Tensor product (separable) multivariate (bi)orthogonal wavelets have been widely used in many applications. On the other hand, non-tensor product (nonseparable) wavelets have been extensively argued in the literature to have many advantages over separable wavelets, for example, more freedom in design of nonseparable wavelets (such design is typically much more complicated and di±cult than the a...

In this paper we show additional properties of the limit of the sequence produced by the subspace correction algorithm proposed by Fornasier and Schönlieb [24] for L2/TV -minimization problems. Inspired by the work of Vonesch and Unser [34], we adapt and specify this algorithm to the case of an orthogonal wavelet space decomposition and for deblurring problems.

We propose a construction of new wavelet-like bases that are well suited for the reconstruction and processing of optically generated Fresnel holograms recorded on CCD-arrays. The starting point is a wavelet basis of L2 to which we apply a unitary Fresnel transform. The transformed basis functions are shift-invariant on a level-by-level basis but their multiresolution properties are governed by...

Satisficing search algorithms are proposed for adaptively selecting near-best basis and near-best frame decompositions in redundant tree-structured wavelet transforms. Any of a variety of additive or non-additive information cost functions can be used as the decision criterion for comparing and selecting nodes when searching through the tree. The algorithms are applicable to tree-structured tra...

It is shown that regularity of orthogonal wavelet matrices, i.e. vanishing of discrete moments of some of their rows, corresponds to maximizing the discrete moments of one of the rows. This leads to an algorithm for calculation of such wavelets by nding a vector which simultaneosly vanishes certain indeenite quadratic forms.

We encounter a wide range of sounds everyday which are harmonic, transient or a mixture of both. A number of models have been developed in recent years to synthesise harmonic sounds but these models do not perform effectively on transient sounds because of the sharp attack and decay part of the transient sounds. This paper presents a new technique for analysis-based synthesis of transient sound...

The main goal of the paper is to show that wavelet transforms and packets have the multiparametric representation in the form of a product of the rotation Jacobi matrices. These representations we call the third and the fourth canonical multiparametric form. Each multiparametric wavelet transform (MPWT) depends on several free Jacobi parameters. When parameters are changed multiparametric trans...

Orthogonal wavelet bases have been developed using multiple mother wavelet functions. Applying the discrete multiwavelet transform requires the input data to be preprocessed to obtain a more economical decomposition. Four characteristics of a preprocessing method are presented: length, degree, orthogonality and frequency response. A minimal preelter is deened to have length one and highest atta...

Ivan W. Selesnick Electrical Engineering, Polytechnic University 6 Metrotech Center, Brooklyn, NY 11201 [email protected] ABSTRACT This paper describes design procedures, based on spectral factorization, for the design of pairs of dyadic wavelet bases where the two wavelets form a Hilbert transform pair. Both orthogonal and biorthogonal FIR solutions are presented, as well as IIR solutions. ...