Imaging multiple reflectors in strongly scattering media. ; Απεικόνιση πολλαπλών ανακλαστήρων σε μέσα με ισχυρή σκέδαση

We consider the problem of imaging small defects embedded in strongly scattering media, often called clutter, using an active array of transducers that can play the dual role of emitters and receivers. Our data is the array response matrix collected by sending short pulses from each source and recording the response at all array elements. Imaging in strong clutter is quite challenging because the array data are dominated by noise due to the multiple scattering of the waves with the medium heterogeneities. To successfully image in this regime using simple coherent imaging functionals we follow the methodology of coherent signal enhancement through data filtering. In particular we consider the approach of [14] and seek to select time-frequency windows that contain the coherent echoes from the reflectors we wish to image using the Local Cosine Transform (LCT). The selection is performed by detecting a pattern disruption in the behavior of the singular values of the local-cosine coefficients transformed matrix. Following [2], we also consider two random matrix theory based selection procedures. The first one is image based and selects time-frequency windows using a criterion that examines the maximum of an appropriately normalized migration image. The second one uses a filter [15] to exclude multiple scattering contributions from the data and then selects the time-frequency windows for which the defect is detectable by looking at the largest singular value of the filtered response matrix. The filter proposed in [15] is a rank one projection (ROP) that is very simple to implement and can be combined with the LCT filter. We study the performance of the different approaches with extensive numerical simulations, carried out in a non-destructive testing setup. Our simulations suggest that the combination of the LCT with the ROP filter gives the best results.