We investigate the formulation of boundary compensated wavelet transforms supported on a nite interval. A uni ed approach to boundary compensated wavelet transforms is presented which fosters new insights into previous constructions, including both continuous and discrete approaches to the problem. The framework enables the design of boundary-compensated transforms with speci c properties, incl...

Tight wavelet frames and orthonormal wavelet bases with a general dilation matrix have applications in many areas. In this paper, for any d × d dilation matrix M , we demonstrate in a constructive way that we can construct compactly supported tight M -wavelet frames and orthonormal M -wavelet bases in L2(R) of exponential decay, which are derived from compactly supported M -refinable functions,...

We propose a construction of periodic rational bases of wavelets First we explain why this problem is not trivial Construction of wavelet basis is not possible neither for the case of alge braic polynomials nor for the case of rational algebraic functions Of course algebraic polynomials do not belong to L R Nevertheless they can belong to the closure of L R in topology of the generalized conver...

The purpose of this presentation is to describe a recent family of basis functions—the fractional B-splines—which appear to be intimately connected to fractional calculus. Among other properties, we show that they are the convolution kernels that link the discrete (finite differences) and continuous (derivatives) fractional differentiation operators. We also provide simple closed forms for the ...

Recent wavelet research has primarily focused on real-valued wavelet bases. However, complex wavelet bases offer a number of potential advantageous properties. For example, it has been recently suggested that the complex Daubechies wavelet can be made symmetric. However, these papers always imply that if the complex basis has a symmetry property, then it must exhibit linear phase as well. In th...

The purpose is to study qualitative and quantitative rates of image compression by using different Haar wavelet banks. The experimental results of adaptive compression are provided. The paper deals with specific examples of orthogonal Haar bases generated by multiresolution analysis. Bases consist of three piecewise constant wavelet functions with a support $[0,1] \times [0,1] $.

Recent wavelet research has primarily focused on real-valued wavelet bases. However, complex wavelet bases ooer a number of potential advantageous properties. For example, it has been recently suggested 1], 2] that the complex Daubechies wavelet can be made symmetric. However, these papers always imply that if the complex basis has a symmetry property then it must exhibit linear phase as well. ...

In this paper, we compare different adaptation criterions of the proposed two dimensional wavelet filter bank with a variable number of zero moments. Twodimensional generalization of the previously reported 1D algorithm is based on nonseparable quincunx scheme. 2-D filters were designed directly, rather then obtained from 1-D filters using pyramid scheme. Filter banks with more zero moments are...

In this paper we present a novel multiresolution scheme for the detection of spiculated lesions in digital mammograms. First, a multiresolution representation of the original mammogram is obtained using a linear phase nonseparable 2-D wavelet transform. A set of features is then extracted at each resolution in the wavelet pyramid for every pixel. This approach addresses the difficulty of predet...

The concepts of basis and frame are studied in the classical literature of functional analysis, Fourier analysis, and wavelet theory in a wide range. In this paper, we consider an operator-theoretic approach to discrete frame theory on a separable Hilbert space. For this purpose, we define a special type of frames and bases, called wavelet-type frames and wavelet-type bases, obtained by acting ...