Multifrequency Impedance Imaging with Multiple Signal Classification
SIAM JOURNAL ON IMAGING SCIENCES(2015)
摘要
We consider a multifrequency impedance imaging technique that has recently been suggested as a modality for mammography screenings. This approach uses observations of boundary voltages generated by a collection of AC boundary currents that have the same spatial distribution and only differ in their driving frequency. The aim is to identify and determine the locations of small focal lesions. We analyze the potential and the limitations of a multiple signal classification-type reconstruction method for this setting. We prove that with sufficiently many different driving frequencies the position of a single planar obstacle will always be detected, but the identification of multiple obstacles may fail for certain exceptional geometrical configurations. We propose a modification of the original scheme for which the set of false negative configurations is reduced. It is also shown that, generically, the given measurements allow the determination of the conductivities and permittivities of the lesions to facilitate their classification. Finally, we provide arguments to support the claim that it should also be possible to extract shape information from these data. Our analysis is based on a well-known asymptotic expansion of solutions to the conductivity equation for infinitesimal planar obstacles and a novel description of the associated polarization tensors as meromorphic functions of frequency.
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关键词
electrical impedance tomography,multiple frequencies,MUSIC,polarization tensor
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