Multisplines provide a method to get piecewise polynomial representations that zoom in on details. Since they use multiple spline-based multiresolution simultaneously, they offer control on the polynomial order (of th...
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ISBN:
(纸本)0819419281
Multisplines provide a method to get piecewise polynomial representations that zoom in on details. Since they use multiple spline-based multiresolution simultaneously, they offer control on the polynomial order (of the piecewise polynomials) as well as the number of continuous derivatives. We explore some of the properties of multisplines and their relationship to piecewise polynomials. We show that instead of using wavelets to transcend resolutions, we can use the even translates of the scaling function.
We explore the relationship between random processes and wavelets in multiple dimensions and their application to statistical signalprocessing. To this end, we introduce a multiresolution Wiener filter (MWF) that is ...
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ISBN:
(纸本)0819419281
We explore the relationship between random processes and wavelets in multiple dimensions and their application to statistical signalprocessing. To this end, we introduce a multiresolution Wiener filter (MWF) that is applied to the wavelet coefficients of a random process. The MWF is based upon the multiresolution Wiener-Hopf (MWH) equation, which is derived using orthogonal projection theorem on a Hilbert space. The MWH is applied to the solution of the signal estimation problem for both stationary and fractional Brownian motion (fBm) processes. A theoretical mean square error is calculated for the MWF and its values compared to experimental data.
A wavelet processing-based automatic target detection technique has been developed at JPL and demonstrated for mine detection applications. In this approach, first, a multiresolution wavelet decomposition method was u...
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ISBN:
(纸本)0819418528
A wavelet processing-based automatic target detection technique has been developed at JPL and demonstrated for mine detection applications. In this approach, first, a multiresolution wavelet decomposition method was utilized to remove clutter from the input scene so that the false alarm rate due to background clutter could be greatly reduced. Second, a shape-specific ternary-valued wavelet filter was used to perform mine detection. This ternary-valued wavelet filter was successfully implemented in an optical wavelet processor and real-time mine detection was demonstrated. Theoretical analysis of this wavelet processing method will be provided. Experimental results illustrating mine detection will also be presented.
The theory of orthogonal polynomials is used to construct a family of orthogonal wavelet bases of L2(R) which are compactly supported, continuous, and piecewise polynomial and have arbitrary approximation order.
ISBN:
(纸本)0819419281
The theory of orthogonal polynomials is used to construct a family of orthogonal wavelet bases of L2(R) which are compactly supported, continuous, and piecewise polynomial and have arbitrary approximation order.
Periodic spline wavelets provide an efficient tool to analyze periodic signals. Wavelet analysis gives its best performance when it is applied to detect transients or local events in the signal. However, it is not wel...
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ISBN:
(纸本)0819419281
Periodic spline wavelets provide an efficient tool to analyze periodic signals. Wavelet analysis gives its best performance when it is applied to detect transients or local events in the signal. However, it is not well suited to characterize stationary phenomena. To overcome this problem we propose a new family of periodic spline functions, capable of playing the role of trigonometric wave-forms. They lead us to an orthogonal decomposition of the signal into quasi-monochromatic spline waves. Further, a full collection of periodic spline wavelet packets is also proposed. These elemental functions can be organized in a large library of orthonormal bases. Thus, one can analyze any periodic signal in accordance with a well adapted strategy.
Sampling `theorems' in `wavelet spaces' are very useful for the integration of `wavelet multiresolution' techniques with various time-domain methods for data processing. In this paper, the application pote...
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ISBN:
(纸本)0819419281
Sampling `theorems' in `wavelet spaces' are very useful for the integration of `wavelet multiresolution' techniques with various time-domain methods for data processing. In this paper, the application potential of `wavelet sampling theorem' will be illustrated through a few examples of dynamical data analysis and filtering. The main results among our recent applications of the wavelet sampling principles for data processing include the `compact- harmonic wavelets' and a new technique for time-frequency analysis. This new analysis technique provides localized wavelet filters with arbitrarily adjustable frequency-resolution, and the exact reconstruction capability. These filter qualities are both useful and essential for the accurate representation of local power-spectra, and segmentation of signals. These results and underlying ideas are also applicable to the fields of imaging and data compression.
An effective video coding algorithm is described. It is based on a new quadtree block merging algorithm and wavelet decomposition of video signals using orthonormal and biorthogonal filter banks. With the merging algo...
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ISBN:
(纸本)0819417661
An effective video coding algorithm is described. It is based on a new quadtree block merging algorithm and wavelet decomposition of video signals using orthonormal and biorthogonal filter banks. With the merging algorithm the motion compensated predicted images are represented by a small set of rectangular regions in order to improve the coding efficiency and to minimize the border effects associated to the wavelet transform. A new solution to the problem of processing finite length signals by wavelet transforms, based on time-varying perfect reconstruction filter banks will be developed. Results of coding simulations using the merging algorithm with 8 x 8 and 16 x 16 blocks are presented. Also, subjects such as, choice of the optimal filter bank, boundary effects, optimal scalar quantization of the wavelet coefficients and prediction error filtering by wavelet decompositions will be discussed.
The main point of the paper is to discuss the control of the correlation for gamma distributed noise images. There is also presented an algorithm of generating uncorrelated noise images of a good statistical quality, ...
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ISBN:
(纸本)0819418137
The main point of the paper is to discuss the control of the correlation for gamma distributed noise images. There is also presented an algorithm of generating uncorrelated noise images of a good statistical quality, with Gaussian, exponential, gamma and Rayleigh distribution.
This paper describes two approaches for accomplishing interactive feature analysis by overcomplete multiresolution representations. We show quantitatively that transform coefficients, modified by an adaptive non-linea...
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We analyze the statistical properties of a new optical encoding method of images for security applications. The encoded image is obtained by random phase encoding in both input and Fourier planes. We show that this en...
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ISBN:
(纸本)0819419249
We analyze the statistical properties of a new optical encoding method of images for security applications. The encoded image is obtained by random phase encoding in both input and Fourier planes. We show that this encoding method converts the input signal to a stationary white noise and that the reconstruction method is very robust.
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