Families of Orthogonal 2d Wavelets

Families of Orthogonal Two-dimensional Wavelets

We construct orthonormal wavelet bases of L2(IR) with compact support for dilation matrices of determinant 2. The key idea is to describe the set H2 of all two-dimensional (2D) scaling coefficients satisfying the orthogonality condition as an implicit function. This set includes the scaling coefficients for induced 1D wavelets. We compute the tangent space of H2 at HN , the scaling coefficients...

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)

Orthogonal quincunx wavelets with fractional orders

We present a new family of 2D orthogonal wavelets which uses quincunx sampling. The orthogonal refinement filters have a simple analytical expression in the Fourier domain as a function of the order α, which may be non-integer. The wavelets have good isotropy properties. We can also prove that they yield wavelet bases of L2(R) for any α > 0. The wavelets are fractional in the sense that the app...

On the Zeros of Daubechies Orthogonal and Biorthogonal Wavelets

In the last decade, Daubechies’ wavelets have been successfully used in many signal processing paradigms. The construction of these wavelets via two channel perfect reconstruction filter bank requires the identification of necessary conditions that the coefficients of the filters and the roots of binomial polynomials associated with them should exhibit. In this paper, orthogonal and Biorthogona...

Signal and Image Denoising via Wavelet Thresholding

{ In this paper we discuss wavelet thresholding in the context of scalar orthogonal, scalar biorthogonal, multiple orthogonal and multiple biorthogonal wavelet transforms. Two types of multiwavelet thresholding are considered: scalar and vector. Both of them take into account the covariance structure of the transform. The form of the universal threshold is carefully formulated. The results of n...