Related papers: Constructing an orthonormal wavelet from an MRA
In constructive quantum field theory (CQFT) it is customary to first regularise the theory at finite UV and IR cut-off. Then one first removes the UV cutoff using renormalisation techniques applied to families of CQFT's labelled by finite…
We introduce a construction of multiscale tight frames on general domains. The frame elements are obtained by spectral filtering of the integral operator associated with a reproducing kernel. Our construction extends classical wavelets as…
In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-supported wavelets and boundary wavelets. We prove that the…
Given any $\varepsilon>0$, we construct an orthonormal system of $n_k$ uniformly bounded polynomials of degree at most $k$ on the unit sphere in $\mathbb R^{m+1}$ where $n_k$ is bigger than $1-\varepsilon$ times the dimension of the space…
An explicit description of all Walsh polynomials generating tight wavelet frames is given. An algorithm for finding the corresponding wavelet functions is suggested, and a general form for all wavelet frames generated by an appropriate…
This paper studies the multi-reference alignment (MRA) problem of estimating a signal function from shifted, noisy observations. Our functional formulation reveals a new connection between MRA and deconvolution: the signal can be estimated…
Ophthalmological imaging utilizes different imaging systems, such as color fundus, infrared, fluorescein angiography, optical coherence tomography (OCT) or OCT angiography. Multiple images with different modalities or acquisition times are…
In this paper we show how wavelets originating from multiresolution analysis of scale N give rise to certain representations of the Cuntz algebras O_N, and conversely how the wavelets can be recovered from these representations. The…
In this paper we present a construction of interpolatory Hermite multiwavelets for functions that take values in nonlinear geometries such as Riemannian manifolds or Lie groups. We rely on the strong connection between wavelets and…
Defect detection by ultrasonic method is limited by the pulse width. Resolution can be improved through a deconvolution process with a priori information of the pulse or by its estimation. In this paper a regularization of the Wiener filter…
In this paper, we show that high-dimensional sparse wavelet signals of finite levels can be constructed from their partial Fourier measurements on a deterministic sampling set with cardinality about a multiple of signal sparsity.
We present applications of variational -- wavelet approach to nonlinear (rational) rms envelope dynamics. We have the solution as a multiresolution (multiscales) expansion in the base of compactly supported wavelet basis.
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
We propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies…
Classical orthogonal wavelets guarantee perfect reconstruction but rely on fixed bases optimized for polynomial smoothness, achieving suboptimal compression on signals with fractal spectral signatures. Conversely, learned methods offer…
Medical imaging modalities including magnetic resonance imaging (MRI), computed tomography (CT), and ultrasound are essential for accurate diagnosis and treatment planning in modern healthcare. However, noise contamination during image…
The goal of MRI reconstruction is to restore a high fidelity image from partially observed measurements. This partial view naturally induces reconstruction uncertainty that can only be reduced by acquiring additional measurements. In this…
This tutorial paper describes the problem of image reconstruction from interferometric data with a particular focus on the specific problems encountered at optical (visible/IR) wavelengths. The challenging issues in image reconstruction…
Wavelet systems on the generalized Vilenkin groups are considered. An algorithmic method for the construction of orthogonal wavelet bases is presented. These bases consist of compactly supported test functions (i.e. functions whose Fourier…
We construct representations of a q-oscillator algebra by operators on Fock space on positive matrices. They emerge from a multiresolution scaling construction used in wavelet analysis. The representations of the Cuntz Algebra arising from…