Metropolis Monte Carlo deconvolution

Metropolis Monte Carlo deconvolution is introduced. The actual input data is reconstructed by means of grains according to a probability distribution function defined by the blurred data. As the blurred data ( convolution of the actual unblurred input data with the instrumental response function) is being reconstructed a grain is place in the actual input domain at every or a finite number of reconstruction steps. To test the method a wide Gaussian Impulse Response Function (IRF) is designed and convolved with an input data set containing 24 points. As the grain size (GS) is reduced the number of Monte Carlo moves and with it the accuracy of the method is increased. The grain sizes ranging from 0.0001 to 1.0 are used. For each GS five different random number seeds are used for accuracy. The Mean-Squared Error (MSE) is calculated and the average MSE is plotted VS. The GS. Sample reconstructed functions ate also given for each GS.