Showing papers on "Multiresolution analysis published in 1999"
TL;DR: In this paper, a multiresolution signal decomposition technique is used to detect and localize transient events and furthermore classify different power quality disturbances, which can also be used to distinguish among similar disturbances.
Abstract: The wavelet transform is introduced as a powerful tool for monitoring power quality problems generated due to the dynamic performance of industrial plants. The paper presents a multiresolution signal decomposition technique as an efficient method in analyzing transient events. The multiresolution signal decomposition has the ability to detect and localize transient events and furthermore classify different power quality disturbances. It can also be used to distinguish among similar disturbances.
603 citations
TL;DR: An additional algorithm for multiwavelet processing of two-dimensional (2-D) signals, two rows at a time, is described, and a new family of multiwavelets (the constrained pairs) are developed that is well-suited to this approach.
Abstract: Multiwavelets are a new addition to the body of wavelet theory. Realizable as matrix-valued filterbanks leading to wavelet bases, multiwavelets offer simultaneous orthogonality, symmetry, and short support, which is not possible with scalar two-channel wavelet systems. After reviewing this theory, we examine the use of multiwavelets in a filterbank setting for discrete-time signal and image processing. Multiwavelets differ from scalar wavelet systems in requiring two or more input streams to the multiwavelet filterbank. We describe two methods (repeated row and approximation/deapproximation) for obtaining such a vector input stream from a one-dimensional (1-D) signal. Algorithms for symmetric extension of signals at boundaries are then developed, and naturally integrated with approximation-based preprocessing. We describe an additional algorithm for multiwavelet processing of two-dimensional (2-D) signals, two rows at a time, and develop a new family of multiwavelets (the constrained pairs) that is well-suited to this approach. This suite of novel techniques is then applied to two basic signal processing problems, denoising via wavelet-shrinkage, and data compression. After developing the approach via model problems in one dimension, we apply multiwavelet processing to images, frequently obtaining performance superior to the comparable scalar wavelet transform.
443 citations
TL;DR: In this paper, a review of recent developments in multiresolution analysis that make it a powerful tool for the systematic treatment of the multiple length scales inherent in the electroniic structure of matter is presented.
Abstract: This article reviews recent developments in multiresolution analysis that make it a powerful tool for the systematic treatment of the multiple length scales inherent in the electroniic structure of matter. While the focus is on electronic structure, the advances described herein are useful for nonlinear problems in the physical sciences in general. Among the reviewed developments is the exact construction of multiresolution representations from extremely limited samples of physical fields in real space. This new and profound result is the critical advance in finally allowing systematic, all electron calculations to compete in efficiency with state-of-the-art electronic structure calculations that depend for their celerity upon freezing the core electronic degrees of freedom. This review presents the theory of wavelets from a physical perspective, provides a unified and self-contained treatment of nonlinear couplings and physical operators, and introduces a modern framework for effective single-particle theories of quantum mechanics.
208 citations
TL;DR: A unified approach to digital watermarking of images and video based on the two- and three-dimensional discrete wavelet transforms is proposed and it is shown that when subjected to distortion from compression or image halftoning, the corresponding watermark can still be correctly identified.
Abstract: This paper proposes a unified approach to digital watermarking of images and video based on the two- and three-dimensional discrete wavelet transforms. The hierarchical nature of the wavelet representation allows multiresolutional detection of the digital watermark, which is a Gaussian distributed random vector added to all the high-pass bands in the wavelet domain. We show that when subjected to distortion from compression or image halftoning, the corresponding watermark can still be correctly identified at each resolution (excluding the lowest one) in the wavelet domain. Computational savings from such a multiresolution watermarking framework is obvious, especially for the video case.
184 citations
TL;DR: New theory and algorithms are presented that allow current wavelet methodology to deal with the two main characteristics of nuclear medicine images: low signal-to-noise ratios and correlated noise.
Abstract: This article develops a theoretical framework for the use of the wavelet transform in the estimation of emission tomography images. The solution of the problem of estimation addresses the equivalent problems of optimal filtering, maximum compression, and statistical testing. In particular, new theory and algorithms are presented that allow current wavelet methodology to deal with the two main characteristics of nuclear medicine images: low signal-to-noise ratios and correlated noise. The technique is applied to synthetic images, phantom studies, and clinical images. Results show the ability of wavelets to model images and to estimate the signal generated by cameras of different resolutions in a wide variety of noise conditions. Moreover, the same methodology can be used for the multiscale analysis of statistical maps. The relationship of the wavelet approach to current hypothesis-testing methods is shown with an example and discussed. The wavelet transform is shown to be a valuable tool for the numerical treatment of images in nuclear medicine. It is envisaged that the methods described here may be a starting point for further developments in image reconstruction and image processing.
