Weak nonhomogeneous wavelet dual frames for Walsh reducing subspace of L2(ℝ+)

In wavelet analysis, refinable functions are the bases of extension principles for constructing (weak) dual wavelet frames for [Formula: see text] and its reducing subspaces. This paper addresses refinable function-based dual wavelet frames construction in Walsh reducing subspaces of [Formula: see text]. We obtain a Walsh–Fourier transform domain characterization for weak [Formula: see text]-adic nonhomogeneous dual wavelet frames; and present a mixed oblique extension principle for constructing weak [Formula: see text]-adic nonhomogeneous dual wavelet frames in Walsh reducing subspaces of [Formula: see text].

Dualwavelet frames in Sobolev spaces on local fields of positive characteristic

Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. In this article, we obtain the characterization of nonhomogeneous wavelet frames and nonhomogeneous dual wavelet frames in a Sobolev spaces on a local field of positive characteristic by means of a pair of equations.

Combining dual-tree complex wavelets and multiresolution in iterative CT reconstruction with application to metal artifact reduction

Background This paper investigates the benefits of data filtering via complex dual wavelet transform for metal artifact reduction (MAR). The advantage of using complex dual wavelet basis for MAR was studied on simulated dental computed tomography (CT) data for its efficiency in terms of noise suppression and removal of secondary artifacts. Dual-tree complex wavelet transform (DT-CWT) was selected due to its enhanced directional analysis of image details compared to the ordinary wavelet transform. DT-CWT was used for multiresolution decomposition within a modified total variation (TV) regularized inversion algorithm. Methods In this study, we have tested the multiresolution TV (MRTV) approach with DT-CWT on a 2D polychromatic jaw phantom model with Gaussian and Poisson noise. High noise and sparse measurement settings were used to assess the performance of DT-CWT. The results were compared to the outcome of the single-resolution reconstruction and filtered back-projection (FBP) techniques as well as reconstructions with Haar wavelet basis. Results The results indicate that filtering of wavelet coefficients with DT-CWT effectively removes the noise without introducing new artifacts after inpainting. Furthermore, adoption of multiple resolution levels yield to a more robust algorithm compared to varying the regularization strength. Conclusions The multiresolution reconstruction with DT-CWT is also more robust when reconstructing the data with sparse projections compared to the single-resolution approach and Haar wavelets.

Dual Wavelet Frame Transforms on Manifolds and Graphs

In this paper, we consider the dual wavelet frames in both continuum setting, i.e., on manifolds, and discrete setting, i.e., on graphs. Firstly, we give sufficient conditions for the existence of dual wavelet frames on manifolds by their corresponding masks. Then, we present the formula of the decomposition and reconstruction for the dual wavelet frame transforms on graphs. Finally, we give a numerical example to illustrate the validity of the dual wavelet frame transformation applied to the graph data.