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Data-driven optimal shrinkage of singular values under high-dimensional noise with separable covariance structure with application Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-09-12 Pei-Chun Su, Hau-Tieng Wu
We develop a data-driven optimal shrinkage algorithm, named extended OptShrink (eOptShrink), for matrix denoising with high-dimensional noise and a separable covariance structure. This noise is colored and dependent across samples. The algorithm leverages the asymptotic behavior of singular values and vectors of the noisy data's random matrix. Our theory includes the sticking property of non-outlier
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Construction of pairwise orthogonal Parseval frames generated by filters on LCA groups Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-09-07 Navneet Redhu, Anupam Gumber, Niraj K. Shukla
The generalized translation invariant (GTI) systems unify the discrete frame theory of generalized shift-invariant systems with its continuous version, such as wavelets, shearlets, Gabor transforms, and others. This article provides sufficient conditions to construct pairwise orthogonal Parseval GTI frames in satisfying the local integrability condition (LIC) and having the Calderón sum one, where
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Robust sparse recovery with sparse Bernoulli matrices via expanders Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-08-20 Pedro Abdalla
Sparse binary matrices are of great interest in the field of sparse recovery, nonnegative compressed sensing, statistics in networks, and theoretical computer science. This class of matrices makes it possible to perform signal recovery with lower storage costs and faster decoding algorithms. In particular, Bernoulli () matrices formed by independent identically distributed (i.i.d.) Bernoulli () random
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The G-invariant graph Laplacian part II: Diffusion maps Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-08-12 Eitan Rosen, Xiuyuan Cheng, Yoel Shkolnisky
The diffusion maps embedding of data lying on a manifold has shown success in tasks such as dimensionality reduction, clustering, and data visualization. In this work, we consider embedding data sets that were sampled from a manifold which is closed under the action of a continuous matrix group. An example of such a data set is images whose planar rotations are arbitrary. The -invariant graph Laplacian
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A lower bound for the Balan–Jiang matrix problem Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-08-06 Afonso S. Bandeira, Dustin G. Mixon, Stefan Steinerberger
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On the concentration of Gaussian Cayley matrices Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-08-06 Afonso S. Bandeira, Dmitriy Kunisky, Dustin G. Mixon, Xinmeng Zeng
Given a finite group, we study the Gaussian series of the matrices in the image of its left regular representation. We propose such random matrices as a benchmark for improvements to the noncommutative Khintchine inequality, and we highlight an application to the matrix Spencer conjecture.
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Needlets liberated Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-08-02 Johann S. Brauchart, Peter J. Grabner, Ian H. Sloan, Robert S. Womersley
Spherical needlets were introduced by Narcowich, Petrushev, and Ward to provide a multiresolution sequence of polynomial approximations to functions on the sphere. The needlet construction makes use of integration rules that are exact for polynomials up to a given degree. The aim of the present paper is to relax the exactness of the integration rules by replacing them with QMC designs as introduced
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Embeddings between Barron spaces with higher-order activation functions Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-07-25 Tjeerd Jan Heeringa, Len Spek, Felix L. Schwenninger, Christoph Brune
The approximation properties of infinitely wide shallow neural networks heavily depend on the choice of the activation function. To understand this influence, we study embeddings between Barron spaces with different activation functions. These embeddings are proven by providing push-forward maps on the measures used to represent functions . An activation function of particular interest is the rectified
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Local structure and effective dimensionality of time series data sets Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-07-25 Monika Dörfler, Franz Luef, Eirik Skrettingland
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Short-time Fourier transform and superoscillations Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-07-25 Daniel Alpay, Antonino De Martino, Kamal Diki, Daniele C. Struppa
In this paper we investigate new results on the theory of superoscillations using time-frequency analysis tools and techniques such as the short-time Fourier transform (STFT) and the Zak transform. We start by studying how the short-time Fourier transform acts on superoscillation sequences. We then apply the supershift property to prove that the short-time Fourier transform preserves the superoscillatory
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EDMD for expanding circle maps and their complex perturbations Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-07-24 Oscar F. Bandtlow, Wolfram Just, Julia Slipantschuk
