RECOVERY OF A SPARSE SPIKE TIME-SERIES BY L(1) NORM DECONVOLUTION

An L1 norm minimization scheme is applied to the determination of the impulse response vector h of flaws detected in practical examples of u ltrasonic nondestructive evaluation in CANDU nuclear reactors. For eac h problem, parametric programming is applied to find the optimum value of the damping parameter that will yield the best estimate of h accor ding to a quantified performance factor. This performance factor is ba sed on a quantified analysis of the transitions in estimates of h as t he damping parameter is varied over a wide range of possible values. I t is shown that for the examined cases in which the true impulse respo nse is a sparsely filled spike strain, the L1 norm provides significan tly better results than the more commonly used L2 norm minimization sc hemes. These results are shown to be consistent with theoretical predi ctions.