Compressive sensing based non-destructive testing using ultrasonic arrays.
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In this thesis, we apply compressive sensing approach and the notion of sparse signal recovery to the non-destructive testing application, using ultrasonic arrays. In many signal processing applications including array signal processing, there is a remarkable effort to use the concept of sparsity to solve an under-determined system of equations which governs today's signal acquisition devices. The research interest in this area is to recover sparse signals using much fewer number of measurements which is offered by the traditional methods. In this study, using a frequency-domain model for the signals received by an ultrasonic array, we propose three approaches to convert the model to the format used by compressive sensing theory. Each proposed approach is tested on the experimental data and their performance is compared with three of the existing array processing algorithms in the time and frequency-domains. The first rearrangement proposed in this thesis, is using the measurement data obtained from individual transmitter elements in the array at a single frequency bin. Multiple problems of this form, for different transmitter indices at different frequency bins have been solved to obtain an image of the region of interest. The experimental results of this approach show the applicability of the compressive sensing in the ultrasonic non-destructive testing application. This method is called incoherent compressive sensing throughout the thesis. The second rearrangement proposed for the model is based on multiple measurement vectors, which allows us to coherently process all the measurement vectors from all dfferent transmitters at each frequency bin. The results of this approach show better imaging performance than the incoherent compressive sensing approach. These results also show that using only half of the ultrasonic elements in the array, we can obtain an image which has comparable performance with other known array processing algorithms. The last approach we have proposed is suing compressive sensing along with synthetic aperture imaging model. In this approach, we show that compressive sensing can be applied to the synthetic aperture imaging in which much fewer spatial measurements are available.