Minimum entropy deconvolution of pulse-echo signals acquired from attenuative layered media

In this article deconvolution of ultrasonic pulse-echo data acquired from attenuative layered media is considered. The problem is divided in two subproblems: treating the sparse reflection sequence caused by the layered structure of the media and treating the frequency-dependent attenuation. The first subproblem is solved by means of joint maximum a posteriori estimation of the assumed zero mean, white, nonstationary reflection sequence and its corresponding sequence of unknown standard deviations. This approach leads to an algorithm that seeks minimum entropy solutions for the reflection sequence and therefore the algorithm serves as a novel link between the classical Wiener filter and methods for sparse or minimum entropy deconvolution. The second subproblem is solved by introducing a new signal processing-oriented, linear discrete-time model for frequency-dependent attenuation in isotropic and homogeneous media. The deconvolution algorithm is tested using simulated data and its performance for real normal incidence pulse-echo data from a composite material is also demonstrated. The results show that the algorithm, in combination with the attenuation model, yields estimates that reveal the internal structure of the composite and, thus, simplify the interpretation of the ultrasonic data.