In this paper we study the application of divergence-free wavelet bases for the analysis of incompressible turbulent flows and perform several experiments. In particular, we analyze various nominally incompressible fields and study the influence of compressible perturbations due to experimental and computational errors. In addition, we investigate the multiscale structure of modes obtained from...

Let • • • C K_ ] c Vq c Vx c • • • be a multiresolution analysis of L2 generated by the mth order 5-spline Nm{x). In this paper, we exhibit a compactly supported basic wavelet i//m(x) that generates the corresponding orthogonal complementary wavelet subspaces .quently, the two finite sequences that describe the two-scale relations of Nm(x) and i//m(x) in terms of Nm(2x-j), ;6Z, yield an efficie...

The orthogonal wavelet lowpassed filters coefficients with arbitrary length are constructed in this paper. When N=2k and N k = − 1 2 , the general analytic constructions of orthogonal wavelet filters are put forward, respectively. The famous Daubechies filter and many other wavelet filters are tested by the proposed novel method, which is very useful for wavelet theory research and many applica...

In this paper, a two-dimensional multi-wavelet is constructed in terms of Chebyshev polynomials. The constructed multi-wavelet is an orthonormal basis for space. By discretizing two-dimensional Fredholm integral equation reduce to a algebraic system. The obtained system is solved by the Galerkin method in the subspace of by using two-dimensional multi-wavelet bases. Because the bases of subs...

The main objective of this course is to conduct a study on wavelet theory from both theoretical and application perspective (such as signal compression, denoising, communication systems, and recognition) in a coherence manner. The course first builds up background on LTI operators and Fourier analysis (including Shannon’s sampling theory) and its short comings. Windowed Fourier Transform (WFT) ...

One important category of non-ideal conditions for iris recognition is off-angle iris images. Practically it is very difficult for images to be captured with no offset. It then becomes necessary to account for off angle information in order to maintain robust performance. A bi-orthogonal wavelet based iris recognition system, previously designed at our lab, is modified and demonstrated to perfo...

We describe bases of smooth wavelets where the coeecients are obtained by integration against ((nite combinations of) boxcar kernels rather than against traditional smooth wavelets. Bases of this type were rst developed in work of Tchamitchian and of Cohen, Daubechies, and Feauveau. Our approach emphasizes the idea of average-interpolation { synthesizing a smooth function on the line having pre...

A refinable function φ(x) : Rn → R or, more generally, a refinable function vector 8(x) = [φ1(x), . . . , φr (x)]T is an L1 solution of a system of (vector-valued) refinement equations involving expansion by a dilation matrix A, which is an expanding integer matrix. A refinable function vector is called orthogonal if {φj (x − α) : α ∈ Zn, 1 ≤ j ≤ r} form an orthogonal set of functions in L2(Rn)...