Fast iterative image reconstruction from linograms

A method for performing accurate iterative reconstruction of an image data set by the Maximum-Likelihood Expectation-Maximization (ML-EM) method, said method being performed with a computing device having a processor, at least one memory unit and an input/output (I/O) device, said method including the steps of:

• a) initializing an estimation image of size N×N pixels to an initial value in all said pixels;
• b) forming back projection of projection weights;
• c) beginning a loop is over i iterations;
• d) forward projecting pixel coordinates into linogram coordinates using an Approximate Discrete Radon Transform (ADRT) method;
• e) forming a correction factor in all said linogram coordinates;
• f) back projecting said correction factors using said ADRT method;
• g) applying a normalization factor;
• and
• h) repeating said steps of back projecting said correction factors and applying a normalization factor through said i iterations until a stopping criterion is satisfied.

A method for performing accurate iterative reconstruction of a Positron Emission Tomography (PET) data set, said method being performed with a computing device having a processor, at least one memory unit and an input/output (I/O) device, said method including the steps of:

• i) initializing all pixels in an estimation image of size N×N pixels;
• j) forming back projection of projection weights;
• k) beginning a loop is over i iterations;
• l) forward projecting pixel coordinates into linogram coordinates using an Approximate Discrete Radon Transform (ADRT) method;
• m) forming a correction factor in all said linogram coordinates;
• n) back projecting said correction factors using said ADRT method;
• o) applying a normalization factor;
• and
• p) repeating said steps of back projecting said correction factors and applying a normalization factor through said i iterations.