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...

When one considers the e ect in the physical space, Daubechies-based wavelet methods are equivalent to nite di erence methods with grid re nement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coe cient is, essentially, equivalent to adding a grid point, or two, at the same ...

We consider the continuous wavelet transform [Formula: see text] associated with the Weinstein operator. We introduce the notion of localization operators for [Formula: see text]. In particular, we prove the boundedness and compactness of localization operators associated with the continuous wavelet transform. Next, we analyze the concentration of [Formula: see text] on sets of finite measure. ...

This paper presents a matrix factorization method for implementing orthonormal M-band wavelet reversible integer transforms. Based on an algebraic construction approach, the polyphase matrix of orthonormal M-band wavelet transforms can be factorized into a finite sequence of elementary reversible matrices that map integers to integers reversibly. These elementary reversible matrices can be furt...

The steerable pyramid decomposition is an invertible representation similar to the two-dimensional discrete wavelet transform, but with interesting shiftand rotation-invariance properties. It is slightly overcomplete and amenable to a filter bank implementation via convolution and downand upsampling operations. This paper presents a simple method for designing the FIR filter kernels required to...

The multiresolution theory of orthogonal wavelets proves that any conjugate mirror filter characterizes a wavelet that generates an orthonormal basis of LR. This paper presents a method to obtain a discrete wavelet function, through FIR filter synthesis starting from a random discrete sequence. This sequence is used as a FIR filter which generates the four conjugate mirror filters necessary to ...

AbstmctMultiresolution analysis via decomposition on wavelet bases has emerged as an important tool in the analysis of signals and images when these objects are viewed as sequences of complex or real numbers. An important class of multiresolution decompositions are the so-called Laplacian pyramid schemes, in which the resolution is successively halved by recursively lowpass filtering the signal...

We characterize Riesz frames and prove that every Riesz frame is the union of a finite number of Riesz sequences. Furthermore, it is shown that for piecewise continuous wavelets with compact support, the associated regular wavelet systems can be decomposed into a finite number of linearly independent sets. Finally, for finite sets an equivalent condition for decomposition into a given number of...

Abstract – This paper introduces some foundations of wavelets over Galois fields. Standard orthogonal finite-field wavelets (FFWavelets) including FF-Haar and FFDaubechies are derived. Non-orthogonal FFwavelets such as B-spline over GF(p) are also considered. A few examples of multiresolution analysis over Finite fields are presented showing how to perform Laplacian pyramid filtering of finite ...