There exist efficient methods to compute the wavelet coefficients of a function f(t) from its point samples f ( T [n + τ ] ) , n ∈ N. However, in many applications the available samples are average samples of the type ∫∞ −∞ f ( T [t + n + τ ] ) u(t)dt, where the averaging function u(t) reflects the characteristic of the acquisition device. In this work, methods to compute the coefficients in a ...

For orthogonal wavelets, the discrete wavelet and wave packet transforms and their inverses are orthogonal operators with perfect numerical stability. For biorthogonal wavelets, numerical instabilities can occur. We derive bounds for the 2-norm and average 2-norm of these transforms, including eecient numerical estimates if the number L of decomposition levels is small, as well as growth estima...

We present a new family of compactly supported and symmetric biorthogonal wavelet systems. Each refinement mask in this family has tension parameter ω. When ω = 0, it becomes the minimal length biorthogonal Coifman wavelet system [17]. Choosing ω away from zero, we can get better smoothness of the refinable functions at the expense of slightly larger support. Though the construction of the new ...

In this paper, it is shown that the higher compression performance of biorthogonal wavelet filters over orthogonal wavelet filters is the combined effect from (1) the asymmetry of the frequency responses of the biorthogonal wavelet filters and (2) the non-flat spectra of the signals to be decomposed. Based upon this observation, an improved wavelet packet decomposition method for natural images...

In this paper, we present the estimation of Poisson intensity based on hypothesis testing in the wavelet domain for any dimensional data. The testing framework for wavelet-based Poisson intensity estimation was first introduced by Kolaczyk, where a thresholding estimator, which realizes the hypothesis testing, is derived for Haar wavelet coefficients. Here we propose for the same wavelet a new ...

The existence in L2(R) of biorthogonal wavelet bases associated with perfect reconstruction 2 channel filter banks comprising finite, real filters is determined by the eigenvalues of two related Lawton matrices. Each Lawton matrix is required to have a simple eigenvalue at one and all remaining eigenvalues must have modulus less than one. This being the case then the wavelet bases are said to b...

On the n-dimensional hypercube, for given k ∈ N, biorthogonal wavelet Riesz bases are constructed for the subspace of divergence-free vector fields of the Sobolev space Hk((0, 1)n)n with general homogeneous Dirichlet boundary conditions, including slip or no-slip boundary conditions. Both primal and dual wavelets can be constructed to be locally supported. The construction of the isotropic wave...