TY - JOUR
T1 - UWB Beam-Based Local Diffraction Tomography-Part I
T2 - Phase-Space Processing and Physical Interpretation
AU - Tuvi, Ram
AU - Heyman, Ehud
AU - Melamed, Timor
N1 - Publisher Copyright:
© 2020 IEEE.
PY - 2020/10
Y1 - 2020/10
N2 - In this two-part article, we study the ultrawideband beam-based schemes for tomographic inverse scattering. The theory utilizes discrete phase-space sets of beam waves, which constitute overcomplete frames everywhere in the propagation domain, and thus can be considered as a local alternative to the conventional plane-wave or Green's function integrals used in conventional diffraction tomography. Specifically, we formulate two inversion schemes, a multi-frequency domain scheme, and a time domain scheme. The former utilizes isodiffracting Gaussian beams, while the latter utilizes isodiffracting pulsed beams. Both schemes consist of two phases: In the preprocessing phase, the scattering data are expanded as a sum of beams whose amplitudes, referred to as the 'beam-domain data,' are extracted from the data using local beam-based transforms. In the imaging phase, the beam data are backpropagated and used for local reconstruction. In this Part I we discuss the preprocessing phase. We define the beam-based transforms, and then use the Born approximation to establish a cogent physical interpretation of the beam-domain data. Specifically, we show that these data are related to the local Radon transform of the medium, which is interpreted physically as a local Snell's law. This relation will be used in Part II to reconstruct the medium.
AB - In this two-part article, we study the ultrawideband beam-based schemes for tomographic inverse scattering. The theory utilizes discrete phase-space sets of beam waves, which constitute overcomplete frames everywhere in the propagation domain, and thus can be considered as a local alternative to the conventional plane-wave or Green's function integrals used in conventional diffraction tomography. Specifically, we formulate two inversion schemes, a multi-frequency domain scheme, and a time domain scheme. The former utilizes isodiffracting Gaussian beams, while the latter utilizes isodiffracting pulsed beams. Both schemes consist of two phases: In the preprocessing phase, the scattering data are expanded as a sum of beams whose amplitudes, referred to as the 'beam-domain data,' are extracted from the data using local beam-based transforms. In the imaging phase, the beam data are backpropagated and used for local reconstruction. In this Part I we discuss the preprocessing phase. We define the beam-based transforms, and then use the Born approximation to establish a cogent physical interpretation of the beam-domain data. Specifically, we show that these data are related to the local Radon transform of the medium, which is interpreted physically as a local Snell's law. This relation will be used in Part II to reconstruct the medium.
KW - Beam summation methods
KW - diffraction tomography (DT)
KW - inverse scattering
UR - http://www.scopus.com/inward/record.url?scp=85092483930&partnerID=8YFLogxK
U2 - 10.1109/TAP.2020.2992806
DO - 10.1109/TAP.2020.2992806
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AN - SCOPUS:85092483930
SN - 0018-926X
VL - 68
SP - 7144
EP - 7157
JO - IEEE Transactions on Antennas and Propagation
JF - IEEE Transactions on Antennas and Propagation
IS - 10
M1 - 9091932
ER -