# American Institute of Mathematical Sciences

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

## A variational approach to waveform design for synthetic-aperture imaging

 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.
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
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