We show that spectral data of the Koopman operator arising from an analytic expanding circle map can be effectively calculated using an EDMD-type algorithm combining a collocation method of order with a Galerkin method of order . The main result is that if , where is an explicitly given positive number quantifying by how much expands concentric annuli containing the unit circle, then the method converges
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Matrix recovery from permutations Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-07-14 Manolis C. Tsakiris
In data science, a number of applications have been emerging involving data recovery from permutations. Here, we study this problem theoretically for data organized in a rank-deficient matrix. Specifically, we give unique recovery guarantees for matrices of bounded rank that have undergone arbitrary permutations of their entries. We use methods and results of commutative algebra and algebraic geometry
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On the accuracy of Prony's method for recovery of exponential sums with closely spaced exponents Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-07-10 Rami Katz, Nuha Diab, Dmitry Batenkov
In this paper we establish accuracy bounds of Prony's method (PM) for recovery of sparse measures from incomplete and noisy frequency measurements, or the so-called problem of super-resolution, when the minimal separation between the points in the support of the measure may be much smaller than the Rayleigh limit. In particular, we show that PM is optimal with respect to the previously established
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Computing sparse Fourier sum of squares on finite abelian groups in quasi-linear time Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-07-10 Jianting Yang, Ke Ye, Lihong Zhi
The problem of verifying the nonnegativity of a function on a finite abelian group is a long-standing challenging problem. The basic representation theory of finite groups indicates that a function on a finite abelian group can be written as a linear combination of characters of irreducible representations of by , where is the dual group of consisting of all characters of and is the of at . In this
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Non-separable multidimensional multiresolution wavelets: A Douglas-Rachford approach Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-07-10 David Franklin, Jeffrey A. Hogan, Matthew K. Tam
After re-casting the wavelet construction problem as a feasibility problem with constraints arising from the requirements of compact support, smoothness and orthogonality, the Douglas–Rachford algorithm is employed in the search for multi-dimensional, non-separable, compactly supported, smooth, orthogonal, multiresolution wavelets in the case of translations along the integer lattice and isotropic
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An unbounded operator theory approach to lower frame and Riesz-Fischer sequences Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-07-09 Peter Balazs, Mitra Shamsabadi
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Beurling dimension of spectra for a class of random convolutions on [formula omitted] Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-07-03 Jinjun Li, Zhiyi Wu
It is usually difficult to study the structure of the spectra for the measures in and higher dimensions. In this paper, by employing the projective techniques and our previous results on the line we prove that the Beurling dimension of spectra for a class of random convolutions in satisfies an intermediate value property.
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Mathematical foundation of sparsity-based multi-snapshot spectral estimation Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-06-07 Ping Liu, Sanghyeon Yu, Ola Sabet, Lucas Pelkmans, Habib Ammari
In this paper, we study the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements in a bounded domain. We aim to provide a mathematical foundation for sparsity-based super-resolution in such spectral estimation problems in both one- and multi-dimensional spaces. In particular, we estimate the resolution and stability
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Adaptive parameter selection for kernel ridge regression Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-06-07 Shao-Bo Lin
This paper focuses on parameter selection issues of kernel ridge regression (KRR). Due to special spectral properties of KRR, we find that delicate subdivision of the parameter interval shrinks the difference between two successive KRR estimates. Based on this observation, we develop an early-stopping type parameter selection strategy for KRR according to the so-called Lepskii-type principle. Theoretical
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On the existence and estimates of nested spherical designs Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-06-04 Ruigang Zheng, Xiaosheng Zhuang
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A sharp sufficient condition for mobile sampling in terms of surface density Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-05-23 Benjamin Jaye, Mishko Mitkovski, Manasa N. Vempati
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Towards a bilipschitz invariant theory Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-05-14 Jameson Cahill, Joseph W. Iverson, Dustin G. Mixon
Consider the quotient of a Hilbert space by a subgroup of its automorphisms. We study whether this orbit space can be embedded into a Hilbert space by a bilipschitz map, and we identify constraints on such embeddings.
