Maximum a posteriori deconvulution of ultrasonic data with applications in nondestructive testing : Multiple transducer and robustness is

Sammanfattning: In the thesis, various aspects of deconvolution of ultrasonic pulse-echo signals in nondestructive testing are treated. The deconvolution problem is formulated as estimation of a reflection sequence which is the impulse characteristic of the inspected object and the estimation is performed using either maximum a posteriori (MAP) or linear minimum mean square error (MMSE) estimators. A multivariable model is proposed for a certain multiple transducer setup allowing for frequency diversity, thereby improving the estimation accuracy. Using the MAP estimator three different material types were treated, with varying amount of sparsity in the reflection sequences. The Gaussian distribution is used for modelling materials containing a large number of small scatters. The Bernoulli-Gaussian distribution is used for sparse data obtained from layered structures and a genetic algorithm approach is proposed for optimizing the corresponding MAP criterion. Sequences with intermediate sparsity suitable of modelling composite materials have been treated using a prior Gaussian distribution with unknown sample variances. An heuristic discrete-time model for modelling dispersion caused by absorption in plastic composite materials is also presented. Robustness against inaccurate impulse responses or position errors in the multiple transducer setup is treated by letting the model of the unknown system belong to an uncertainty set of possible models. The robustness is accomplished by designing linear MMSE estimators that minimize the average estimation error over the models in the uncertainty set. It is verified experimentally that the robust estimators outperform candidate estimators on the average. The problem of transducer normalization encountered when calibrating an input signal to an automatic characterization system is also treated. It is shown that the solution to this problem decouples into the solution of the deconvolution problem followed by a trivial filter operation.