NDE imaging of flaws using rapid computation of Shannon entropy

Previous work has demonstrated the advantages of Shannon entropy (H) analysis for the image-based detection of defects in both plexiglas and graphite/epoxy composites [1][2][3]. Application to experimental data shows that the analysis is fast and robust in the presence of noise. However, it suffers from the shortcoming that when signal averaging is employed, H converges to a constant, independent of the underlying waveform characteristics (log₂(N_σ), where N_σ is the number of gated time domain sample points). By considering a generalization of the Shannon entropy to the continuous waveform case, H _c, we eliminate this problem and obtain a stable numerical scheme for evaluation of H_c based on the use of Fourier series. As described previously, however, this approach requires a network of 20 workstations over 20 hours to complete analysis of one 41 by 201 pixel image. We describe a new approach for calculating continuous waveform entropy H_c, based on the use of a Green´s function. We show that the new approach produces the same or higher image contrast in a time that is roughly three orders of magnitude smaller than that required by the Fourier series method. This improvement arises from two sources. The Green´s function approach has greater inherent immunity to noise, and requires fewer calculations than the Fourier series approach. The resulting algorithm makes it feasible to perform H_c analysis on a personal computer