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 - Funding Information:
Manuscript received December 15, 2018; revised November 27, 2019; accepted April 25, 2020. Date of publication May 12, 2020; date of current version October 6, 2020. This work was supported by the Israeli Science Foundation (ISF) under Grant 412/15 and Grant 1111/19. (Corresponding author: Ehud Heyman.) Ram Tuvi was with the School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel. He is now with the Jackson School of Geosciences, Institute for Geophysics, The University of Texas at Austin, Austin, TX 78758 USA (e-mail: ram.tuvi@gmail.com).
Publisher Copyright:
© 2020 IEEE.
PY - 2020/10/1
Y1 - 2020/10/1
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
M3 - Article
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 -