An Optimization Method for Quantitative Impedance Tomography

A near-field ultrasonic tomography method providing high resolution imaging for soft tissue in the reflection mode is reported. When the Born approximation is valid, the main limitation of this method is that it requires an incident pulse with infinite bandwidth, whereas the incident pulses used in practice have a limited bandwidth, which makes quantitative reconstruction impossible. The reconstructed image is qualitative in the sense that it is a band-pass filtered reconstruction of the impedance distribution. An optimization method based on the use of the geometrical information provided by the tomographic reconstruction is developed to obtain the quantitative information required. The object was approximated locally by an equivalent canonical body, on the basis of the previous global estimation. The inversion procedure is then carried out using the minimization of a cost function, which is the average over frequency of the difference between the measured field scattered by the object and the estimated field scattered by the equivalent canonical body. Assuming the object to be homogeneous by regions, the last step consists of assigning the estimated local impedance value to the region of interest. When the geometry of the real body is almost canonical, the optimization method yields accurate impedance assessments.