International Journal of Wavelets, Multiresolution and Information Processing

Let T be a Calderón–Zygmund operator on Heisenberg group ℍ^d. In this paper, by wavelets, we introduce a class of pseudo-annular operators {T_R}_R≥1 to decompose T. By controlling the bandwidth of T_R, we could obtain the approximate rate of T from L²(ℍ^d) to L²(ℍ^d) at an ideal rate.

In this paper, we describe an approach to construct of biorthogonal N-periodic discrete MRA wavelets on the basis of generalized Walsh functions. The proposed method is illustrated by a numerical example.

The purpose of this paper is to investigate some properties of the Wiener amalgam spaces. As applications, we study the boundedness properties of some singular convolution operators on such spaces. From our results, we will see that, besides modulation spaces, Wiener amalgam spaces are another good substitutions for Lebesgue spaces.

In this paper, we introduce the notion of a nonuniform N-multiwavelet set and provide a characterization for it. Besides, we describe the counterpart of wavelet induced isomorphism for a dyadic multiwavelet set as well as for a nonuniform N-multiwavelet set of order L.

The idea of multiplexing motivates us to develop the theory on the Fourier transform (FT) of multivector-valued functions. In this paper, in the framework of Clifford analysis, we establish a Heisenberg–Pauli–Weyl type uncertainty principle for the FT of multivector-valued functions.

The image registration problem involves determining a geometric transformation to properly align images of interest. This paper proposes a transformation approach called Continuous Piecewise Affine Transformation (CPAT) to model the geometric distortion in images. The associated design methodology for the 2D registration problem is also discussed. Registration on CPAT has two advantages: (1) The optimal transformation has a closed form analytical solution; and (2) the transformation is invertible and transitive. Because of these advantages, CPAT could be used for real-time registration and progressive registration, where the registration speed and transitivity property are important for the successful completion of the tasks. The results of experiments demonstrate the efficacy of CPAT in resolving the image registration problem.

In this paper, a simple method is given in order to construct an area preserving mapping from a developable surface M to a plane. Based on the area preserving projection, we give some important formulas on M, and define a multi-resolution analysis on L²(M). We provide the conditions to further discuss the continuous wavelet transform and discrete wavelet transform on developable surface. At the same time, we derived two-scale equations that the scaling function and wavelet function on developable surface satisfied, we also define and discuss the orthogonality, and several important theorems are given. Finally, we construct the numerical examples. The focus of this paper is the area preserving mapping that from developable surface M to a plane, and the discrete wavelet transform on developable surface.