On the SNR Variability in Noisy Compressed Sensing

Anastasia Lavrenko*, Florian Romer, Giovanni Del Galdo, Reiner Thoma

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

9 Citations (Scopus)


Compressed sensing (CS) is a sampling paradigm that allows us to simultaneously measure and compress signals that are sparse or compressible in some domain. The choice of a sensing matrix that carries out the measurement has a defining impact on the system performance and it is often advocated to draw its elements randomly. It has been noted that in the presence of input (signal) noise, the application of the sensing matrix causes signal-to-noise ratio (SNR) degradation due to the noise folding effect. In fact, it might also result in the variations of the output SNR in compressive measurements over the support of the input signal, potentially resulting in unexpected nonuniform system performance. In this letter, we study the impact of a distribution from which the elements of a sensing matrix are drawn on the spread of the output SNR. We derive analytic expressions for several common types of sensing matrices and show that the SNR spread grows with the decrease of the number of measurements. This makes its negative effect especially pronounced for high compression rates that are often of interest in CS.

Original languageEnglish
Article number7888934
Pages (from-to)1148-1152
Number of pages5
JournalIEEE signal processing letters
Issue number8
Publication statusPublished - Aug 2017
Externally publishedYes


  • Noise folding
  • noisy compressed sensing (CS)
  • sensing matrix
  • signal-to-noise ratio (SNR) variability
  • sparse signals

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