Bayesian Image Reconstruction

Problem Description

This problem is described in Exercise 8.4.5 in [1]

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

  1. D. P. Kroese and R. Y. Rubinstein.
    The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning.
    Springer, 2004.