We derive the conditions for the existence of the unique solution of the two scale integral equation and the form of the solution, according to the method of the construction of the dyadic scale function. We give the ...We derive the conditions for the existence of the unique solution of the two scale integral equation and the form of the solution, according to the method of the construction of the dyadic scale function. We give the construction of the dyadic wavelet and its necessary and sufficient condition. As an application, we also develop a pyramid algorithm of the dyadic wavelet decomposition.展开更多
Using the Walsh-Fourier transform, we give a construction of compactly supported nonstationary dyadic wavelets on the positive half-line. The masks of these wavelets are the Walsh polynomials defined by finite sets of...Using the Walsh-Fourier transform, we give a construction of compactly supported nonstationary dyadic wavelets on the positive half-line. The masks of these wavelets are the Walsh polynomials defined by finite sets of parameters. Application to compression of fractal functions are also discussed.展开更多
A new method for constructing locally supported radial wavelet frame or basis, which is different from the multiresolution analysis, is proposed. A continuously differentiable radial function with a local, support is ...A new method for constructing locally supported radial wavelet frame or basis, which is different from the multiresolution analysis, is proposed. A continuously differentiable radial function with a local, support is chosen at first. Then a radial wavelet is obtained by the first and second derivatives of the radial function. If the radial function is both locally supported and infinitely differentiable, so is the radial wavelet. It is shown that the radial wavelet is a multidimensional dyadic one. I. Daubechies’ wavelet frame Theorem is extended from one dimension ton dimensions. It is proven that the family generated by dilations and translations from a single radial wavelet can constitute a frame inL 2(? n ). Consequently, it is concluded that the radial wavelet family generated by dilations and translations combined with their linear combination can constitute an orthonormal basis inL 2(? n ). Finally, an example of the radial wavelet, which is inseparable and with a local support and infinitely high regularity, is given based on the framework given here. As an application, a class of wavelet network for image denoising is designed, and an underrelaxation iterative fastlearning algorithm with varied learning rate is given as well.展开更多
文摘We derive the conditions for the existence of the unique solution of the two scale integral equation and the form of the solution, according to the method of the construction of the dyadic scale function. We give the construction of the dyadic wavelet and its necessary and sufficient condition. As an application, we also develop a pyramid algorithm of the dyadic wavelet decomposition.
文摘Using the Walsh-Fourier transform, we give a construction of compactly supported nonstationary dyadic wavelets on the positive half-line. The masks of these wavelets are the Walsh polynomials defined by finite sets of parameters. Application to compression of fractal functions are also discussed.
基金Project supported by the National Natural Science Foundation of China (Grant No. 69735010) and Doctorate Foundation of Xi' an Jiaotong University.
文摘A new method for constructing locally supported radial wavelet frame or basis, which is different from the multiresolution analysis, is proposed. A continuously differentiable radial function with a local, support is chosen at first. Then a radial wavelet is obtained by the first and second derivatives of the radial function. If the radial function is both locally supported and infinitely differentiable, so is the radial wavelet. It is shown that the radial wavelet is a multidimensional dyadic one. I. Daubechies’ wavelet frame Theorem is extended from one dimension ton dimensions. It is proven that the family generated by dilations and translations from a single radial wavelet can constitute a frame inL 2(? n ). Consequently, it is concluded that the radial wavelet family generated by dilations and translations combined with their linear combination can constitute an orthonormal basis inL 2(? n ). Finally, an example of the radial wavelet, which is inseparable and with a local support and infinitely high regularity, is given based on the framework given here. As an application, a class of wavelet network for image denoising is designed, and an underrelaxation iterative fastlearning algorithm with varied learning rate is given as well.
