Recovery of a sparse spike time series by L/sub 1/ norm deconvolution

An L/sub 1/ norm minimization scheme is applied to the determination of the impulse response vector h of flaws detected in practical examples of ultrasonic nondestructive evaluation in CANDU nuclear reactors. For each problem, parametric programming is applied to find the optimum value of the damping parameter that will yield the best estimate of h according to a quantified performance factor. This performance factor is based on a quantified analysis of the transitions in estimates of h as the damping parameter is varied over a wide range of possible values. It is shown that for the examined cases in which the true impulse response is a sparsely filled spike strain, the L/sub 1/ norm provides significantly better results than the more commonly used L/sub 2/ norm minimization schemes. These results are shown to be consistent with theoretical predictions.<
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