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5 September 2008 Inversion of strongly scattered data: shape and permittivity recovery
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Reconstructing an object from scattered field data has always been very challenging, especially when dealing with strong scatterers scatterers. Several techniques have been proposed to address this problem but either they fail to provide a good estimate . of the object or they are computationally very expensive. We have proposed a straightforward non non-linear signal processing method in which we fir first process the scattered field data to generate a minimum phase function in the object st domain. This is accomplished by adding a reference wave whose amplitude and phase satisfy certain conditions. Minimum Minimum-phase functions are causal transforms and their ph phase is continuous in the interval -π and +π i.e. it is always unwrapped. Following this step, we compute the Fourier transform of the logarithm of this minimum phase function, referred to as its cepstrum. In this domain one can filter cepstral frequencie frequencies arising from the object from those of the s scattered field. Cepstral data are meaningless for non non-minimum phase functions because of phase wraps. We apply low pass filters in the cepstral domain to isolate information about the object and then perform an inverse transform and exponentiation. We have applied this technique to measured data provided by Institut Fresnel (Marseille, France) and investigated in a systematic way the dependence of the approach on the properties of the reference wave and filter. We show that while being a robust method, one can identify optimal parameters for the reference wave that result in a good reconstruction of a penetrable, strongly scattering permittivity distribution.
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U. Shahid, M. A. Fiddy, and M. E. Testorf "Inversion of strongly scattered data: shape and permittivity recovery", Proc. SPIE 7076, Image Reconstruction from Incomplete Data V, 707606 (5 September 2008);


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