Diffraction tomography: a geometrical distortion free procedure.

Ductal echography (DE) is a recent anatomically-led method of investigation of internal mammary structures that provides direct observation of ductolobular structures in mammary lobes. Indeed, breast cancer initiates from the epithelium (hypoechogenic) and develops first in ductolobular structures. Our research aims at developing an ultrasonic scanner (hemispherical antenna) that will allow three-dimensional measurement of the field diffracted by the gland. The present reconstruction procedure is an alternative solution to the standard elliptic back-projection (EBP) technique based on the Born approximation (weak scattering assumption). The latter implicitly assumes that the sound speed is (almost) constant within the breast. This unrealistic a priori is inconsistent with our heterogeneous media characterization purpose, and leads both to geometrical distortion in the reconstruction and to poor focusing of the backpropagated waves (low contrast imaging). However, the EBP technique retains a two-fold advantage: firstly it does not make any other assumption concerning the distribution of mechanical parameters apart from low gradients. Secondly, it shows great robustness, a high resolving power, and is easy to implement. Thus, in order to account for strong wavefront distortions, we integrate temporal compensation of the scattered signals acquired into the scattering EBP technique. The adjustment relies on a time of flight estimation based on a "layer stripping" approach. Numerical tests based on finite difference time domain simulations of data scattered by a random tissue-like phantom are proposed.