Signal to Noise Ratio Analysis in Virtual Source Array Imaging

Abstract

Abstract. We consider correlation-based imaging of a reflector located on one side of a passive array where the medium is homogeneous. On the other side of the array the illumination by remote impulsive sources goes through a strongly scattering medium. It has been shown in [J. Garnier and G. Papanicolaou, Inverse Problems 28 (2012), 075002] that migrating the cross correlations of the passive array gives an image whose resolution is as good as if the array was active and the array response matrix was that of a homogeneous medium. In this paper we study the signal to noise ratio of the image as a function of statistical properties of the strongly scattering medium, the signal bandwidth and the source and passive receiver array characteristics. Using a Kronecker model for the strongly scattering medium we show that image resolution is as expected and that the signal to noise ratio can be computed in an essentially explicit way. We show with direct numerical simulations using full wave propagation solvers in random media that the theoretical predictions based on the Kronecker model are accurate.

Matched-Filter and Correlation-Based Imaging for Fast Moving Objects Using a Sparse Network of Receivers

“…Other important parameters of the imaging system are the central frequency, f o , and the bandwidth, B, which are determined by the emitter. We consider here a system operating at high frequency with a relatively large bandwidth, such as the X-Band (8)(9)(10)(11)(12) or the S-Band (2-4 GHz) regimes.…”

“…This would be true for receivers that are not located on the ground but are flying above the turbulent atmosphere. Indeed, considering airborne receivers transforms the passive correlation-based problem to a virtual source array imaging problem that has been studied for stationary receiver arrays in [9,10,11]. The key idea is that passive correlation-based imaging becomes equivalent to having a virtual active array at the location of the passive receivers.…”

Passive Synthetic Aperture Imaging

“…(2) It can provide images that are essentially unaffected by the scattering inhomogeneities of the medium between the source array and the auxiliary passive array, and may even benefit from them by diversifying the illumination of the reflectors. Further, this will occur even with strong scattering that would make imaging with data from the main, active surface array impossible [14,15,16].…”

“…Note that, when the auxiliary array is permanent and not synthetic as in the previous sections, then one can get the full cross correlation matrix even with asynchronous and staggered sources, that is, without knowing the emission times, because the signals coming from a source can be recorded by all the receivers at once. A mathematical and numerical analysis of the imaging function (5.4) is given in [14,15,16].…”

Time and direction of arrival detection and filtering for imaging in strongly scattering random media

“…Heavy clutter arises in applications of imaging through foliage or the turbulent atmosphere, in nondestructive testing of materials, and so on. It has received much attention lately, specially in the context of imaging with passive arrays of receivers which are either near the imaging region or are separated from it by a non scattering medium [18]. In these problems the waves emitted from remote sources travel through clutter before reaching the receivers and the small reflectors.…”