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Sparse array design using statistical restricted isometry property.

Charles F Gaumond1, Geoffrey F Edelmann

  • 1Acoustics Division, Naval Research Laboratory, Washington, DC 20375, USA. charles.gaumond@nrl.navy.mil

The Journal of the Acoustical Society of America
|August 10, 2013
PubMed
Summary
This summary is machine-generated.

The statistical reduced isometry property (StRIP) effectively predicts underwater acoustic line array performance for compressive sensing. Golomb arrays, with unique spacings, show superior invertibility and real-world utility.

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Area of Science:

  • Underwater acoustics
  • Array signal processing
  • Compressive sensing

Background:

  • Underwater acoustic line arrays are crucial for sensing applications.
  • Compressive sensing (CS) offers efficient data acquisition but requires specific array properties.
  • The statistical reduced isometry property (StRIP) and statistical null space property (SNSP) are theoretical tools for predicting CS performance.

Purpose of the Study:

  • To numerically apply and demonstrate StRIP and SNSP for designing subsampled underwater acoustic line arrays.
  • To evaluate the theoretical utility of Random, Golomb, and Wichmann subsampling schemes for CS.
  • To assess the practical performance of these arrays using at-sea data.

Main Methods:

  • Numerical application of StRIP and SNSP to analyze subsampled array designs.
  • Comparison of Random, Golomb (no repeated spacings), and Wichmann (all possible intervals) subsampling methods.
  • Validation of theoretical predictions with real-world at-sea data.

Main Results:

  • SNSP was found to be insensitive to the different subsampling cases (Random, Golomb, Wichmann).
  • StRIP analysis predicted superior invertibility for the Golomb array.
  • The Golomb array demonstrated strong performance in practical at-sea experiments.

Conclusions:

  • StRIP is a valuable predictor for the performance of subsampled arrays in compressive sensing applications.
  • Golomb arrays offer a promising design for underwater acoustic line arrays due to their superior invertibility and practical effectiveness.
  • The theoretical framework of StRIP and SNSP aids in the efficient design of acoustic sensing systems.