144 citations
TL;DR: The result shows that the Fourier-wavelet descriptor is an efficient representation which can provide for reliable recognition of complex patterns such as roadsigns, keys, aircrafts, characters, etc.
125 citations
TL;DR: In this paper, the authors compared three signal processing tools for power quality analysis: the continuous wavelet transform, the multiresolution analysis and the quadratic transform, and showed that the Fourier transform appears to be a reliable method for detecting and measuring voltage sags, flicker and transients.
Abstract: This paper deals with the comparison of new signal processing tools for power quality analysis. Three new signal processing techniques are considered: the continuous wavelet transform, the multiresolution analysis and the quadratic transform. Their theoretical behaviours are investigated using the basic theory of the Fourier transform. Then, examples of the four most frequent disturbances met in the power system are chosen. Finally, each kind of electrical disturbance is analyzed with example representing each tool. A qualitative comparison of results shows the advantages and drawbacks of each new signal processing technique applied to voltage disturbance analysis. The continuous wavelet transform appears to be a reliable method for detecting and measuring voltage sags, flicker and transients in power quality analysis.
125 citations
TL;DR: Multiresolution analysis, specifically the discrete wavelet transform modulus-maxima (mod-max) method, is utilized for the extraction of mammographic mass shape features to classify masses as round, nodular, or stellate in a classification system.
Abstract: In this article, multiresolution analysis, specifically the discrete wavelet transform modulus-maxima (mod-max) method, is utilized for the extraction of mammographic mass shape features. These shape features are used in a classification system to classify masses as round, nodular, or stellate. The multiresolution shape features are compared with traditional uniresolution shape features for their class discriminating abilities. The study involved 60 digitized mammographic images. The masses were segmented manually by radiologists, prior to introduction to the classification system. The uniresolution and multiresolution shape features were calculated using the radial distance measure of the mass boundaries. The discriminating power of the shape features were analyzed via linear discriminant analysis (LDA). The classification system utilized a simple Euclidean metric to determine class membership. The system was tested using the apparent and leave-one-out test methods. The classification system when using the multiresolution and uniresolution shape features resulted in classification rates of 83% and 80% for the apparent and leave one-out test methods, respectively. In comparison, when only the uniresolution shape features were used, the classification rates were 72 and 68% for the apparent and leave-one-out test methods, respectively.
123 citations
TL;DR: Drawing on the rich theory of wavelets, a system identification scheme based on orthogonal wavelets is proposed and illustrated by applying the procedure to determine a speed-controller for an electric vehicle.
Abstract: Compactly supported orthogonal wavelets have certain properties that are useful for system identification and learning control. Drawing on the rich theory of wavelets, we propose a system identification scheme based on orthogonal wavelets. Better accuracy of estimation can be obtained by adding more terms to the wavelet based identifier, and these terms do not alter the coefficients of the existing terms. These terms can be selectively added depending upon the region of interest, for example we may require more terms in regions where the identified functions vary rapidly. We illustrate the concepts by applying the procedure to determine a speed-controller for an electric vehicle.
122 citations
12 Jul 1999
TL;DR: This paper provides fundamentals of wavelet based image compression and the results of image quality measurements for different wavelet functions, image contents, compression ratios and resolutions are given.
Abstract: The discrete wavelet transform (DWT) represents images as a sum of wavelet functions (wavelets) on different resolution levels. The basis for the wavelet transform can be composed of any function that satisfies requirements of multiresolution analysis. It means that there exists a large selection of wavelet families depending on the choice of wavelet function. The choice of wavelet family depends on the application. In image compression application this choice depends on image content. This paper provides fundamentals of wavelet based image compression. The options for wavelet image representations are tested. The results of image quality measurements for different wavelet functions, image contents, compression ratios and resolutions are given.
116 citations
TL;DR: In this article, a wavelet-Galerkin scheme based on the time-dependent Maxwell's equations is presented, and the storage effectiveness, execution time reduction, and accuracy of this scheme are demonstrated by calculating the resonant frequencies of the homogeneous and inhomogeneous cavities.
Abstract: A wavelet-Galerkin scheme based on the time-dependent Maxwell's equations is presented. Daubechies' wavelet with two vanishing wavelet moments is expanded for basis function in spatial domain, and Yee's leap-frog approach is applied. The shifted interpolation property of Daubechies' wavelet family leads to the simplified formulations for inhomogeneous media without the additional matrices for the integral or material operator. The storage effectiveness, execution time reduction, and accuracy of this scheme are demonstrated by calculating the resonant frequencies of the homogeneous and inhomogeneous cavities.
