The goal of this paper is to develop novel algorithms for inverse scattering problems such as EEG/MEG, microwave
imaging, and/or diffuse optical tomograpahy, and etc. One of the main contributions of this paper is
a class of novel non-iterative exact nonlinear inverse scattering theory for coherent source imaging and moving
targets. Specifically, the new algorithms guarantee the exact recovery under a very relaxed constraint on the
number of source and receivers, under which the conventional methods fail. Such breakthrough was possible
thanks to the recent theory of compressive MUSIC and its extension using support correction criterion, where
partial support are estimated using the conventional compressed sensing approaches, then the remaining supports
are estimated using a novel generalized MUSIC criterion. Numerical results using coherent sources in
EEG/MEG and dynamic targets confirm that the new algorithms outperform the conventional ones.
Inverse scattering refers the retrieval of the unknown constitutive parameters from measured scattered wave
fields, and has many applications such as ultrasound imaging, optics, T-ray imaging, radar, and etc. Two
distinct imaging strategies have been commonly used: narrow band inverse scattering approaches using a large
number of transmitters and receivers, or wideband imaging approaches with smaller number of transmitters and
receivers. In some biomedical imaging applications, the limited accessibility of scattered fields using externally
located antenna arrays usually prefers the wideband imaging approaches. The main contribution of this paper is,
therefore, to analyze the wideband inverse scattering problem from compressive sensing perspective. Specifically,
the mutual coherence of the wideband imaging geometry is analyzed, which reveals a significant advantage to
identify the sparse targets from very limited number of measurements.
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