Optimizing Iterative Noise Removal and Deconvolution by Simulation

Optimization of iterative noise removal and deconvolution establishes the number of iterations needed. One approach to optimization utilizes statistical analysis of numerous trials on noise-added signals. Fixing approximately the signal-to-noise ratio (SNR) for each set of trials makes possible the determination of iteration number and expected error versus SNR as well as the statistical standard deviation of these quantities. The advantage of this approach is that it allows 1) any computer-generated noise type, 2) any criterion for optimization which is calculable, and 3) the use of nonlinear constraints. Analytic approaches to optimization do not in general allow this flexibility. Since nonlinear constraints such as nonnegativity are often the key to superresolution, the ability to perform this type of optimization is quite important. Details concerning the simulations are addressed, including stopping criteria when the rate of change in the optimization measure is very slow. Although minimization of the mean squared error and absolute error have been the main criteria examined thus far in the work because of their current pervasiveness, a number of criteria, especially those related to resolution, may be more appropriate for many data types and goals.