TL;DR: A general Fourier method that provides an accurate prediction of the approximation error, irrespective of the scaling properties of the approximating functions is proposed, and sharp, asymptotically optimal upper bounds for the least-squares approximation error are computed.
Abstract: For pt.I see ibid., vol.47, no.10, p.2783-95 (1999). In a previous paper, we proposed a general Fourier method that provides an accurate prediction of the approximation error, irrespective of the scaling properties of the approximating functions. Here, we apply our results when these functions satisfy the usual two-scale relation encountered in dyadic multiresolution analysis. As a consequence of this additional constraint, the quantities introduced in our previous paper can be computed explicitly as a function of the refinement filter. This is, in particular, true for the asymptotic expansion of the approximation error for biorthonormal wavelets as the scale tends to zero. One of the contributions of this paper is the computation of sharp, asymptotically optimal upper bounds for the least-squares approximation error. Another contribution is the application of these results to B-splines and Daubechies (1988, 1992) scaling functions, which yields explicit asymptotic developments and upper bounds. Thanks to these explicit expressions, we can quantify the improvement that can be obtained by using B-splines instead of Daubechies wavelets. In other words, we can use a coarser spline sampling and achieve the same reconstruction accuracy as Daubechies. Specifically, we show that this sampling gain converges to /spl pi/ as the order tends to infinity.
TL;DR: The framework of conforming domain decomposition to generate wavelet bases and second-order operators is considered and a coupling of the iterative solver with an adaptive space refinement technique is proposed.
Abstract: Wavelet methods allow us to combine high-order accuracy, efficient preconditioning techniques, and adaptive approximations in order to solve efficiently elliptic operator equations. Many difficulties remain, in particular, related to the adaptation of wavelet decompositions to bounded domains with prescribed boundary conditions, leading to possibly high constants in the ${\cal O}(1)$ preconditioning. In this paper we consider the framework of conforming domain decomposition to generate our wavelet bases and second-order operators. We emphasize the choice of the wavelets near the boundary of the tensor product reference domain in order to optimize the efficiency of the diagonal preconditioning of elliptic operators. In order to improve the constants obtained by such diagonal preconditionings, we propose to take into account interactions between the scales through the computation of a sparse approximate inverse (SPAI) on a set of nonzero entries obtained from the compression of the operator itself in the wavelet basis. The efficiency of these methods is illustrated by solving elliptic second-order problems with variable or constant coefficients and homogeneous boundary conditions on a uniform discretization. Finally, we propose a coupling of the iterative solver with an adaptive space refinement technique. On the Laplacian model problem, our experiments show that this algorithm generates an optimal nonlinear approximation of the solution.
TL;DR: This work shows how least‐squares data fitting can be used to “reverse” a subdivision rule, how this reversal is related to wavelets, and how this relationship can provide a multilevel representation.
Abstract: This work explores how three techniques for defining and representing curves and surfaces can be related efficiently The techniques are subdivision, least-squares data fitting, and wavelets We show how least-squares data fitting can be used to “reverse” a subdivision rule, how this reversal is related to wavelets, how this relationship can provide a multilevel representation, and how the decomposition/reconstruction process can be carried out in linear time and space through the use of a matrix factorization
Some insights that this work brings forth are that the inner product used in a multiresolution analysis in uences the support of a wavelet, that wavelets can be constructed by straightforward matrix observations, and that matrix partitioning and factorization can provide alternatives to inverses or duals for building efficient decomposition and reconstruction processes We illustrate our findings using an example curve, grey-scale image, and tensor-product surface
TL;DR: A multirate interacting multiple model (MRIMM) tracking algorithm has been developed that significantly outperforms a full-rate IMM filter when no manoeuvres occur and performs comparably with the IMMfilter when manoeuvre detection occurs, with a certain amount of computational savings.
Abstract: A multirate interacting multiple model (MRIMM) tracking algorithm has been developed. The algorithm is based on a reformulation of the interacting multiple model (IMM) filter under the assumption that each model operates at an update rate proportional to the model's assumed dynamics. A set of multirate models is derived based on the geometrical interpretation of a discrete wavelet transform. A wavelet transform is used to generate equivalent multirate measurements, which exhibit the additional property of lower equivalent measurement noise for low-rate data. Using this filtering approach, the MRIMM algorithm significantly outperforms a full-rate IMM filter when no manoeuvres occur and performs comparably with the IMM filter when manoeuvres occur, with a certain amount of computational savings. This approach also has the advantages of improved sensitivity for manoeuvre detection.
