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Seismic imaging in wavelet domain: Decomposition and compression of imaging operator

Seismic imaging in wavelet domain: Decomposition and compres...

引用

conference on wavelet applications in signal and image processing V

作者： Wu, RS Yang, F Univ. of California/Santa Cruz (United States)

ISBN: (纸本)0819425915

We study the decomposition and compression of one-way wave propagation and imaging operators using wavelet transform. We show that the matrix representation of the Kirchhoff imaging operator (Kirchhoff migration operator) in space domain is a dense matrix, while the compressed beamlet-operator matrix which is the wavelet decomposition of the Kirchhoff operator, is a highly sparse matrix. The beamlet imaging operator represents the backpropagation of multiscale orthonormal beams (beamlets) at different positions with different angles. The beamlet-operator behaves differently in different wavelet bases. For sharp and short bases, such as the Daubechies 4 (D4), both the interscale and intrascale coupling are strong. On the other hand, the interscale coupling is relatively weak for smooth bases, such as higher-order Daubechies wavelets, Coiflets, and spline wavelets. The images obtained by the compressed beamlet operators are almost identical to the images from a full-aperture Kirchhoff operator. Compared with the conventional limited-aperture Kirchhoff migration (imaging), beamlet migration (imaging) can retain the wide effective aperture of a full-aperture operator, and hence achieve higher resolution and image quality with reduced computational cost. The compression ratio of the imaging operator ranges from a few times to a few hundred times, depending on the frequency, step length and the wavelet basis.

关键词： wavelets image compression image quality image resolution Space operations Wave propagation wavelet transforms

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Chirp correlation in the wavelet domain

Chirp correlation in the wavelet domain

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conference on image processing, signal processing, and Synthetic Aperture Radar for Remote Sensing

作者： Datcu, M Schwarz, G German Aerosp Res Estab DLR German Remote Sensing Data Ctr DFD D-82234 Oberpfaffenhofen Germany

ISBN: (纸本)0819426490

The wavelet transform developed during the last years into a mature and very pragmatic formalism for the analysis of the scale behaviour of signals. However, it also remains a tool to serve its very initial goal: the time-frequency analysis. In this article we summarize the basics of time-frequency-scale formalism for signal representation and analysis, and we overview several applications with promising results for the Synthetic Aperture Radar (SAR) signal processing.

关键词： SAR chirp wavelets ambiguity function

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wavelets for texture analysis, an overview

Wavelets for texture analysis, an overview

引用

Proceedings of the 1997 6th International conference on image processing and its applications. Part 2 (of 2)

作者： Livens, S. Scheunders, P. Van de Wouwer, G. Van Dyck, D. RUCA Univ of Antwerp Antwerp Belgium

The wavelet paradigm is now well established and has found many applications in signal and image processing. Since also some of its precursors can be reformulated into wavelet terminology, it has become a preferred tool for multiresolution analysis. We have given an overview of the application of wavelet multiresolution image analysis to texture. Results of recent studies prove the merits of the methods in practical segmentation and classification problems. Some aspects still need further investigation. Two were discussed: rotation invariance and colour texture.

关键词： image processing

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Optimal wavelet decomposition of wire-frame meshes using box-splines

Optimal wavelet decomposition of wire-frame meshes using box...

引用

conference on wavelet applications in signal and image processing V

作者： Strintzis, MG Malassiotis, S Univ. of Thessaloniki (Greece)

ISBN: (纸本)0819425915

Optimal mechanisms are determined for the hierarchical decomposition of wire-frame surfaces. A family of box-splines with compact support, suitable for the approximation of wire-frames is first defined, generated by arbitrary sampling matrices with integer eigenvalues. For each such box-spline, the optimal positioning of the wire-frame nodes is determined for each level of the hierarchical wire-frame decomposition. Criterion of optimality is the minimization of the variance of the error difference between the original surface and its representation at each resolution levels. This is needed so as to ensure that the wire mesh produces at each resolution as close a replica of the original surface as possible. The application of the proposed scheme to the hierarchical coding of 3D wire meshes is experimentally evaluated.

