Deconvolution under normalized autocorrelation constraints

Abstract

In this paper we describe a time domain algorithm for determining the influence function from the measured input and output signals of the system. The deconvolution, which is a highly unstable inverse problem with measurement errors, is an important step for obtaining the system's influence function that provides insight about flow regimes normally masked by the time-dependent input signal. The algorithms presented for deconvolution in the literature are generally based on data reduction, with the exception of constrained deconvolution methods. We propose a constrained least-squares deconvolution method to reconstruct the influence function from noisy data. The constraints are the lower bounds on the first few lags of the normalized autocorrelation coefficients of the influence function. The lower bounds may represent known or desirable smoothness properties of the function. By choosing the constraint values larger, a smoother deconvolution can be obtained. We also impose an energy constraint on the derivative of the reconstructed signal for further regularization.