Multiparameter optimization of inverse filtering algorithms

This paper investigates inverse filtering of transient signals. The problem is ill-conditioned, which means that a small uncertainty in the measurement causes large deviations in the reconstructed signal. This amplified noise has to be suppressed at the price of bias in the estimation. The most difficult task is to find the optimal degree of noise reduction. Deconvolution algorithms are usually controlled by one or a few parameters. Several algorithms can be found in the literature to find the best setting of inverse filtering methods; however, usually methods with only one free parameter are handled. In this paper, an algorithm is proposed to optimize several parameters, on the basis of a spectral model. Multiparameter inverse filtering methods have the advantage that they can be better adapted to the measurement system, and to the noise and signal to be measured. The superiority of the proposed optimization method is demonstrated both on simulated and on experimental data.