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Sparse Based Super Resolution Multilayer Ultrasonic Array Imaging

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Document pages: 14 pages

Abstract: In this paper, we model the signal propagation effect in ultrasonic imagingusing Huygens principle and use this model to develop sparse signalrepresentation based imaging techniques for a two-layer object immersed inwater. Relying on the fact that the image of interest is sparse, we cast suchan array based imaging problem as a sparse signal recovery problem and developtwo types of imaging methods, one method uses only one transducer to illuminatethe region of interest {and for this case the system is modeled as a singleinput multiple output (SIMO) system. The second method relies on alltransducers to transmit ultrasonic waves into the material under test and inthis case the system is modeled as a multiple input multiple output (MIMO)system}. We further extend our work to a scenario where the propagationvelocity of the wave in the object under test is not known precisely. {Wediscuss different techniques such as greedy based algorithms as well as$ ell 1$-norm minimization based approach to solve the proposed sparse signalrepresentation based method. We give an assessment of the computationalcomplexity of the $ ell 1$-norm minimization based approach for the SIMO andthe MIMO cases. We further point out the superiority of the $ ell 1$-normminimization based approach over the greedy based algorithms. Then we give acomprehensive analysis of error for both the greedy based approaches as well asthe $ ell 1$-norm minimization based technique for both the SIMO and the MIMOcases. The analysis utilizes tools from two powerful branches of modernanalysis, emph{local analysis in Banach spaces} and emph{concentration ofmeasure}}. We finally apply our methods to experimental data gathered from asolid test sample immersed in water and show that sparse signal recovery basedtechniques outperform the conventional methods available in the literature.

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