Blind deconvolution through parametric identification using second and fourth order cumulants

Deconvolution of signals that have been distorted by an ultrasonic transducer is usually made in order to obtain improved image resolution. In NDE applications efficient deconvolution would make possible comparison of images obtained using different transducers. Classical deconvolution methods are based on some a priori knowledge of the transducer. In blind deconvolution the distortion is estimated from the signals at hand and later on used in the deconvolution process. Both parametric and nonparametric methods are available. A standard parametric approach is to find the model that minimizes the squared prediction error. This method which is based on second order statistics has the disadvantage of not being able to correctly identify nonminimum-phase systems. An alternative method based on both second and fourth order cumulants, referred as to HOCM, is proposed to circumvent this problem. In order to see advantages and disadvantages with the proposed method comparisons are made with the prediction error method, PEM, and also with a nonparametric method. The nonparametric method is based on the complex cepstrum, and is known to be capable of identifying nonminimum-phase systems. The results presented in the paper show that the proposed method is capable of finding nonminimum-phase systems and therefore is a step towards identification of the true distorting system (transducer). The results are obtained using real and simulated ultrasonic data. The B-scans have been acquired in inspection of graphite-epoxy composite materials, and the simulated data is generated by a simple model of the layered structure materials.