The three-dimensional biorthogonal multi-resolution time-domain (Bi-MRTD) method is presented for both free-space and half-space scattering problems. The perfectly matched layer (PML) is used as an absorbing boundary condition. It has been shown that improved numerical-dispersion properties can be obtained with the use of smooth, compactly-supported wavelet functions as the basis, where here we...

Surface wavelet representations [1] are a generalization of classical wavelets on the real line. They allow us to build a multilevel model of spatial data that is defined on an irregular mesh describing a general domain. Such wavelet representations differ from the classical case in that the wavelet filters are spatially variant. Using surface wavelets, one can develop a biorthogonal geometry-a...

As ideal tools, autonomous underwater vehicles (AUVs) are used to implement underwater monitoring missions instead of human. Because the underwater images captured are many close-range images, the mosaicing and fusion method is applicable to create large visual representations of the sea floor. A novel mosaicing and fusion approach based on weighted aggregation energy threshold using Biorthogon...

The method of Dubuc and Deslauriers on symmetric interpolatory subdivision is extended to study the relationship between interpolation processes and wavelet construction. Refinable and interpolatory functions are constructed in stages from B-splines. Their method constructs the filter sequence (its Laurent polynomial) of the interpolatory function as a product of Laurent polynomials. This provi...

A three-dimensional multi-resolution time-domain (MRTD) analysis is presented based on a biorthogonal-wavelet expansion, with application to electromagnetic-scattering problems. We employ the Cohen-Daubechies-Feauveau (CDF) biorthogonal wavelet basis, characterized by the maximum number of vanishing moments for a given support. We utilize wavelets and scaling functions of compact support, yield...

This paper clarifies the concepts and relationship between image fusion rules and operators based on wavelet transform. According to wavelet decomposition characteristic, a new strategy of calculating spatial frequency is put forward. Fusion experiments are performed on QuickBird panchromatic (PAN)and multispectral (MS) images based on orthogonal and biorthogonal wavelet, in which a method of c...

Orthogonal, semiorthogonal and biorthogonal wavelet bases are special cases of oblique multiwavelet bases. One of the advantage of oblique multiwavelets is the flexibility they provide for constructing bases with certain desired shapes and/or properties. The decomposition of a signal in terms of oblique wavelet bases is still a perfect reconstruction filter bank. In this paper, we present sever...

Wavelet transforms for discrete-time periodic signals are developed. In this nite-dimensional context, key ideas from the continuous-time papers of Daubechies and of Cohen, Daubechies, and Feauveau are isolated to give a concise, rigorous derivation of the discrete-time periodic analogs of orthonormal and symmetric biorthogonal bases of compactly supported wavelets. These discrete-time periodic...

We make a deep study of the distance between frames and between subspaces of a Hilbert space. There are many surprises here. First, of the six standard ways of measuring distance between subspaces, 5 of them are equal and the sixth, chordal distance, is within a factor of 2 of the others. We also show that the vectors giving chordal distance are biorthogonal which the definition does not indica...

The aim of the paper is to examine the wavelet-Galerkin method for the solution of filtering equations. We use a wavelet biorthogonal basis with compact support for approximations of the solution. Then we compute the Zakai equation for our filtering problem and consider the implicit Euler scheme in time and the Galerkin scheme in space for the solution of the Zakai equation. We give theorems on...