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 opera...
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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.
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 ...
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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) signalprocessing.
The wavelet paradigm is now well established and has found many applications in signal and imageprocessing. Since also some of its precursors can be reformulated into wavelet terminology, it has become a preferred to...
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The wavelet paradigm is now well established and has found many applications in signal and imageprocessing. 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.
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 a...
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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.
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. Mor...
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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.
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, t...
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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.
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. Th...
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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.
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 prop...
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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.
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 an...
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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.
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...
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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.
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