Related papers: On alternative wavelet reconstruction formula: a c…
The generalized Morse wavelets are shown to constitute a superfamily that essentially encompasses all other commonly used analytic wavelets, subsuming eight apparently distinct types of analysis filters into a single common form. This…
The influence of higher-order wavelet properties on the analytic wavelet transform behavior is investigated, and wavelet functions offering advantageous performance are identified. This is accomplished through detailed investigation of the…
A wavelet is a localized function having a prescribed number of vanishing moments. In this correspondence, we provide precise arguments as to why the Hilbert transform of a wavelet is again a wavelet. In particular, we provide sharp…
This paper aims to study the $q$-wavelet and the $q$-wavelet transforms, associated with the $q$-Bessel operator for a fixed $q\in ]0, 1[$. As an application, an inversion formulas of the $q$-Riemann-Liouville and $q$-Weyl transforms using…
We revisit the feasibility approach to the construction of compactly supported smooth orthogonal wavelets on the line. We highlight its flexibility and illustrate how symmetry and cardinality properties are easily embedded in the design…
In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT…
We obtain a characterization of all wavelets leading to analytic wavelet transforms (WT). The characterization is obtained as a by-product of the theoretical foundations of a new method for wavelet phase reconstruction from magnitude-only…
The wavelet analysis technique is a powerful tool and is widely used in broad disciplines of engineering, technology, and sciences. In this work, we present a novel scheme of constructing continuous wavelet functions, in which the wavelet…
Using continuous wavelet transform it is possible to construct a regularization procedure for scale-dependent quantum field theory models, which is complementary to functional renormalization group method in the sense that it sums up the…
In this paper we consider the continuous wavelet transform using Gaussian wavelets multiplied by an appropriate rational term. The zeros and poles of this rational modifier act as free parameters and their choice highly influences the shape…
Orthogonal wavelet transforms are a cornerstone of modern signal and image denoising because they combine multiscale representation, energy preservation, and perfect reconstruction. In this paper, we show that these advantages can be…
The representation of solutions of Maxwell's equations as superpositions of scalar wavelets with vector coefficients developed earlier is generalized to wavelets with polarization, which are matrix-valued. The construction proceeds in four…
We introduce an extension of continuous wavelet theory that enables an efficient implementation of multiplicative operators in the coefficient space. In the new theory, the signal space is embedded in a larger abstract signal space -- the…
A new construction of a directional continuous wavelet analysis on the sphere is derived herein. We adopt the harmonic scaling idea for the spherical dilation operator recently proposed by Sanz et al. but extend the analysis to a more…
In the present work the well known Farey map is exploited to consruct a new mother wavelet. Properties such as admissibility, moments, 2-scale relation and reconstruction rule have been established. The constructed mother may be a good…
Marchenko focusing functions are in their essence wavefields that satisfy the wave equation subject to a set of boundary, initial, and focusing conditions. Here, we show how Marchenko focusing functions can be modeled by finding the…
Wavelet transformation stands as a cornerstone in modern data analysis and signal processing. Its mathematical essence is an invertible transformation that discerns slow patterns from fast ones in the frequency domain. Such an invertible…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
Using distribution theory we present the moment asymptotic expansion of continuous wavelet transform in different distributional spaces for large and small values of dilation parameter $a$. We also obtain asymptotic expansions for certain…
In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet…