Work

Restricted Isometry for Variable-Density Continuous Frequency Sampling for Off-the-Grid Sparse Signals

Year: 2026

Type: conference-paper

Abstract: Restricted isometry-type guarantees for continuous random sampling of Fourier frequencies in off-the-grid sparse models observed through a known point-spread function (PSF) are established. Specifically, for spike trains convolved with a fixed kernel and sampled on a finite bandwidth according to an arbitrary probability density, it is proven that the empirical frequency-domain energy concentrates around its expectation with near-linear sample complexity in the sparsity level. The constants are governed by two simple summaries of the PSF and the sampling density: an in-band energy term and a bounded-variation penalty that captures the effect of spike separation. Our analysis yields a practical design principle for variable-density sampling and admits a convex discretization. Numerical experiments illustrate tangible gains in localization when the sampling density is optimized accordingly.

Source: IEEE International Conference on Acoustics Speech and Signal Processing

DOI: 10.1109/icassp55912.2026.11461010

Authors: Joseph Gabet, Maxime Ferreira Da Costa, Kiryung Lee

Institutions: Centre National de la Recherche Scientifique, Laboratoire des signaux et systèmes, CentraleSupélec, The Ohio State University

Language: English

Topic: Sparse and Compressive Sensing Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Agence Nationale de la Recherche

Awards: Bilinear Inversion Theory for Self-calibration and Security, HNDS-I: Decennial Census Linkage Project, CAREER: Nonlinear Models and Regularization for Infinite-Dimensional Inverse Problems, G6671297155