Related papers: Phase-Shifting Separable Haar Wavelets and Applica…
Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier…
In this paper, after reviewing the main points of Haar wavelet transform and chaotic trigonometric maps, we introduce a new perspective of Haar wavelet transform. The essential idea of the paper is given linearity properties of the scaling…
The dual-tree complex wavelet transform (DT-CWT) is known to exhibit better shift-invariance than the conventional discrete wavelet transform. We propose an amplitude-phase representation of the DT-CWT which, among other things, offers a…
Phase unwrapping is a key problem in many coherent imaging systems, such as synthetic aperture radar (SAR) interferometry. A general formulation for redundant integration of finite differences for phase unwrapping (Costantini et al., 2010)…
One of the major open problems in computer vision is detection of features in visually impaired images. In this paper, we describe a potential solution using Phase Stretch Transform, a new computational approach for image analysis, edge…
The Special Affine Fourier Transformation(SAFT), which generalizes several well-known unitary transformations, has been demonstrated as a valuable tool in signal processing and optics. In this paper, we explore the multivariate dynamical…
In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the…
It is increasingly being realised that many real world time series are not stationary and exhibit evolving second-order autocovariance or spectral structure. This article introduces a Bayesian approach for modelling the evolving wavelet…
With the development of human communications the usage of Visual Communications has also increased. The advancement of image compression methods is one of the main reasons for the enhancement. This paper first presents main modes of image…
In this paper, we propose a new technique for two-dimensional phase unwrapping. The unwrapped phase is found as the solution of an inverse problem that consists in the minimization of an energy functional. The latter includes a weighted…
Nonlinear metasurfaces that dynamically manipulate the phase of a passing light beam are of interest for a wide range of applications. The controlled operation of such devices requires accurate measurements of the optical transmission phase…
In this paper, we consider domain-invariant deep learning by explicitly modeling domain shifts with only a small amount of domain-specific parameters in a Convolutional Neural Network (CNN). By exploiting the observation that a…
Based on hierarchical partitions, we provide the construction of Haar-type tight framelets on any compact set $K\subseteq \mathbb{R}^d$. In particular, on the unit block $[0,1]^d$, such tight framelets can be built to be with adaptivity and…
This paper is concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to data and a total variation constraint.…
In this paper, we present a new modified Newton method a use of Haar wavelet formula for solving non-linear equations. This new method do not require the use of the second-order derivative. It is shown that the new method has third-order of…
The constant center frequency to bandwidth ratio (Q-factor) of wavelet transforms provides a very natural representation for audio data. However, invertible wavelet transforms have either required non-uniform decimation -- leading to…
We propose an amplitude-phase representation of the dual-tree complex wavelet transform (DT-CWT) which provides an intuitive interpretation of the associated complex wavelet coefficients. The representation, in particular, is based on the…
Haar wavelet is one of the best mathematical tools in image cryptography and analysis. Because of the specific structure, this wavelet has the ability which is combined with other mathematical tools such as chaotic maps. The rational order…
A new phase-coherent technique for the calibration of polarimetric data is presented. Similar to the one-dimensional form of convolution, data are multiplied by the response function in the frequency domain. Therefore, the system response…
Phase shifters are fundamental reconfigurable components in photonic circuits. In conjunction with passive elements, they control light flow and serve as foundational building blocks for diverse applications, including communication,…