Enhanced compressibility tomography

We are interested here in the inversion of data leading to high quality imaging of physical parameters. We deal with ultrasonic diffraction tomography and first show how far field diffraction measurements of an incident plane wave give access to the spatial Fourier transform of a composite object. In the case of an acoustic model (soft tissues), this object is characterized by two parameters, e.g., the compressibility and density, each being affected by its own point spread function. The development of quantitative imaging proceeds from the separation of each parameter contribution. This can be done by measuring the scattered field over an arc for several transmitter positions around the object. This allows us, under specified conditions, to reconstruct either the compressibility, or the velocity, or the impedance maps. We have focused on compressibility imaging for which we propose a novel algorithm based on a redundant reconstruction procedure. We present tomograms of biological phantoms obtained with our experimental set-up.