Recovery of Ultrasonic Impulse Response by Spectral Extrapolation

Abstract

Recovery of the impulse response of a layered medium from band-limited ultrasonic echo data is considered. Spectral components within the pass-band are used to restore that part of the spectrum which is not transmitted by the measurement system. The impulse response is then found by an inverse Fourier transform. The first approach formulates the spectral extrapolation as an L1-norm minimization problem. The transmitted spectrum within the pass-band is used to define the range of possible solutions. The missing components are found by minimizing the L1-norm of the calculated impulse response, so that it may consist of a series of narrow spikes which are expected to represent a layered medium with the highest interpretability. The second approach is based on a linear prediction theory of spectral estimation, which will directly give a squared impulse response. The band-limited spectrum is actually extrapolated by the prediction coefficients and Fourier-transformed to an impulse response. Special consideration is given to determining the optimum order of the prediction. The criterion makes use of the L1-norm and is very promising even with noisy data. The impulse response is used to reconstruct the impedance profile which is a measure of local properties of the material. Multiple reflections are included in the reconstruction process by methods of characteristics. These approaches are applied to semi-synthetic data and also to completely experimental results.

This research is partially supported by the Deutsche Forschungsgemeinshaft (DFG)

On Leave from Kyoto Institute of Technology (Sakyo-Ku Matsugasaki, Kyoto 606, Japan). This report is a part of the results he obtained as a research fellow of the Alexander von Humboldt-Foundation.