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SUMMARY:C5 - Coherent interferometric imaging in random media IV - Borcea\
 , L (Rice)
DTSTART:20110729T104500Z
DTEND:20110729T113000Z
UID:TALK32177@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:I will describe the the mathematical problem of imaging remote
  sources or reflectors in heterogeneous (cluttered) media with passive and
  active arrays of sensors. Because the inhomogeneities in the medium are n
 ot known\, and they cannot be estimated in detail from the data gathered a
 t the array\, we model the uncertainty about the clutter with spatial rand
 om perturbations of the wave speed. The goal of the lectures is to carry o
 ut analytically a comparative study of the resolution and signal-to-noise 
 ratio (SNR) of two\narray imaging methods: the widely used Kirchhoff migra
 tion (KM) and coherent interferometry (CINT). By noise in the images we me
 an fluctuations that are due to the random medium.\n\nKirchhoff migration 
 [2\, 3] and its variants are widely used in seismic inversion\, radar [10]
  and elsewhere.  It forms images by superposing the wave fields received a
 t the array\, delayed by the travel times from the array sensors to the im
 aging points. KM works well in smooth and known media\, where there is no 
 wave scattering and the travel times can be estimated accurately. It also 
 works well with data that has additive\, uncorrelated\nmeasurement noise\,
  provided the array is large\, because the noise is averaged out by the su
 mmation over the many sensors\, as expected from the law of large numbers.
  KM images in heterogeneous (cluttered) media are unreliable and difficult
  to interpret because of the significant wave distortion by the inhomogene
 ities. The distortion is very different from additive\, uncorrelated noise
 \, and it cannot be reduced by simply summing over the sensors in the arra
 y. CINT images efficiently in clutter [5\, 6\, 7]\, at ranges that do not 
 exceed one or two transport mean free paths [11]. Beyond such ranges the p
 roblem becomes much more difficult\, specially in the case of active array
 s\, because the clutter backscatter overwhelms the echoes from the reflect
 ors thatwe wish to image. Coherent imaging in such media may work only aft
 er pre-processing the data with filters\nof clutter backscatter\, as is do
 ne in [9\, 1].\n\nThe CINT method has been introduced in [5\, 6\, 7] for m
 itigating wave distortion effects induced by clutter. It forms images by s
 uperposing time delayed\, local cross-correlations of the wave fields rece
 ived at the array. Here local cross correlations means that they are compu
 ted in appropriate time windows and over limited array sensor offsets. It 
 has been shown with analysis and verified with numerical simulations [5\, 
 6\, 7\, 8\, 4] that the time and offset thresholding in the computation of
  the cross-correlations is essential in CINT\, because it introduces a smo
 othing that is necessary to achieve statistical stability\, at the expense
  of some loss in resolution. By statistical stability we mean negligibly s
 mall fluctuations in the CINT image even when cumulative fluctuation effec
 ts in the random medium are not small.  The lectures will give a detailed 
 comparative study between KM and CINT in som scattering regimes wh\n
LOCATION:Seminar Room 1\, Newton Institute
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