadratic stiffness nonlinearity. For this system, it is shown that accurate kernel estimates can be obtained in terms of a relatively small number of wavelet coefficients. These results indicate the potential of the multiwavelet-based algorithm for obtaining reduced-order models for a large class of weakly nonlinear systems.

Wavelet video denoising with regularized multiresolution motion estimation

Abstract: This paper develops a new approach to video denoising, in which motion estimation/compensation, temporal filtering, and spatial smoothing are all undertaken in the wavelet domain. The key to making this possible is the use of a shift-invariant, overcomplete wavelet transform, which allows motion between image frames to be manifested as an equivalent motion of coefficients in the wavelet domain. Our focus is on minimizing spatial blurring, restricting to temporal filtering when motion estimates are reliable, and spatially shrinking only insignificant coefficients when the motion is unreliable. Tests on standard video sequences show that our results yield comparable PSNR to the state of the art in the literature, but with considerably improved preservation of fine spatial details.