Bayesian Image Reconstruction
Problem Description
Program Descriptions
 bayes.m
This program reconstructs the image in the first problem via the CE method.Usage:
Call the program from MATLAB, with the following syntax:
[ x , y ] = bayes( N , rho , alpha , sigma , y )
Example: [ reimage , oldimage ] = bayes( 500 , 0.04 , 0.7 , 0.1 , image )
In this example, image is a matrix, consisting of two unique gray levels (eg. 0's and 1's), and the noise to be added is distributed Normally, with a standard deviation of 0.1.Inputs: N  number of samples each iteration rho  fraction of best performing samples to take alpha  smoothing paramter sigma  std. deviation for image noise (optional) y  image data (optional) Outputs: x  reconstructed image y  original image  bayes2.m
This program reconstructs the image in the second problem via the CE method.Usage:
Call the program from MATLAB, with the following syntax:
[ x , y , v ] = bayes2( N , rho , alpha , sigma , y )
Example: [ reimage , oldimage , probs ] = bayes2( 500 , 0.04 , 0.7 )
In this example, a default image is used.Inputs: N  number of samples each iteration rho  fraction of best performing samples to take alpha  smoothing paramter sigma  std. deviation for image noise y  image data Outputs: x  reconstructed image y  original image v  probabilities at the end  scoreb.m
This program is used internally by both of the above programs to evaluate the performance of the algorithm.
Bibliography

D. P. Kroese and R. Y. Rubinstein.
The CrossEntropy Method: A Unified Approach to Combinatorial Optimization, MonteCarlo Simulation and Machine Learning.
Springer, 2004.