Maximum a posteriori deconvolution of ultrasonic signals using multiple transducers

A new method for deconvolution of ultrasonic pulse-echo measurements employing multiple-transducer setup is proposed in the paper. An optimal way of estimating the material reflection sequence for a linear signal generation model using maximum a posteriori estimation is proposed. The method combines the measurements from a number of transducers covering different frequency bands yielding an optimal estimate of the reflection sequence. The main idea of this approach is to complement the information unavailable from one transducer in some frequency bands with the information from the other transducers. The method is based on the assumption that the measurements are performed using transducers with identical apertures and apodization, which are located exactly at the same position relative to the test object during the measurement. An error analysis presented in the paper proves that when the above assumptions are fulfilled, the proposed method, by utilizing more data for estimation, consistently yields more accurate reflection sequence estimates than the classical Wiener filter. Experimental evidence is presented using both simulated and real ultrasonic data as a verification of the correctness of the multiple-transducer model and the estimation scheme. An illustration of the advantages of the method is also given using real ultrasonic data.