Air-based synthetic aperture sonar tomography using compressive sensing

Compressive sensing (CS) also known as compressive sampling is a technique used to reconstruct or recover the full-length of a signal with only a few non-adaptive measurements. This technique has been applied to synthetic aperture radar (SAR) tomography to obtain super-resolution three-dimensional (3D) focusing of SAR data acquired over multiple baselines. In this work, synthetic aperture sonar (SAS) tomography in air was carried out using the compressive sampling technique to obtain 3D focusing of SAS data. SAS data is acquired over a total of 9 baselines using 9 ultrasonic receiving transducers and 1 ultrasonic transmitting transducer that operate at 40kHz. Data acquired from each baseline is range compressed by using a deconvolution filter which compensates for linear system effects. Two-dimensional (2D) SAS image focusing is then carried out using the accelerated chirp scaling algorithm. Compressive sampling was then applied to the stack of focused 2D SAS images to reconstruct the reflectivity profile of the scene in the elevation direction. 3D scenes containing point targets (corner reflectors) were successfully reconstructed using this technique with a super-resolution factor of 3. The results confirm that CS is effective in super-resolution tomographic reconstructions provided the baseline span is small compared to the range of imaging.