Uncertainty Principles and Signal Recovery

1989/06/01 by David L. Donoho, Philip B. Stark · 2 citations
Mathematics · Computer Science · #Mathematical Analysis and Transform Methods #Image and Signal Denoising Methods #Digital Filter Design and Implementation

paper · doi:10.1137/0149053

openalex publication_date 1989/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/18

Abstract

The uncertainty principle can easily be generalized to cases where the “sets of concentration” are not intervals. Such generalizations are presented for continuous and discrete-time functions, and for several measures of “concentration” (e.g., L₂ and L₁ measures). The generalizations explain interesting phenomena in signal recovery problems where there is an interplay of missing data, sparsity, and bandlimiting.

Citations

• Recovery of the acoustic impedance from reflection seismograms
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - I
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - II

Cited by

• Entropy-based uncertainty measures for L/sup 2/(/spl Ropf//sup n/), /spl lscr//sup 2/(/spl Zopf/), and /spl lscr//sup 2/(/spl Zopf//N/spl Zopf/) with a Hirschman optimal transform for /spl lscr//sup 2/(/spl Zopf//N/spl Zopf/)
• Discrete Fourier transform [wikipedia]