American Institute of Mathematical Sciences

Advanced
August  2007, 1(3): 577-592. doi: 10.3934/ipi.2007.1.577

A variational approach to waveform design for synthetic-aperture imaging

T. Varslo 1, , C E Yarman 1, , M. Cheney 1, and  B Yazıcı 1,

1. 

Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, NY 12180, United States, United States, United States

Received  February 2007 Published  July 2007

We derive an optimal transmit waveform for filtered backprojection-based synthetic-aperture imaging. The waveform is optimal in terms of minimising the mean square error (MSE) in the resulting image. Our optimization is performed in two steps: First, we consider the minimum-mean-square-error (MMSE) for an arbitrary but fixed waveform, and derive the corresponding filter for the filtered backprojection reconstruction. Second, the MMSE is further reduced by finding an optimal transmit waveform. The transmit waveform is derived for stochastic models of the scattering objects of interest (targets), other scattering objects (clutter), and additive noise. We express the waveform in terms of spatial spectra for the random fields associated with target and clutter, and the spectrum for the noise process. This approach results in a constraint that involves only the amplitude of the Fourier transform of the transmit waveform. Therefore, considerable flexibility is left for incorporating additional requirements, such as minimal variation of transmit amplitude and phase-coding.
Keywords: Synthetic-aperture, filtered backprojection, radar imaging., waveform design.
Mathematics Subject Classification: Primary: 78A46, 78M35; Secondary: 44A12, 78M3.
Citation: T. Varslo, C E Yarman, M. Cheney, B Yazıcı. A variational approach to waveform design for synthetic-aperture imaging. Inverse Problems & Imaging, 2007, 1 (3) : 577-592. doi: 10.3934/ipi.2007.1.577
[1]

Kaitlyn Muller. The relationship between backprojection and best linear unbiased estimation in synthetic-aperture radar imaging. Inverse Problems & Imaging, 2016, 10 (2) : 549-561. doi: 10.3934/ipi.2016011
[2]

Venkateswaran P. Krishnan, Eric Todd Quinto. Microlocal aspects of common offset synthetic aperture radar imaging. Inverse Problems & Imaging, 2011, 5 (3) : 659-674. doi: 10.3934/ipi.2011.5.659
[3]

Raluca Felea, Romina Gaburro, Allan Greenleaf, Clifford Nolan. Microlocal analysis of Doppler synthetic aperture radar. Inverse Problems & Imaging, 2019, 13 (6) : 1283-1307. doi: 10.3934/ipi.2019056
[4]

Jean-François Crouzet. 3D coded aperture imaging, ill-posedness and link with incomplete data radon transform. Inverse Problems & Imaging, 2011, 5 (2) : 341-353. doi: 10.3934/ipi.2011.5.341
[5]

Peter Kuchment, Leonid Kunyansky. Synthetic focusing in ultrasound modulated tomography. Inverse Problems & Imaging, 2010, 4 (4) : 665-673. doi: 10.3934/ipi.2010.4.665
[6]

Pierre-Emmanuel Mazaré, Olli-Pekka Tossavainen, Daniel B. Work. Computing travel times from filtered traffic states. Discrete & Continuous Dynamical Systems - S, 2014, 7 (3) : 557-578. doi: 10.3934/dcdss.2014.7.557
[7]

Filipa Caetano, Martin J. Gander, Laurence Halpern, Jérémie Szeftel. Schwarz waveform relaxation algorithms for semilinear reaction-diffusion equations. Networks & Heterogeneous Media, 2010, 5 (3) : 487-505. doi: 10.3934/nhm.2010.5.487
[8]

Cicely K. Macnamara, Mark A. J. Chaplain. Spatio-temporal models of synthetic genetic oscillators. Mathematical Biosciences & Engineering, 2017, 14 (1) : 249-262. doi: 10.3934/mbe.2017016
[9]

Masaru Ikehata, Esa Niemi, Samuli Siltanen. Inverse obstacle scattering with limited-aperture data. Inverse Problems & Imaging, 2012, 6 (1) : 77-94. doi: 10.3934/ipi.2012.6.77
[10]

Josselin Garnier, Knut Solna. Filtered Kirchhoff migration of cross correlations of ambient noise signals. Inverse Problems & Imaging, 2011, 5 (2) : 371-390. doi: 10.3934/ipi.2011.5.371
[11]

Daniela Calvetti, Erkki Somersalo. Microlocal sequential regularization in imaging. Inverse Problems & Imaging, 2007, 1 (1) : 1-11. doi: 10.3934/ipi.2007.1.1
[12]

Guillaume Bal, Olivier Pinaud, Lenya Ryzhik. On the stability of some imaging functionals. Inverse Problems & Imaging, 2016, 10 (3) : 585-616. doi: 10.3934/ipi.2016013
[13]

Lassi Roininen, Markku S. Lehtinen, Petteri Piiroinen, Ilkka I. Virtanen. Perfect radar pulse compression via unimodular fourier multipliers. Inverse Problems & Imaging, 2014, 8 (3) : 831-844. doi: 10.3934/ipi.2014.8.831
[14]

Markku Lehtinen, Baylie Damtie, Petteri Piiroinen, Mikko Orispää. Perfect and almost perfect pulse compression codes for range spread radar targets. Inverse Problems & Imaging, 2009, 3 (3) : 465-486. doi: 10.3934/ipi.2009.3.465
[15]

Gang Bao, Jun Lai. Radar cross section reduction of a cavity in the ground plane: TE polarization. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 419-434. doi: 10.3934/dcdss.2015.8.419
[16]

Shenglong Hu, Zheng-Hai Huang, Hong-Yan Ni, Liqun Qi. Positive definiteness of Diffusion Kurtosis Imaging. Inverse Problems & Imaging, 2012, 6 (1) : 57-75. doi: 10.3934/ipi.2012.6.57
[17]

Peijun Li, Yuliang Wang. Near-field imaging of obstacles. Inverse Problems & Imaging, 2015, 9 (1) : 189-210. doi: 10.3934/ipi.2015.9.189
[18]

Kaitlyn (Voccola) Muller. SAR correlation imaging and anisotropic scattering. Inverse Problems & Imaging, 2018, 12 (3) : 697-731. doi: 10.3934/ipi.2018030
[19]

Josselin Garnier. Ghost imaging in the random paraxial regime. Inverse Problems & Imaging, 2016, 10 (2) : 409-432. doi: 10.3934/ipi.2016006
[20]

Liliana Borcea, Dinh-Liem Nguyen. Imaging with electromagnetic waves in terminating waveguides. Inverse Problems & Imaging, 2016, 10 (4) : 915-941. doi: 10.3934/ipi.2016027

2018 Impact Factor: 1.469

Tools

Metrics

  • PDF downloads (14)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences