Compressive sensing based non-destructive testing using ultrasonic arrays.
Date
2013-08-01
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Abstract
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.
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Keywords
Compressive sensing, Sparsity, Non-destructive testing, Array signal processing, Ultrasound imaging