Wavelet-Based Compressive Sensing Imaging of 2D Non-Sparse Scatterers

Hannan, M. (2015) Wavelet-Based Compressive Sensing Imaging of 2D Non-Sparse Scatterers. Masters thesis, University of Trento.

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Abstract

The application of Compressive Sensing (CS) techniques are becoming more and more popular in microwave imaging, thanks to their ability to mitigate the theoretical and practical difficulties arising in the associated inverse problem, while properly complying with several common applicative requirements (e.g., reduced computational costs, high spatial resolution, and robustness to the noise). A key requirement to be satisfied for employing CS methods in inverse scattering problems is that the unknowns (e.g., the contrast function or the equivalent current) are sparse with respect to their expansion basis either in the spatial domain or in a transformed one. Indeed, it is worthwhile pointing out that sparseness is not an absolute concept, but a relative one and the relation is with or versus a basis. A scatterer can be sparse with respect to a basis and not sparse versus another one. In this framework this project activity aims to investigate the use of different Wavelet Functions (e.g., Daubechies, Morlet, Coiflet, Spline...) for microwave imaging of non-sparse scatterers, that are large with respect to the investigated domain and with a contrast profile that show some similarities with the used wavelet functions.

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