Compressive sensing (CS) is compared with conventional beamforming using horizontal beamforming of at-sea, towed-array data. They are compared qualitatively using bearing time records and quantitatively using signal-to-interference ratio. Qualitatively, CS exhibits lower levels of background interference than conventional beamforming. Furthermore, bearing time records show increasing, but tolerable, levels of background interference when the number of elements is decreased. For the full array, CS generates signal-to-interference ratio of 12 dB, but conventional beamforming only 8 dB. The superiority of CS over conventional beamforming is much more pronounced with undersampling.

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This paper presents a derivation of the time reversal operator decomposition ͑DORT͒ using the sonar equation. DORT is inherently a frequency-domain technique, but the derivation is shown in the time-frequency domain to preserve range resolution. The magnitude of the singular values is related to sonar equation parameters. The time spreading of the time-domain back-propagation image is also related to the sonar equation. Noise-free, noise-only, and signal-plus-noise data are considered theoretically. Contamination of the echo singular component by noise is shown quantitatively to be very small at a signal-to-noise ratio of 0 dB. Results are shown from the TREX-04 experiment during April 22 to May 4, 2004 in 94 m deep, shallow water southwest of the Hudson Canyon. Rapid transmission of short, 500 Hz wide linear frequency modulated beams with center frequencies of 750, 1250, 1750, 2250, 2750, and 3250 Hz are used. Degradation caused by a lack of time invariance is found to be small at 750 Hz and nearly complete at 3250 Hz. A back-propagation image at 750 Hz shows focusing on the echo repeater. These results are discussed with comments about further research.

The numerical application of the statistical reduced isometry property (StRIP) and statistical null space property (SNSP) is presented and demonstrated for the design of underwater acoustic line arrays. This recent approach predicts the theoretical utility of specific subsampled arrays for compressive sensing. Three subsamplings are presented: Random, Golomb, and Wichmann. The Golomb array has no repeated spacings. The Wichmann array includes every possible interval of spacings. The SNSP is shown insensitive to the cases presented. The StRIP of the Golomb array predicts superior invertibility and is shown to perform well using at-sea data.

Knowledge of the structural impedance is significantly important in the computation of acoustic scattering and radiation because it contains all the information about the structure which is necessary for the evaluation of the scattered or radiated field in any fluid medium. The inverse problem of determining, or reconstructing, the structural impedance from scattering measurements is treated. An algorithm is developed for the reconstruction of the structural impedance from knowledge of scattered field for a set of incident plane wave directions. An intermediate step includes the reconstruction of the surface pressure and normal velocity fields using acoustical holography. The resolution limit of the reconstruction is found in the case of the infinite cylinder and the sphere. The case of the sphere is generalizable to other finite shapes. Problems caused by noise in the inversion of the data are discussed. Alternative reconstructions of wet impedance and wet admittance which can be performed for any scattering data are defined.