TL;DR: A new strategy to automatically identify epileptiform activity in EEG is described, based upon detecting epileptic spikes, via multiresolution analysis, a relatively new tool in signal processing, which allows for dramatic improvements in the efficiency of basic wavelet analysis.
TL;DR: It is shown that non-extensive information measures used in the study of human EEG-signals seem to be of particular usefulness, and this opens up perspectives of building up automatic detection devices.
Abstract: We undertake the study of human EEG-signals by recourse to a wavelet based multiresolution analysis as adapted to an Information-Measure-Scenario. Dierent information measures are employed. It is shown that non-extensive ones seem to be of particular usefulness. Their use opens up perspectives of building up automatic detection devices. Conjectures concerning general characteristics of focal epilepsy are formulated on the basis of a Tsallis-type of analysis. c 1999 Elsevier Science B.V. All rights reserved.
TL;DR: A multiresolution analysis technique for performing correlations on wavelet representations of images is derived, which produces the correlations at lowest resolution by applying the convolution theorem to subband correlations.
Abstract: This paper derives a multiresolution analysis technique for performing correlations on wavelet representations of images. The technique maps the images into the wavelet-frequency domain to take advantage of high-speed correlation in the frequency domain. It builds on Vaidyanathan's (1993) wavelet correlation theorem, which shows that subsamples of correlations of two signals can be obtained from a sum of correlations of subbands of wavelet representations of those signals. Our algorithm produces the correlations at lowest resolution by applying the convolution theorem to subband correlations. A new multiresolution technique fills in the missing correlation data by incrementally inverting the wavelet transform and refining the Fourier transform. When applied to JPEG representations of data, the lowest resolution correlations can he performed directly on the JPEG images to produce 1/64th of the correlation points. Each of three incremental steps quadruple the number of correlation points, and the process can be halted at any point if the intermediate results indicate that the correlation will not find a match.
25 Jun 1999
TL;DR: This work introduces a new image texture segmentation algorithm, HMTseg, based on wavelet-domain hidden Markov tree (HMT) models, a tree-structured probabilistic graph that captures the statistical properties of wavelet coefficients.
Abstract: We introduce a new image texture segmentation algorithm, HMTseg, based on wavelet-domain hidden Markov tree (HMT) models. The HMT model is a tree-structured probabilistic graph that captures the statistical properties of wavelet coefficients. Since the HMT is particularly well suited to images containing singularities (edges and ridges), it provides provides a good classifier for textures. Utilizing the inherent tree structure of the wavelet HMT and its fast training and likelihood computation algorithms, we perform multiscale texture classification at various scales. We then fuse these multiscale classifications using a Bayesian probabilistic graph to obtain a reliable final segmentation. Since HMTseg works on the wavelet transform of the image, it can directly segment wavelet-compressed images, without the need for decompression. We demonstrate the performance of HMTseg with synthetic, aerial photo, and document image segmentations.
TL;DR: In this article, an analysis and denoising of cosmic microwave background (CMB) maps using wavelet multiresolution techniques is performed using 12.8×12.8 × 12.2 maps, with the resolution resembling the experimental one expected for future high-resolution space observations.
Abstract: Analysis and denoising of cosmic microwave background (CMB) maps are performed using wavelet multiresolution techniques. The method is tested on 12.8×12.8 deg2 maps, with the resolution resembling the experimental one expected for future high-resolution space observations. Semi-analytic formulae of the variance of wavelet coefficients are given for the Haar and Mexican Hat wavelet bases. Results are presented for the standard cold dark matter (CDM) model. Denoising of simulated maps is carried out by removal of wavelet coefficients dominated by instrumental noise. CMB maps with a signal-to-noise ratio, SN∼1, are denoised with an error improvement factor between 3 and 5. Moreover, we have also tested how well the CMB temperature power spectrum is recovered after denoising. We are able to reconstruct the Cls up to l∼1500 with errors always below 20 per cent in cases with SN1.
TL;DR: Out of the three methods compared, respectively based on highpass filtering (HPF), wavelet transform (WT), and generalized Laplacian pyramid (GLP), the latter two are far more efficient than the former, thus establishing the advantages for data fusion of a formally multiresolution analysis.
Abstract: Goal of this paper is to provide a quantitative performance evaluation of multiresolution schemes capable to carry out feature-based fusion of data collected by multispectral and panchromatic imaging sensors having different spectral and ground resolutions. To this aim a set of quantitative parameters has been recently proposed. Both visual quality, regarded as contrast, presence of fine details, and absence of impairments and artifacts (e.g., blur, ringing), and spectral fidelity (i.e., preservation of spectral signatures) are concerned and embodied in the measurements. Out of the three methods compared, respectively based on highpass filtering (HPF), wavelet transform (WT), and generalized Laplacian pyramid (GLP), the latter two are far more efficient than the former, thus establishing the advantages for data fusion of a formally multiresolution analysis.
