NDLI: Generalized poisson summation formula for tempered distributions

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2015 International Conference on Sampling Theory and Applications (SampTA)

Foreword of the proceedings of the 11th international conference on sampling theory and applications

Technical program committee

Generalized poisson summation formula for tempered distributions

On a time-frequency approach to translation on finite graphs

UWB signal processing: Projection, B-splines, and modified Gegenbauer bases

Maximally concentrated signals in the special affine fourier transformation domain

Cardinal sine series: Oversampling and non-existence

Compressive sensing with redundant dictionaries and structured measurements

Analysis of sparse recovery in MIMO radar

Nonuniform sparse recovery with random convolutions

Modeling and recovering non-transitive pairwise comparison matrices

Regular operator sampling for parallelograms

On boundedness inequalities of some semi-discrete operators in connection with sampling operators

On approximation properties of generalized Kantorovich-type sampling operators

Unified convex optimization approach to super-resolution based on localized kernels

Wavelet coorbit theory in higher dimensions: An overview

Sampling, amenability and the Kunze-Stein phenomenon

Sampling and interpolation on certain nilpotent lie groups

Reconstruction of sparse multiband wavelet signals from Fourier measurements

Sampling solutions of Schro¨dinger equations on combinatorial graphs

A class of frames for Paley-Wiener spaces with multiple lattice tiles support

On minimal scalings of scalable frames

A characterization of tight and dual generalized translation invariant frames

The dual frame induced by an invertible frame multiplier

Stable nonuniform sampling with weighted Fourier frames and recovery in arbitrary spaces

Weaving properties of Hilbert space frames

Prolate shift frames and their duals

Wavelet frames generated by bandpass prolate functions

Sampling and recovery using multiquadrics

Time-frequency representations for nonlinear frequency scales — Coorbit spaces and discretization

An Amalgam Balian-Low Theorem for symplectic lattices of rational density

The finite Balian-Low conjecture

Duality results for co-compact Gabor systems

On optimal frame conditioners

Deterministic construction of Quasi-Cyclic sparse sensing matrices from one-coincidence sequence

Stability in blind deconvolution of sparse signals and reconstruction by alternating minimization

Nonlinear sampling for sparse recovery

Matrix coherency graph: A tool for improving sparse coding performance

From quantum tomography to phase retrieval and back

The fisher information matrix and the CRLB in a non-AWGN model for the phase retrieval problem

Projection retrieval: Theory and algorithms

Polarization based phase retrieval for time-frequency structured measurements

Spherical designs as a tool for derandomization: The case of PhaseLift

A small frame and a certificate of its injectivity

The structure of test functions that determine weighted composition operators

Directionally sensitive weight functions

A general approach for convergence analysis of adaptive sampling-based signal processing

On the strong divergence of Hilbert transform approximations from sampled data

Sampling and (sparse) stochastic processes: A tale of splines and innovation

Statistical optimality of Hermite splines

Interpretation of continuous-time autoregressive processes as random exponential splines

Compressibility of symmetric-α-stable processes

Kramer's generalized sampling of stochastic processes

Weighted total generalized variation for compressive sensing reconstruction

Parameter estimation from samples of stationary complex Gaussian processes

Nonuniform sampling with adaptive expectancy based on local variance

Analysis of generalized ridge functions in high dimensions

Numerical solution of underdetermined systems from partial linear circulant measurements

Correctly sizing FIR filter architecture in the framework of non-uniform sampling

On the existence of equivalence class of RIP-compliant matrices

Dictionary-sparse and disjointed recovery

Event-driven sampling of signal with quadratic prediction

Compressed sensing MRI using sparsity induced from adjacent slice similarity

Construction of orthonormal directional wavelets based on quincunx dilation subsampling

On random and deterministic compressed sensing and the Restricted Isometry Property in levels

Bivariate splines in piecewise constant tension

Universal embeddings for kernel machine classification

Unique recovery from edge information

Superresolution of remotely sensed images with anisotropic features

Reconstruction from fourier measurements using compactly supported shearlets

Fast Gabor wavelet transform based on synthesis of Gabor spectrum using convolution of Gaussian

Resolution of the wave front set using general wavelet transforms

Signal recovery on graphs: Random versus experimentally designed sampling

Error bounds for noisy compressive phase retrieval

Steiner equiangular tight frames redux

On R-duals and the duality principle

Graph theoretic uncertainty principles

Unconditional convergence constants of Hilbert space frame expansions

2D sparse sampling algorithm for ND Fredholm equations with applications to NMR relaxometry

From paley graphs to deterministic sensing matrices with real-valued Gramians

Non-negative dimensionality reduction for audio signal separation by NNMF and ICA

On the minimal number of measurements in low-rank matrix recovery

Analysis of low rank matrix recovery via Mendelson's small ball method

Fast and exact reconstruction of arbitrary multivariate algebraic polynomials in Chebyshev form

Recovery of third order tensors via convex optimization

Low rank matrix recovery from few orthonormal basis measurements

Complete dictionary recovery over the sphere

Phase retrieval without small-ball probability assumptions: Stability and uniqueness

Some results concerning rank-one truncated steepest descent directions in tensor spaces

Greedy rank updates combined with Riemannian descent methods for low-rank optimization

Compressive sampling of stochastic multiband signal using time encoding machine

Sampling circuits for 1D and 2D sensors for low-power purpose

Dynamical sampling with an additive forcing term

Dynamical sampling of two-dimensional temporally-varying signals

Filter recovery in infinite spatially invariant evolutionary system via spatiotemporal trade off

Mobile sampling of bandlimited fields

Spatially distributed sampling and reconstruction of high-dimensional signals

Greedy algorithm for subspace clustering from corrupted and incomplete data

Optimally sparse image approximation by adaptive linear splines over anisotropic triangulations

Sampling and distortion tradeoffs for bandlimited periodic signals

Adaptive estimation and compensation of the time delay in a periodic non-uniform sampling scheme

Efficient dictionary learning via very sparse random projections

Parameter estimation for mixture models via convex optimization

Signal model specification testing via kernel reconstruction methods

Parameter estimation for bivariate exponential sums

Randomized Kaczmarz algorithm for inconsistent linear systems: An exact MSE analysis

Aperiodic geometry design for DOA estimation using compressive sensing

Optimal recovery from compressive measurements via denoising-based approximate message passing

Blind compressed sensing using sparsifying transforms

Recovery guarantees for TV regularized compressed sensing

Energy allocation for parameter estimation in block CS-based distributed MIMO systems

Compressed sensing Petrov-Galerkin approximations for parametric PDEs

Spike detection using FRI methods and protein calcium sensors: Performance analysis and comparisons

GSURS: Generalized sparse uniform resampling with application to MRI

Recovery of piecewise smooth images from few fourier samples

Resolution limits for atomic decompositions via Markov-Bernstein type inequalities

Error estimates for filtered back projection

Dynamic optimal transport with mixed boundary condition for color image processing

Sparse source localization in presence of co-array perturbations

Uniqueness in bilinear inverse problems with applications to subspace and joint sparsity models

Balayage and pseudo-differential operator frame inequalities

Exact reconstruction of a class of nonnegative measures using model sets

Operator identification on the circle

Universal factorizations of quasiperiodic functions

On the effective measure of dimension in total variation minimization

A novel geometric multiscale approach to structured dictionary learning on high dimensional data

Pseudo prolate spheroidal functions

Eigenvector localization on data-dependent graphs

On a lower bound for a periodic uncertainty constant

Accuracy of spike-train Fourier reconstruction for colliding nodes

Phase retrieval without small-ball probability assumptions: Recovery guarantees for phaselift

Optimal trade-off between sampling rate and quantization precision in Sigma-Delta A/D conversion

Generalized poisson summation formula for tempered distributions

Content Provider	IEEE Xplore Digital Library
Author	Nguyen, H.Q. Unser, M.
Copyright Year	2015
Description	Author affiliation: Biomed. Imaging Group, Ecole Polytech. Fed. de Lausanne (EPFL), Lausanne, Switzerland (Nguyen, H.Q.; Unser, M.)
Abstract	The Poisson summation formula (PSF), which relates the sampling of an analog signal with the periodization of its Fourier transform, plays a key role in the classical sampling theory. In its current forms, the formula is only applicable to a limited class of signals in $L_{1}.$ However, this assumption on the signals is too strict for many applications in signal processing that require sampling of non-decaying signals. In this paper we generalize the PSF for functions living in weighted Sobolev spaces that do not impose any decay on the functions. The only requirement is that the signal to be sampled and its weak derivatives up to order 1/2+ ε for arbitrarily small ε > 0, grow slower than a polynomial in the $L_{2}$ sense. The generalized PSF will be interpreted in the language of distributions.
Starting Page	1
Ending Page	5
File Size	291593
Page Count	5
File Format	PDF
ISBN	9781467373531
DOI	10.1109/SAMPTA.2015.7148838
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-05-25
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Presses Fourier transforms Convolution Polynomials Splines (mathematics) Kernel
Content Type	Text
Resource Type	Article

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