Superresolution inverse ultrasound scattering

Summary form only given, as follows. A new approach is developed to solve inverse-scattering-based ultrasound imaging. While usual ultrasound imaging uses pulse echo analysis of the reflection data, this technique is based on the inversion of the Lippman-Schwinger equation with the use of constraints. It is found that by requiring the impedance profile to be a set of consecutive layers, one obtains a system of nonlinear equations, relating the reflection amplitude to the parameters of the mode. Upon use of the Born approximation this set of equations can be reduced to a linear prediction spectral estimation problem, which can be solved exactly using the LPSVD algorithm of R. Kumaresan and D. W. Tufts (1982). In model calculations performed with simulated data, it is found not only that the resolution is better, but also that the performance in noisy conditions is significantly improved, and that the quality of the results is not as dependent on the bandwidth as it usually is for the standard Fourier-transform-based Born approximation. When the actual impedance profile is not a set of layers, one can still get good results provided the number of data points is high enough to allow a reasonable fit in terms of the model constraint. Extension of the method to more general model constraints, as well as for higher values of the impedance, is currently under consideration.