TL;DR: A new method for filtering an image, based on a new definition of its entropy, is presented, which outperforms existing wavelet-based methods on a large number of examples.
01 Jun 1999
TL;DR: In this article, it was shown that certain Theta functions are asymptotically optimal for the periodic time frequency uncertainty principle described by Breitenberger in [3], and these extremal functions give rise to a periodic multiresolution analysis where the corresponding wavelets also show similar localization properties.
Abstract: In this paper, it is shown that certain Theta functions are asymptotically optimal for the periodic time frequency uncertainty principle described by Breitenberger in [3]. These extremal functions give rise to a periodic multiresolution analysis where the corresponding wavelets also show similar localization properties.
TL;DR: The smoothing effect of the wave let-based speckle filtering that the authors proposed is investigated and a theoretical investigation with the Haar basis derives a functional relation between the ENL and two parameters: the wavelet level and the degree of the amplitude reduction.
Abstract: The smoothing effect of the wavelet-based speckle filtering that the authors proposed is investigated. The filtering reduces the amplitude of wavelet coefficients, and a theoretical investigation with the Haar basis derives a functional relation between the ENL and two parameters: the wavelet level and the degree of the amplitude reduction.
TL;DR: A two-pass algorithm, collection and verification, is proposed to study dissolve and wipe transition detection problems, the most difficult shot Transition detection problems.
12 Mar 1999
TL;DR: Preliminary subjective image fusion results demonstrate clearly the advantage which the proposed cross-band selection technique offers, when compared to conventional area based pixel selection.
Abstract: The work described in this paper focuses on cross band pixel selection as applied to pixel level multi-resolution image fusion. In addition, multi-resolution analysis and synthesis is realized via QMF sub-band decomposition techniques. Thus cross-band pixel selection is considered with the aim of reducing the contrast and structural distortion image artifacts produced by existing wavelet based, pixel level, image fusion schemes. Preliminary subjective image fusion results demonstrate clearly the advantage which the proposed cross-band selection technique offers, when compared to conventional area based pixel selection.
TL;DR: In this paper, the authors presented a construction principle for locally supported wavelets on manifolds once a multiresolution analysis is given, which provided a stable (or unconditional) basis for a scale of Sobolev spaces H s, 0 ≤ s ≤ s.
TL;DR: A family of nearly orthonormal affine Riesz bases of compact support and arbitrary degrees of smoothness, obtained by perturbing the one-dimensional Haar mother wavelet using B -splines, was given in this article.
TL;DR: A new block-matching algorithm that is much faster than the full search algorithm and occasionally even produces better rate-distortion curves than theFull search algorithms.
Abstract: Motion estimation is known to be the main bottleneck in real-time encoding applications, and the search for an effective motion estimation algorithm (in terms of computational complexity and compression efficiency) has been a challenging problem for years. This paper describes a new block-matching algorithm that is much faster than the full search algorithm and occasionally even produces better rate-distortion curves than the full search algorithms. We observe that a piecewise continuous motion field reduces the bit rate for differentially encoded motion vectors. Our motion estimation algorithm exploits the spatial correlations of motion vectors effectively in the sense of producing better rate-distortion curves. Furthermore, we incorporate such correlations in a multiresolution framework to reduce the computational complexity. Simulation shows that this method is successful because of the homogeneous and reliable estimation of the displacement vectors. In nine out of our ten benchmark simulations, the performance of the full search algorithm and that of our subblock multiresolution method is about the same. In one out of our ten benchmark simulations, our method has improvement.
TL;DR: A method of representing scattered spherical data by multiscale spherical wavelets is introduced and it is employed to analyze and compress a real-data set consisting of the surface air temperatures observed on a global network of weather stations.
Abstract: Classic wavelet methods were developed in the Euclidean spaces for multiscale representation and analysis of regularly sampled signals (time series) and images. This paper introduces a method of representing scattered spherical data by multiscale spherical wavelets. The method extends the recent pioneering work of Narcowich and Ward [Appl. Comput. Harmon. Anal., 3 (1996), pp. 324--336] by employing multiscale rather than single-scale spherical basis functions and by introducing a bottom-up procedure for network design and bandwidth selection. Decomposition and reconstruction algorithms are proposed for efficient computation. An analytical investigation confirms the localization property of the resulting spherical wavelets. The proposed method is illustrated by numerical examples. It is also employed to analyze and compress a real-data set consisting of the surface air temperatures observed on a global network of weather stations.