A method for performing accurate iterative reconstruction of three dimensional image data sets based on Approximate Discrete Radon Transformation (ADRT) using two dimensional linograms for each of a plurality of defined planes tilted from the (x, y, 0) plane by a tilt angle and orientation angle. Image data is arranged with respect to the defined tilted planes ADRT and its inverse are implemented to provide exactly matched forward and backward projectors suitable for the Maximum-Likelihood Expectation-Maximization (ML-EM) reconstruction in PET. An EM reconstruction algorithm is accomplished by initializing an estimation image.