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Gaussian random field approximation via Stein's method with applications to wide random neural networks Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-05-13 Krishnakumar Balasubramanian, Larry Goldstein, Nathan Ross, Adil Salim
We derive upper bounds on the Wasserstein distance (), with respect to sup-norm, between any continuous valued random field indexed by the -sphere and the Gaussian, based on Stein's method. We develop a novel Gaussian smoothing technique that allows us to transfer a bound in a smoother metric to the distance. The smoothing is based on covariance functions constructed using powers of Laplacian operators
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Differentially private federated learning with Laplacian smoothing Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-05-07 Zhicong Liang, Bao Wang, Quanquan Gu, Stanley Osher, Yuan Yao
Federated learning aims to protect data privacy by collaboratively learning a model without sharing private data among users. However, an adversary may still be able to infer the private training data by attacking the released model. Differential privacy provides a statistical protection against such attacks at the price of significantly degrading the accuracy or utility of the trained models. In this
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The mystery of Carleson frames Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-04-17 Ole Christensen, Marzieh Hasannasab, Friedrich M. Philipp, Diana Stoeva
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Effectiveness of the tail-atomic norm in gridless spectrum estimation Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-04-16 Wei Li, Shidong Li, Jun Xian
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Complex-order scale-invariant operators and self-similar processes Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-04-04 Arash Amini, Julien Fageot, Michael Unser
In this paper, we perform the joint study of scale-invariant operators and self-similar processes of complex order. More precisely, we introduce general families of scale-invariant complex-order fractional-derivation and integration operators by constructing them in the Fourier domain. We analyze these operators in detail, with special emphasis on the decay properties of their output. We further use
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Error bounds for kernel-based approximations of the Koopman operator Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-04-04 Friedrich M. Philipp, Manuel Schaller, Karl Worthmann, Sebastian Peitz, Feliks Nüske
We consider the data-driven approximation of the Koopman operator for stochastic differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the estimation error if the data are collected from long-term ergodic simulations. We derive both an exact expression for the variance of the kernel cross-covariance operator, measured in the Hilbert-Schmidt norm, and probabilistic bounds
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Frame set for Gabor systems with Haar window Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-03-18 Xin-Rong Dai, Meng Zhu
We describe the full structure of the frame set for the Gabor system with the window being the Haar function . This is the first compactly supported window function for which the frame set is represented explicitly.
