Publisher:
Society for Industrial and Applied Mathematics
Issued date:
2015-07-30
Citation:
SIAM Journal Imaging Sciences, v. 8, Issue 3, pp. 1547-1573
ISSN:
1936-4954
DOI:
10.1137/140994617
Sponsor:
The work of A. Novikov was supported by NSF grant DMS-0908011. The work of M. Moscoso was supported by Spanish MICINN Grant FIS2013-41802-R. The work of G. Papanicolaou was supported by AFOSR grant FA9550-11-1-0266
We propose a new strategy for narrow band, active array imaging of weak localized scatterers when only the intensities are recorded and measured at the array. We consider a homogeneous medium so that wave propagation is fully coherent. We show that imaging witWe propose a new strategy for narrow band, active array imaging of weak localized scatterers when only the intensities are recorded and measured at the array. We consider a homogeneous medium so that wave propagation is fully coherent. We show that imaging with intensity-only measurements can be carried out using the time reversal operator of the imaging system, which can be obtained from intensity measurements using an appropriate illumination strategy and the polarization identity. Once the time reversal operator has been obtained, we show that the images can be formed using its singular value decomposition (SVD). We use two SVD-based methods to image the scatterers. The proposed approach is simple and efficient. It does not need prior information about the sought image, and it guarantees exact recovery in the noise-free case. Furthermore, it is robust with respect to additive noise. Detailed numerical simulations illustrate the performance of the proposed imaging strategy when only the intensities are captured.[+][-]