Normalized split-spectrum: A detection approach

We consider in this paper the problem of automatic detection of ultrasonic echo pulses in a grain noise background. We start by assuming a reference model for grain noise: multivariate correlated Gaussian model having, in general, different variances under every hypothesis. We show that, even for this simple model, there is not practical optimum solution, except if the variances are equal under every hypothesis and the echo pulse satisfies a spectral constraint. Then we consider split-spectrum (SS) suboptimum solutions. Firstly, SS algorithms are formulated following an algebraic approach which is appropriate in an automatic detection framework. Popular minimization and polarity thresholding algorithms are considered under this framework. Then a new detector called normalized SS (NSS) is proposed. The underlying idea is to actually exploit the tuning frequency sensitivity (i.e., variability of the output magnitudes from one SS channel to another), making this measurement independent of the absolute magnitudes. Different experiments with simulated and real data show evidences of the interest of the new method in an automatic detection framework. Derivations of the formulas for fitting the probability of false alarm in every detector are included in the paper.