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Frame set for shifted sinc-function Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-03-16 Yurii Belov, Andrei V. Semenov
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Eigenmatrix for unstructured sparse recovery Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-03-14 Lexing Ying
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Solving PDEs on unknown manifolds with machine learning Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-02-29 Senwei Liang, Shixiao W. Jiang, John Harlim, Haizhao Yang
This paper proposes a mesh-free computational framework and machine learning theory for solving elliptic PDEs on unknown manifolds, identified with point clouds, based on diffusion maps (DM) and deep learning. The PDE solver is formulated as a supervised learning task to solve a least-squares regression problem that imposes an algebraic equation approximating a PDE (and boundary conditions if applicable)
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Marcinkiewicz–Zygmund inequalities for scattered and random data on the q-sphere Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-02-29 Frank Filbir, Ralf Hielscher, Thomas Jahn, Tino Ullrich
The recovery of multivariate functions and estimating their integrals from finitely many samples is one of the central tasks in modern approximation theory. Marcinkiewicz–Zygmund inequalities provide answers to both the recovery and the quadrature aspect. In this paper, we put ourselves on the -dimensional sphere , and investigate how well continuous -norms of polynomials of maximum degree on the sphere
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Separation-free spectral super-resolution via convex optimization Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-02-29 Zai Yang, Yi-Lin Mo, Zongben Xu
Atomic norm methods have recently been proposed for spectral super-resolution with flexibility in dealing with missing data and miscellaneous noises. A notorious drawback of these convex optimization methods however is their lower resolution in the high signal-to-noise (SNR) regime as compared to conventional methods such as ESPRIT. In this paper, we devise a simple weighting scheme in existing atomic
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Exponential lower bound for the eigenvalues of the time-frequency localization operator before the plunge region Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-02-28 Aleksei Kulikov
For a pair of sets the time-frequency localization operator is defined as , where is the Fourier transform and are projection operators onto and Ω, respectively. We show that in the case when both and Ω are intervals, the eigenvalues of satisfy if , where is arbitrary and , provided that . This improves the result of Bonami, Jaming and Karoui, who proved it for . The proof is based on the properties
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Uniform approximation of common Gaussian process kernels using equispaced Fourier grids Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-02-27 Alex Barnett, Philip Greengard, Manas Rachh
The high efficiency of a recently proposed method for computing with Gaussian processes relies on expanding a (translationally invariant) covariance kernel into complex exponentials, with frequencies lying on a Cartesian equispaced grid. Here we provide rigorous error bounds for this approximation for two popular kernels—Matérn and squared exponential—in terms of the grid spacing and size. The kernel
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Small time asymptotics of the entropy of the heat kernel on a Riemannian manifold Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-02-22 Vlado Menkovski, Jacobus W. Portegies, Mahefa Ratsisetraina Ravelonanosy
We give an asymptotic expansion of the relative entropy between the heat kernel of a compact Riemannian manifold and the normalized Riemannian volume for small values of and for a fixed element . We prove that coefficients in the expansion can be expressed as universal polynomials in the components of the curvature tensor and its covariant derivatives at , when they are expressed in terms of normal
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The G-invariant graph Laplacian Part I: Convergence rate and eigendecomposition Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-02-21 Eitan Rosen, Paulina Hoyos, Xiuyuan Cheng, Joe Kileel, Yoel Shkolnisky
Graph Laplacian based algorithms for data lying on a manifold have been proven effective for tasks such as dimensionality reduction, clustering, and denoising. In this work, we consider data sets whose data points lie on a manifold that is closed under the action of a known unitary matrix Lie group . We propose to construct the graph Laplacian by incorporating the distances between all the pairs of
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Variable bandwidth via Wilson bases Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-02-21 Beatrice Andreolli, Karlheinz Gröchenig
We introduce a new concept of variable bandwidth that is based on the frequency truncation of Wilson expansions. For this model we derive sampling theorems, a complete reconstruction of from its samples, and necessary density conditions for sampling. Numerical simulations support the interpretation of this model of variable bandwidth. In particular, chirps, as they arise in the description of gravitational
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Conditional expectation using compactification operators Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-02-09 Suddhasattwa Das
