Simultaneous optimization by simulation of iterative deconvolution and noise removal for non-negative data

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 square of the difference between the deconvolution result and the input, for optimization. As an example of the iterative methods of noise removal and deconvolution, the always convergent method of Ioup is used for the simultaneous optimization by simulation research presented in this paper. This method is applied to achieve optimization for two Gaussian impulse response functions, one narrow (rapidly converging) and the other wide (slowly converging). The input function used consists of three narrow peaks selected to give some overlap after convolution with the Gaussian impulse response function. Normal distributed noise is added to the convolution of the input with the impulse response function. A range of signal-to-noise ratio is used to optimize the always convergent iterations for both of these Gaussians. For the narrow Gaussian 15 signal-to-noise ratio cases are studied while for the wide Gaussian 11 signal-to-noise ratios cases are considered. To achieve statistically reliable results 50 noisy data sets are generated for each signal-to-noise ratio case. For a given signal-to-noise ratio case the optimum deconvolution and noise removal iteration numbers are found and tabulated. The tabulated results are given in tables one through three. Once these optimum numbers are found they can be used in an equivalent window in the Fourier transform domain, although the non-negativity constraint can only be applied in the function domain.