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This dissertation discusses the problem of optimally reconstructing a soft acoustic scattering potential using inverse scattering techniques when the reflection coefficient data is incomplete or with low signal-to-noise ratio. As it has been noticed in the past, inverse scattering techniques can help overcome the finite spatial size resolution barrier of conventional ultrasonic imaging. However, in practical experimental conditions the reflection coefficient data is bandlimited and noisy. Under these circumstances the quality of the results obtained through the use of the standard inverse scattering techniques is far from satisfactory. A new parametric approach based on local polynomial approximations to the scattering target is introduced. Its lower level formulation, which corresponds to a layered medium, is studied in particular detail in both the non-lossy and lossy case, since it can be easily applied in a number of different scenarios after minor modifications. For calculations performed with calculated and experimental data it was found that this technique yields superior results when compared to the standard spectral inversion techniques, provided the scattering target can be well represented by the model constraint. Otherwise a compromise between resolution and noise is found. Further improvements of the technique as well as applications to other related fields are also discussed. |
