In this paper,a Littlewood-Paley function characterization of the spaces L p（R）,1〈p〈∞,is first established by means of the equivalent conditions of tight wavelet frames,wherein the Littlewood-Paley function is as...In this paper,a Littlewood-Paley function characterization of the spaces L p（R）,1〈p〈∞,is first established by means of the equivalent conditions of tight wavelet frames,wherein the Littlewood-Paley function is associated with a tight wavelet frame generated by the so-called extension principles.With the above characterization,another characterization of L p（R）,1〈p〈∞,is also established in terms of the weighted l 2-norm of the wavelet frame coefficients,which can be a useful tool in harmonic analysis,approximation theory,and image processing.展开更多
A new adaptive learning algorithm for constructing and training wavelet networks is proposed based on the time-frequency localization properties of wavelet frames and the adaptive projection algorithm. The exponential...A new adaptive learning algorithm for constructing and training wavelet networks is proposed based on the time-frequency localization properties of wavelet frames and the adaptive projection algorithm. The exponential convergence of the adaptive projection algorithm in finite-dimensional Hilbert spaces is constructively proved, with exponential decay ratios given with high accuracy. The learning algorithm can sufficiently utilize the time-frequency information contained in the training data, iteratively determines the number of the hidden layer nodes and the weights of wavelet networks, and solves the problem of structure optimization of wavelet networks. The algorithm is simple and efficient, as illustrated by examples of signal representation and denoising.展开更多
The homogeneous approximation property （HAP） states that the number of building blocks involved in a reconstruction of a function up to some error is essentially invariant under time-scale shifts. In this paper, we ...The homogeneous approximation property （HAP） states that the number of building blocks involved in a reconstruction of a function up to some error is essentially invariant under time-scale shifts. In this paper, we show that every wavelet frame with nice wavelet function and arbitrary expansive dilation matrix possesses the HAP. Our results improve some known ones.展开更多
基金Supported by the National High Technology Research and Development Program of China (863 Program) (2009AA12Z203,2008AA 12Z201)
文摘In this paper,a Littlewood-Paley function characterization of the spaces L p（R）,1〈p〈∞,is first established by means of the equivalent conditions of tight wavelet frames,wherein the Littlewood-Paley function is associated with a tight wavelet frame generated by the so-called extension principles.With the above characterization,another characterization of L p（R）,1〈p〈∞,is also established in terms of the weighted l 2-norm of the wavelet frame coefficients,which can be a useful tool in harmonic analysis,approximation theory,and image processing.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 69872030) the Natural Science Foundation of Shaanxi Province (Grant No. 98 × 08) Elite Young Teacher Foundation of Ministry of China (1997).
文摘A new adaptive learning algorithm for constructing and training wavelet networks is proposed based on the time-frequency localization properties of wavelet frames and the adaptive projection algorithm. The exponential convergence of the adaptive projection algorithm in finite-dimensional Hilbert spaces is constructively proved, with exponential decay ratios given with high accuracy. The learning algorithm can sufficiently utilize the time-frequency information contained in the training data, iteratively determines the number of the hidden layer nodes and the weights of wavelet networks, and solves the problem of structure optimization of wavelet networks. The algorithm is simple and efficient, as illustrated by examples of signal representation and denoising.
基金Supported partially by National Natural Science Foundation of China(Grant Nos.10971105and10990012)Natural Science Foundation of Tianjin(Grant No.09JCYBJC01000)
文摘The homogeneous approximation property （HAP） states that the number of building blocks involved in a reconstruction of a function up to some error is essentially invariant under time-scale shifts. In this paper, we show that every wavelet frame with nice wavelet function and arbitrary expansive dilation matrix possesses the HAP. Our results improve some known ones.
