[MatLab] EM – Expectation Maximization reconstruction technique implementation

EM – Expectation Maximization is an iterative algorithm used in tomographic images (as in CT) reconstruction, very useful when the FBP – Filtered Back Projection technique is not applicable.

Basic formula is:

f_k+1 = (f_k / alpha) (At (g / (A f_k)))


  • f_k is solution (the resulting reconstructed image) at k-th iteration, at first iteration it is our guess
  • g is image sinogram (what we get from the scanning)
  • A f_k is Radon transform of f_k
  • At is inverse Radon
  • alpha is inverse Radon of a sinogram with all values 1 which represents our scanning machine

Get the source code here.

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