Maximum a posteriori deconvolution of sparse ultrasonic signals using genetic optimization

Deconvolution of sparse spike sequences has received much attention in the field of seismic exploration. In certain situations in ultrasonic non-destr uctive testing (NDT) of materials, similar conditions as those found in sei smic exploration occur. One example is the problem of detecting disbonds in layered aluminum structures. The reflection sequence convolved with the im pulse response of the transducer results in masking closely spaced reflecti ons. Deconvolution of these signals may reveal the reflection sequence and thus make the interpretation easier. In this paper we use the Bernoulli-Gau ssian (BC) distribution for modeling the signal generation. This relatively simple model allows maximum a posteriori (MAP) estimation of the reflectio n sequence. A derivation of the MAP criterion is given for clarity. We prop ose a genetic algorithm for optimizing the MAP criterion. The genetic algor ithm approach is motivated by the fact that the criterion is non-convex, im plying that the criterion may have more than one local minimum point. The p robability of obtaining the global optimal solution is increased by using t he proposed genetic algorithm. One of the key features in genetic algorithm s, the so-called cross-over operator, has been modified and adapted to the structure of the BG deconvolution problem to improve the efficiency of the search. The algorithm is tested on simulated data using the probability of detection (P-D) and probability of false alarm (P-FA) as evaluation criteri a. The algorithm is also tested on real ultrasonic data from a layered alum inum structure. The results show considerable improvements in the possibili ty of interpreting the signals. (C) 1999 Elsevier Science B.V. All rights r eserved.