On this paper, wavelet analysis has been used for internal wave detection in ERS SAR and ASTER images data over Tsushima strait, southwest of Japan, during 1993-2004 period. Various wavelet transforms, such as Haar wavelet, Symlet wavelet, Coif wavelet, Daubechies wavelet, and Discreet Meyer wavelet, are tested comparably with different level of synthesize image on horizontal, diagonal, and ver...

As shown by Dahmen, Harbrecht and Schneider [7, 23, 32], the fully discrete wavelet Galerkin scheme for boundary integral equations scales linearly with the number of unknowns without compromising the accuracy of the underlying Galerkin scheme. The supposition is a wavelet basis with a sufficiently large number of vanishing moments. In this paper we present several constructions of appropriate ...

The multiscale (wavelet) decomposition of the solution is proposed for the analysis of the Poisson problem. The approximate solution is computed with respect to a finite dimensional wavelet space [4, 5, 7, 8, 16, 15] by using the Galerkin method. A fundamental role is played by the connection coefficients [2, 7, 11, 9, 14, 17, 18], expressed by some hypergeometric series. The solution of the Po...

A new set of wavelet filter families has been added to the systematized collection of Daubechies wavelets. This new set includes complex and real, orthogonal and biorthogonal, least and most disjoint families defined using constraints derived from the principle of separably disjoint root sets in the complex z-domain. All of the new families are considered to be constraint selected without a sea...

, where C0 = ∫ 1 0 f(t)dt. j ∼ scale, k ∼ position. Key properties: 1. vanishing moments: We say ψ has M vanishing moments when ∫ 1 0 tψj,k(t)dt = 0 form = 0, 1, . . . ,M− 1 This means the wavelet is “blind” to polynomial segment with degree α ≤M − 1 2. compact support: a daubechies wavelet with M vanishing moments has support ∝ 2M. Together, these properties imply that only O(l log n) nonzero ...

An iterative scheme for constructing compactly supported orthonormal (o.n.) multi-wavelets with vanishing moments of arbitrarily high order is established. Precisely, let φ = [φ1, · · · , φr] be an r-dimensional o.n. scaling function vector with polynomial preservation of order (p.p.o.) m, and ψ = [ψ1, · · · , ψr] an o.n. multiwavelet corresponding to φ, with two-scale symbols P and Q, respecti...

Explicit solutions are given for the rational function P (z) for two classes of IIR orthogonal 2-band wavelet bases, for which the scaling lter is maximally at. P (z) denotes the rational transfer function H(z)H(1=z) where H(z) is the (lowpass) scaling lter. The rst is the class of solutions that are intermediate , between the Daubechies and the Butterworth wavelets. It is found that the Daubec...