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This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc., to appear
Externí odkaz:
http://arxiv.org/abs/2501.01929
While ridges in the scalogram, determined by the squared modulus of analytic wavelet transform (AWT), have been widely applied in time series analysis and time-frequency analysis, their behavior in noisy environments remains underexplored. We fill in
Externí odkaz:
http://arxiv.org/abs/2501.00270
Autor:
Khachiaa, Najib
The aim of this work is to study (Multi-window) Gabor systems in the space \(\ell^2(\mathbb{Z} \times \mathbb{Z}, \mathbb{H})\), denoted by $\mathcal{G}(g,L,M,N)$, and defined by: \[ \left\{ (k_1,k_2)\in \mathbb{Z}^2\mapsto e^{2\pi i \frac{m_1}{M}k_1
Externí odkaz:
http://arxiv.org/abs/2411.16988
We prove a sharp quantitative version of recent Faber-Krahn inequalities for the continuous Wavelet transforms associated to a certain family of Cauchy wavelet windows . Our results are uniform on the parameters of the family of Cauchy wavelets, and
Externí odkaz:
http://arxiv.org/abs/2411.16010
Autor:
Khachiaa, Najib
This paper aims to explore the concept of continuous \( K \)-frames in quaternionic Hilbert spaces. First, we investigate \( K \)-frames in a single quaternionic Hilbert space \( \mathcal{H} \), where \( K \) is a right $\mathbb{H}$-linear bounded op
Externí odkaz:
http://arxiv.org/abs/2411.07937
Autor:
Lu, Ran
Interpolatory filters are of great interest in subdivision schemes and wavelet analysis. Due to the high-order linear-phase moment property, interpolatory refinement filters are often used to construct wavelets and framelets with high-order vanishing
Externí odkaz:
http://arxiv.org/abs/2411.04485
Autor:
Khachiaa, Najib
The aim of this paper is to study $K$-frames for quaternionic Hilbert spaces. First, we present the quaternionic version of Douglas's theorem and then investigate $K$-frames for a quaternionic Hilbert space $\mathcal{H}$, where $K \in \mathbb{B}(\mat
Externí odkaz:
http://arxiv.org/abs/2411.04154
Autor:
Khachiaa, Najib
The aim of this work is to study frame theory in quaternionic Hilbert spaces. We provide a characterization of frames in these spaces through the associated operators. Additionally, we examine frames of the form $\{Lu_i\}_{i \in I}$, where $L$ is a r
Externí odkaz:
http://arxiv.org/abs/2411.03790
Autor:
Svela, Erling A. T.
Daubechies-type theorems for localization operators are established in the multi-variate setting, where Hagedorn wavepackets are identified as the proper substitute of the Hermite functions. The class of Reinhardt domains is shown to be the natural c
Externí odkaz:
http://arxiv.org/abs/2410.18769
Publikováno v:
IET Image Processing, Vol.12, No.9, 1626--1638, August 2018
Wavelet-based segmentation approaches are widely used for texture segmentation purposes because of their ability to characterize different textures. In this paper, we assess the influence of the chosen wavelet and propose to use the recently introduc
Externí odkaz:
http://arxiv.org/abs/2410.19191