Fast transforms for acoustic imaging--part II: applications.

Area of Science:

• Acoustic imaging
• Signal processing
• Array signal processing

Background:

• The Kronecker array transform (KAT) was introduced for fast imaging with separable arrays.
• The KAT generates the spectral matrix measured by a separable sensor array from a given source distribution.

Purpose of the Study:

• To establish connections between the KAT, beamforming, and 2-D convolutions.
• To demonstrate the acceleration of classical and state-of-the-art array imaging algorithms using these connections.
• To propose the KAT for accelerating regularized least-squares solvers in array imaging.

Main Methods:

• Establishing theoretical links between the KAT, beamforming, and 2-D convolutions.
• Applying the KAT to accelerate existing and novel array imaging algorithms.
• Utilizing the KAT to enhance general-purpose regularized least-squares solvers.
• Analyzing KAT performance for near-field source distributions.

Main Results:

• The KAT accelerates array imaging algorithms by leveraging its connections to beamforming and convolutions.
• Using the KAT with regularized least-squares solvers avoids ill-conditioned deconvolution, leading to more accurate reconstructions with low computational cost.
• The KAT demonstrates a trade-off between accuracy and computational complexity for near-field imaging.
• Separable array designs with KAT achieve accuracy comparable to multi-arm logarithmic spiral geometries, with superior computational efficiency.

Conclusions:

• The KAT is a powerful tool for accelerating acoustic array imaging.
• The KAT offers a computationally efficient and accurate alternative for reconstructing source distributions, including near-field scenarios.
• The findings support the use of separable array designs for efficient and accurate acoustic imaging applications.