The separate tasks of denoising, least squares expectation, and manifold learning can often be posed in a common setting of finding the conditional expectations arising from a product of two random variables. This paper focuses on this more general problem and describes an operator theoretic approach to estimating the conditional expectation. Kernel integral operators are used as a compactification
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Geometric scattering on measure spaces Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-02-06 Joyce Chew, Matthew Hirn, Smita Krishnaswamy, Deanna Needell, Michael Perlmutter, Holly Steach, Siddharth Viswanath, Hau-Tieng Wu
The scattering transform is a multilayered, wavelet-based transform initially introduced as a mathematical model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks' stability and invariance properties. In subsequent years, there has been widespread interest in extending the success of CNNs to data sets with non-Euclidean structure, such
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Convergent bivariate subdivision scheme with nonnegative mask whose support is non-convex Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-02-01 Li Cheng
Recently we have characterized the convergence of bivariate subdivision scheme with nonnegative mask whose support is convex by means of the so-called connectivity of a square matrix, which is derived by a given mask. The convergence in this case can be checked in linear time with respected to the size of a square matrix. This paper will focus on the characterization of such schemes with non-convex
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High-probability generalization bounds for pointwise uniformly stable algorithms Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-01-27 Jun Fan, Yunwen Lei
Algorithmic stability is a fundamental concept in statistical learning theory to understand the generalization behavior of optimization algorithms. Existing high-probability bounds are developed for the generalization gap as measured by function values and require the algorithm to be uniformly stable. In this paper, we introduce a novel stability measure called pointwise uniform stability by considering
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New theoretical insights in the decomposition and time-frequency representation of nonstationary signals: The IMFogram algorithm Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-01-26 Antonio Cicone, Wing Suet Li, Haomin Zhou
The analysis of the time–frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have been developed over the decades, which provide alternative time–frequency representations of a signal each with its advantages and limitations. In this work, following the success of nonlinear methods for the decomposition
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On representations of the Helmholtz Green's function Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-01-24 Gregory Beylkin
We consider the free space Helmholtz Green's function and split it into the sum of oscillatory and non-oscillatory (singular) components. The goal is to separate the impact of the singularity of the real part at the origin from the oscillatory behavior controlled by the wave number k. The oscillatory component can be chosen to have any finite number of continuous derivatives at the origin and can be
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Multivariate compactly supported C∞ functions by subdivision Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-01-19 Maria Charina, Costanza Conti, Nira Dyn
This paper discusses the generation of multivariate C∞ functions with compact small supports by subdivision schemes. Following the construction of such a univariate function, called Up-function, by a non-stationary scheme based on masks of spline subdivision schemes of growing degrees, we term the multivariate functions we generate Up-like functions. We generate them by non-stationary schemes based
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Dimension reduction, exact recovery, and error estimates for sparse reconstruction in phase space Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-01-11 M. Holler, A. Schlüter, B. Wirth
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal consistency between the different measurement times. The strongest consistency can be achieved by reconstructing data directly in phase space, the space of positions
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A divide-and-conquer algorithm for distributed optimization on networks Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2024-01-02 Nazar Emirov, Guohui Song, Qiyu Sun
In this paper, we consider networks with topologies described by some connected undirected graph G=(V,E) and with some agents (fusion centers) equipped with processing power and local peer-to-peer communication, and optimization problem minx{F(x)=∑i∈Vfi(x)} with local objective functions fi depending only on neighboring variables of the vertex i∈V. We introduce a divide-and-conquer algorithm to solve
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Time-frequency analysis on flat tori and Gabor frames in finite dimensions Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2023-12-12 L.D. Abreu, P. Balazs, N. Holighaus, F. Luef, M. Speckbacher
We provide the foundations of a Hilbert space theory for the short-time Fourier transform (STFT) where the flat tori TN2=R2/(Z×NZ)=[0,1]×[0,N] act as phase spaces. We work on an N-dimensional subspace SN of distributions periodic in time and frequency in the dual S0′(R) of the Feichtinger algebra S0(R) and equip it with an inner product. To construct the Hilbert space SN we apply a suitable double
