Brett Borden and Margaret Cheney 2005 Inverse Problems 21 1 doi:10.1088/0266-5611/21/1/001
Brett Borden1 and Margaret Cheney2
Show affiliationsWe develop the theory of radar imaging from data measured by a moving antenna emitting a single-frequency waveform. We show that, under a linearized (Born) scattering model, the signal at a given Doppler shift is due to a superposition of returns from stationary scatterers on a cone whose axis is the flight velocity vector. This cone reduces to a hyperbola when the scatterers are known to lie on a planar surface. In this case, reconstruction of the scatterer locations can be accomplished by a tomographic inversion in which the scattering density function is reconstructed from its integrals over hyperbolas. We give an approximate reconstruction formula and analyse the resolution of the resulting image. We provide a numerical shortcut and show results of numerical tests in a simple case.
84.40.Xb Telemetry: remote control, remote sensing; radar
78A46 Inverse scattering problems
94A08 Image processing (compression, reconstruction, etc.) (See also 68U10)
Issue 1 (February 2005)
Received 14 April 2004, in final form 4 October 2004
Published 9 November 2004
Brett Borden and Margaret Cheney 2005 Inverse Problems 21 1
P J Allisy-Roberts 2005 J. Radiol. Prot. 25 97
M J Davis and C W Gardiner 2002 J. Phys. B: At. Mol. Opt. Phys. 35 733
Stephen O'Dell 2006 Inverse Problems 22 1579
J M Nichols et al 2004 Smart Mater. Struct. 13 241
D S Broomhead et al 1987 J. Phys. A: Math. Gen. 20 L563
Henk van Elst and George F R Ellis 1996 Class. Quantum Grav. 13 1099
A M Stewart 2005 Eur. J. Phys. 26 635
George Chavchanidze 2004 J. Phys. A: Math. Gen. 37 2253
Jason Lindler and Norman M Wereley 2003 Smart Mater. Struct. 12 305