Jideani, Josiah Chimnanu. Synthetic aperture sonar imaging using compressive sensing and an ultrasound transducer array. MSc Dissertation. Department of Electrical Engineering, University of Cape Town, 2013.
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. It is a model-based framework for data acquisition and signal recovery that is based on the principles of sparsity and incoherence. Sparsity refers to the fact that a signal of interest is sparse and compressible and can be represented concisely in a given basis. Incoherence refers to the idea that a sparse signal is spread out in the basis in which it is acquired. A prominent area of application of this technique is tomography such as magnetic resonance imaging (MRI), X-ray CT, and in 3D synthetic aperture radar (SAR) imaging for reconstructing the elevation reflectivity profile.
This dissertation describes the investigation into three-dimensional (3D) synthetic aperture sonar (SAS) imaging in air using compressive sampling. In the work, a 3D SAS simulator using compressive sampling was implemented in MATLAB. The effect of the number of baselines as well as the super-resolution factor on the final image was also investigated. A real 3D SAS imaging system was designed and the results were compared with the results of the simulated system.
In the system, the SAS data was captured in a multiple transducer (baseline), single-pass configuration with 15 ultrasonic receivers and a single ultrasonic transmitter that operate at about 40 kHz. Signal conditioning circuits for the transmit and receive signals were built on pieces of veroboard. A PC which ran a custom designed LabVIEW virtual instrument (VI) was used for the synchronous transmission and reception of ultrasonic signals, and the control of the SAS platform via the NI PCI-6070E data acquisition card. The received 2D SAS signal from each transducer was focused using the accelerated chirp scaling algorithm. Compressive sensing was applied to a stack of focused 2D SAS images to achieve focusing in the elevation direction. 3D scenes containing point targets were successfully reconstructed in 3D SAS images using this technique with 9 baselines and a super-resolution factor of 3.
The results confirm that CS is an effective technique in super-resolution tomographic reconstructions provided the baseline span is small compared to the imaging range. Also for reliable reconstructions, the appropriate super-resolution factor and number of acquisitions must be chosen.