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On the eigenvalue distribution of spatio-spectral limiting operators in higher dimensions Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2023-12-13 Arie Israel, Azita Mayeli
Prolate spheroidal wave functions are an orthogonal family of bandlimited functions on R that have the highest concentration within a specific time interval. They are also identified as the eigenfunctions of a time-frequency limiting operator (TFLO), and the associated eigenvalues belong to the interval [0,1]. Previous work has studied the asymptotic distribution and clustering behavior of the TFLO
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Laplace-Beltrami operator on the orthogonal group in ambient (Euclidean) coordinates Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2023-12-12 Petre Birtea, Ioan Caşu, Dan Comănescu
Using the embedded gradient vector field method (see P. Birtea, D. Comănescu (2015) [7]), we present a general formula for the Laplace-Beltrami operator defined on a constraint manifold, written in the ambient coordinates. Regarding the orthogonal group as a constraint submanifold of the Euclidean space of n×n matrices, we give an explicit formula for the Laplace-Beltrami operator on the orthogonal
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Spline manipulations for empirical mode decomposition (EMD) on bounded intervals and beyond Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2023-12-05 Charles K. Chui, Wenjie He
Empirical mode decomposition (EMD), introduced by N.E. Huang et al. in 1998, is perhaps the most popular data-driven computational scheme for the decomposition of a non-stationary signal or time series f(t), with time-domain R:=(−∞,∞), into finitely many oscillatory components {f1(t),⋯,fK(t)}, called intrinsic mode functions (IMFs), and some “almost monotone” remainder r(t), called the trend of f(t)
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Estimates on learning rates for multi-penalty distribution regression Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2023-11-23 Zhan Yu, Daniel W.C. Ho
This paper is concerned with functional learning by utilizing two-stage sampled distribution regression. We study a multi-penalty regularization algorithm for distribution regression in the framework of learning theory. The algorithm aims at regressing to real-valued outputs from probability measures. The theoretical analysis of distribution regression is far from maturity and quite challenging since
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Dilational symmetries of decomposition and coorbit spaces Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2023-11-17 Hartmut Führ, Reihaneh Raisi-Tousi
We investigate the invariance properties of general wavelet coorbit spaces and Besov-type decomposition spaces under dilations by matrices. We show that these matrices can be characterized by quasi-isometry properties with respect to a certain metric in frequency domain. We formulate versions of this phenomenon both for the decomposition and coorbit space settings. We then apply the general results
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The metaplectic action on modulation spaces Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2023-11-08 Hartmut Führ, Irina Shafkulovska
We study the mapping properties of metaplectic operators Sˆ∈Mp(2d,R) on modulation spaces of the type Mmp,q(Rd). Our main result is a full characterization of the pairs (Sˆ,Mp,q(Rd)) for which the operator Sˆ:Mp,q(Rd)→Mp,q(Rd) is (i) well-defined, (ii) bounded. It turns out that these two properties are equivalent, and they entail that Sˆ is a Banach space automorphism. For polynomially bounded weight
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Image denoising based on a variable spatially exponent PDE Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2023-11-10 Amine Laghrib, Lekbir Afraites
Image denoising is always considered an important area of image processing. In this work, we address a new PDE-based model for image denoising that have been contaminated by multiplicative noise, specially the Speckle one. We propose a new class of PDEs whose nonlinear structure depends on a spatially tensor depending quantity attached to the desired solution, which takes into account the gray level
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On the intermediate value property of spectra for a class of Moran spectral measures Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2023-11-08 Jinjun Li, Zhiyi Wu
We prove that the Beurling dimensions of the spectra for a class of Moran spectral measures are in 0 and their upper entropy dimensions. Moreover, for such a Moran spectral measure μ, we show that the Beurling dimension for the spectra of μ has the intermediate value property: let t be any value in 0 and the upper entropy dimension of μ, then there exists a spectrum whose Beurling dimension is t. In
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Exponential bases for partitions of intervals Appl. Comput. Harmon. Anal. (IF 2.6) Pub Date : 2023-10-29 Götz Pfander, Shauna Revay, David Walnut
For a partition of [0,1] into intervals I1,…,In we prove the existence of a partition of Z into Λ1,…,Λn such that the complex exponential functions with frequencies in Λk form a Riesz basis for L2(Ik), and furthermore, that for any J⊆{1,2,…,n}, the exponential functions with frequencies in ⋃j∈JΛj form a Riesz basis for L2(I) for any interval I with length |I|=∑j∈J|Ij|. The construction extends to infinite