This paper introduces a method by which one can find the optimum iteration numbers for noise removal and deconvolution of sampled data. The method employs the mean squared error, which is the pointwise square of the difference between the deconvolution result and the input, for optimization. The always convergent iterative deconvolution and noise removal methods of Ioup are used for the simultaneous optimization by simulation research presented in this paper. This method is applied to achieve optimization for a seismic wavelet impulse response function. The optimized always convergent results are compared to those of least square inverse filtering and the reblurring procedure of Kawata and Ichioka. The input data used is a spike train of various separations to give a calibrated measure of resolution. A range of signal-to-noise ratios (SNR’s) is used in the optimization procedure. No noise removal is applied prior to unfolding for the reblurring procedure and the least squares inverse filtering methods. To achieve statistically reliable results 50 noisy data sets are generated for each SNR case for the always convergent method and 10 noisy cases for the reblurring procedure and the least squares inverse filtering techniques. For a given SNR case the average mean squared error, the average optimum deconvolution, and the average noise removal iteration numbers are found and tabulated. The tabulated results are plotted versus the average SNR. Once these optimum numbers are found they can be used in an equivalent window in the Fourier transform domain.

Date Published: 23 May 2013
PDF: 11 pages
Proc. SPIE 8745, Signal Processing, Sensor Fusion, and Target Recognition XXII, 87451S (23 May 2013); doi: 10.1117/12.2014180

Published in SPIE Proceedings Vol. 8745:
Signal Processing, Sensor Fusion, and Target Recognition XXII
Ivan Kadar, Editor(s)