[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)))

where:

• 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.