A planar large sieve and sparsity of time-frequency representations

2017/02/27 by Luís Daniel Abreu, Michael Speckbacher, Abreu, Luis Daniel +1 · 1 citation
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1702.08274

openalex publication_date 2017/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

With the aim of measuring the sparsity of a real signal, Donoho and Logan introduced the concept of maximum Nyquist density, and used it to extend Bombieri's principle of the large sieve to bandlimited functions. This led to several recovery algorithms based on the minimization of the L₁-norm. In this paper we introduce the concept of planar maximum Nyquist density, which measures the sparsity of the time-frequency distribution of a function. We obtain a planar large sieve principle which applies to time-frequency representations with a gaussian window, or equivalently, to Fock spaces, F₁( ℂ) , allowing for perfect recovery of the short-Fourier transform (STFT) of functions in the modulation space M₁ (also known as Feichtinger's algebra S₀) corrupted by sparse noise and for approximation of missing STFT data in M₁, by L₁-minimization.

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