Improved-Speed Parameter Tuning of Deconvolution Algorithm

Deconvolution (or inverse filtering) is applied if a time, space, or other domain signal is distorted by a measurement system and one wants to reconstruct the signal to be measured. This is an estimation process since the measurement is always corrupted by noise. The estimation problem is usually ill posed, meaning that even very slight changes in the measured signal caused by moderate noise will cause extreme fluctuation in the estimate. Different kinds of regularizations are applied to suppress this noise amplification, which can be accomplished only at the price of bias in the estimate. The big challenge is to set the tradeoff between the variance and bias. Most deconvolution algorithms can be tuned with one parameter or several parameters. This paper presents a systematic algorithm to optimize the parameters of deconvolution algorithms. Its advantage is that it is directly derived from the input error criterion with some approximations and spectral modeling. Spectral models of the signals are built automatically, and thus no user interaction is needed and the procedure is completely automatic. The optimization method is based on a former algorithm of one of the authors, for which a significant improvement in computational speed (approximately 100 to 150 times) has been achieved for the Tikhonov-type deconvolution method by replacing one of the iteration processes by a closed form expression. The convergence of the method is analyzed. The usefulness of the proposed method is demonstrated on simulated and measured data. Error benchmarks and robustness comparisons with competitor algorithms are also presented.