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We present an imaging technique particularly suited to the detection of atarget embedded in a strongly scattering medium. Classical imaging techniquesbased on the Born approximation fail in this kind of configuration because ofmultiply scattered echoes and aberration distortions. The experimental set upwe consider uses an array of programmable transmitters/receivers. A target isplaced behind a scattering medium. The impulse responses between all arrayelements are measured and form a matrix. The core of the method is to separatethe single-scattered echo of the target from the multiple scatteringbackground. This is possible because of a deterministic coherence along theantidiagonals of the array response matrix, which is typical of singlescattering. Once this operation is performed, target detection is achieved byapplying the DORT method (French acronym for decomposition of the time reversaloperator). Experimental results are presented in the case of wide-bandultrasonic waves around 3 MHz. A 125-element array is placed in front of acollection of randomly distributed steel rods (diameter 0.8mm). The slabthickness is three times the scattering mean free path. The target is a largersteel cylinder (diameter 15 mm) that we try to detect and localize. The qualityof detection is assessed theoretically based on random matrix theory and isshown to be significantly better than what is obtained with classical imagingmethods. Aside from multiple scattering, the technique is also shown to reducethe aberrations induced by an heterogeneous layer.

Detection and imaging in a random medium: A matrix method to overcome multiple scattering and aberration