On-grid compressive sampling for spherical field measurements in acoustics.

Area of Science:

• Acoustics
• Signal Processing
• Applied Mathematics

Background:

• Acoustic field reconstruction is crucial for various applications.
• Traditional methods like Nyquist sampling require numerous measurements.
• Compressive sampling offers a potential solution for efficient data acquisition.

Purpose of the Study:

• To develop a novel compressive sampling method for acoustic field reconstruction.
• To enable reconstruction of band-limited spherical harmonic or Wigner D-function series.
• To compare the new method's performance against classical and existing compressive sampling techniques.

Main Methods:

• Derivation of a compressive sampling method using field measurements on a spherical grid.
• Application to band-limited spherical harmonic or Wigner D-function series with sparse coefficients.
• Transformation of reconstruction into a multi-dimensional Fourier domain problem using periodic extension.
• Random sampling on an equiangular grid, a practical sampling pattern.

Main Results:

• The method guarantees relations between signal sparsity, measurement number, and reconstruction accuracy.
• Numerical studies confirm the bounded effect of the transformation on sparsity.
• The new approach performs comparably to other guaranteed compressive sampling methods.
• It requires a fraction of measurements compared to Nyquist sampling.
• Achieves over 20 dB better de-noising than oversampling with classical Fourier theory using less than one-third of measurements.

Conclusions:

• The developed compressive sampling method is efficient for acoustic field reconstruction.
• It offers significant advantages in terms of measurement reduction and de-noising.
• The equiangular sampling strategy is practical and effective for Wigner D-function series reconstruction.