Inverse Problems and Imaging (IPI)

On the stability of some imaging functionals

Pages: 585 - 616, Volume 10, Issue 3, August 2016      doi:10.3934/ipi.2016013

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Guillaume Bal - Department of Applied Physics and Applied Mathematics, Columbia University, New York NY, 10027, United States (email)
Olivier Pinaud - Department of Mathematics, Colorado State University, Fort Collins CO 80523, United States (email)
Lenya Ryzhik - Department of Mathematics, Stanford University, Stanford, CA 94305, United States (email)

Abstract: This work is devoted to the stability/resolution analysis of several imaging functionals in complex environments. We consider both linear functionals in the wavefield as well as quadratic functionals based on wavefield correlations. Using simplified measurement settings and reduced functionals that retain the main features of functionals used in practice, we obtain optimal asymptotic estimates of the signal-to-noise ratios depending on the main physical parameters of the problem. We consider random media with possibly long-range dependence and with a correlation length that is less than or equal to the central wavelength of the source we aim to reconstruct. This corresponds to the wave propagation regimes of radiative transfer or homogenization.

Keywords:  Imaging in random media, resolution, stability.
Mathematics Subject Classification:  Primary: 35R30; Secondary: 78A48.

Received: January 2015;      Available Online: August 2016.