关键词： multiresolution surfaces box-splines minimum variance approximation

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General discrete centered image pyramids

General discrete centered image pyramids

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conference on wavelet applications in signal and image processing V

作者： Brigger, P Unser, M National Institutes of Health (United States)

ISBN: (纸本)0819425915

We present an improved type of image pyramid based on general approximation functions. The type of pyramid proposed maintains the good properties of symmetry and consistent boundary conditions of the Haar pyramid. Moreover, it is not restricted to a piece-wise constant image model, but allows the use of any generating sequence. The centered topology guarantees a clearly defined up-projection of labels and may be employed in applications for contour detection, object recognition and segmentation. We start by introducing the general discrete framework for the design of least squares pyramids using the standard filtering and decimation tools based on arbitrary basis functions. Our design criterion is to minimize the l(2) norm of the approximation error. We then define the centered pyramid and give explicit filter coefficients for odd and even spline approximation functions. Finally, we compare the centered pyramid to the ordinary one and highlight some applications.

关键词： splines multi-resolution decomposition image pyramids least squares pyramids centered pyramids

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Weighted time-frequency and time-scale transforms for non-stationary signal detection

Weighted time-frequency and time-scale transforms for non-st...

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conference on wavelet applications in signal and image processing V

作者： Weiss, LG Sibul, LH The Pennsylvania State Univ. (United States)

ISBN: (纸本)0819425915

Maximum likelihood detectors of narrowband, non-stationary random echos in Gaussian noise can be efficiently implemented in the time-frequency domain. When the transmitted signals have large time-bandwidth products, the natural implementation of estimators and detectors is the time-scale or wavelet transform domain implementation. This paper extends the wavelet transform implementations to include weighted time-frequency or time-scale (TF/TS) transforms. We define weighted TF/TS transforms using Reproducing Kernel Hilbert Space (RKHS) inner products. Inverses of these weighted TF/TS transforms are also given. The particular case of the weight being the inverse noise covariance is presented. We show how weighted transforms are used in the estimator-correlator detection statistic for complex scattering environments in conjunction with cascaded scattering functions so that the resulting detection statistic is much more robust. The weighted TF/TS transform turns out to be a natural transform for solving nonstationary detection, estimation, and filtering problems and has important applications to transient signal estimation in multipath channels with colored non-stationary Gaussian noise.

关键词： weighted time-frequency time-scale transforms cascaded scattering functions nonstationary signal detection

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Pyramid-based multi-sensor image data fusion

Pyramid-based multi-sensor image data fusion

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conference on wavelet applications in signal and image processing V

作者： Aiazzi, B Alparone, L Baronti, S Carla, R Mortelli, L Nello Carrara Research Institute on Electromagnetic Waves (Italy) Univ. of Florence (Italy)

ISBN: (纸本)0819425915

In this work, a multi-resolution procedure based on a generalized Laplacian pyramid (GLP), with p : q (i.e. rational) scale factor, is proposed to merge image data of any resolution and represent them at any scale. The GLP-based data fusion is shown to be slightly superior to those of a similar scheme based on the discrete wavelet transform, (WT) according to a set of parameters established in the literature. Not only fused images look sharper than their original versions, but also textured regions are enhanced without losing their spectral signatures. The pyramid-generating filters can be easily designed for data of any resolutions, differently from the WT, whose filter-bank design is non-trivial when the ratio between the scales of the images to be merged is not a pourer of two. Eventually, remotely sensed images from LandSat TM and from Panchromatic SPOT are fused together. The resulting bands capture multi-spectral features with enhanced contrast and texture, and an increased spatial resolution, thereby expediting automatic analyses for contextual interpretation of the environment.

关键词： multi-sensor image fusion multi-spectral images wavelet transform Laplacian pyramid

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Electrogram analysis during atrial fibrillation using wavelet and neural network techniques

Electrogram analysis during atrial fibrillation using wavele...

引用

conference on wavelet applications in signal and image processing V

作者： Govindan, A Deng, G Power, J La Trobe Univ. (Australia) Austin Hospital (Australia)

ISBN: (纸本)0819425915

Atrial fibrillation (AF) is a common arrhythmia associated with many heart diseases and has a high rate of incidence in the older population. Many of the symptoms of AF are poorly tolerated by patients and if not properly managed, may lead to fatal conditions like embolic stroke. The atrial electrograms during AF show a high degree of non-stationarity AF being progressive in nature, we aim to link the the degree of non-stationarity of the atrial electrogram to the stage of advancement of the disease, the duration of episodes of AF, possibility of spontaneous reversion to sinus rhythm and the defibrillation energy requirement. In this paper we describe a novel algorithm for classifying bipolar electrograms from the right atrium of sheep into four groups - normal sinus rhythm, atrial flutter, paroxysmal AF, chronic AF. This algorithm uses features derived from a wavelet transform representation of the signal to train an artificial neural network which is then used to classify the different arrhythmia. The success rates achieved for each subclass indicates that this approach is well suited for the study of atrial arrhythmia.

关键词： wavelet transform artificial neural networks pattern recognition atrial fibrillation kurtosis non-stationary signal analysis

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Lossless and progressive image coding using optimal pyramidal analysis

Lossless and progressive image coding using optimal pyramida...

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conference on wavelet applications in signal and image processing V

作者： Strintzis, MG Sevintikidis, T Boulgouris, N Univ. of Thessaloniki (Greece)

ISBN: (纸本)0819425915

Pyramidal decomposition is known to be highly useful for progressive and lossless image coding. The present paper presents a methodology for the optimal construction of pyramids by selecting the analysis prefilters and interpolation synthesis postfilters so as to minimize the error variance at each level of the pyramid. This establishes optimally efficient pyramidal lossless compression. It also has the added advantage of producing lossy replicas of the original which, at lower resolutions retain as much similarity to the original as possible. Thus, optimal progressive coding of signals or images is produced, as is needed for many applications such as fast browsing through image databases or hybrid lossless / lossy medical image coding. To achieve efficient lossless coding a scheme is utilized for the reduction of the number of data needed to be transmitted to reconstruct the original from the low resolution image and the errors produced at the various pyramid stages. This scheme in effect renders the pyramid into a ''reduced'' pyramid without sacrificing, however, the optimal analysis prefilters of the pyramid. Experimental application of this methodology shows that it outperforms existing methods for lossless and progressive image coding.

关键词： progressive image transmission lossless image compression reduced pyramids minimum variance filters

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Characterizations of wavelet bases and frames in Hilbert spaces

Characterizations of wavelet bases and frames in Hilbert spa...

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conference on wavelet applications in signal and image processing V

作者： Lee, SL Tang, WS National Univ. of Singapore (Singapore)

ISBN: (纸本)0819425915

Let U = (U-1,..., U-d) be an ordered d-tuple of distinct commuting unitary operators on a complex Hilbert space H, and Y = {y(1),..., y(s)} a finite subset of H. Let U-Zd(Y) = {U(n)y(j) : n is an element of Z(d),j = 1,..., s}, and let Phi(theta) be the s by s matrix function Phi(theta) = ((n is an element of Zd)Sigmae(in-theta))(k,j=1)(s) defined on the d-dimensional torus. We obtain characterizations, in terms of the matrix function Phi(theta), for the set U-Zd(Y) to be (1) a Bessel sequence;or (2) a (tight) frame;or (3) a Riesz basis for its closed linear span in H. Connections with other related work Will also be discussed.

关键词： Bessel sequences frames Riesz bases

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