1. In a positron emission tomography (PET) system, a method for producing an image using independent component analysis and separation of components of a mixed electronic signal generated by the PET system, the method comprising: sensing signals of interest with detectors of the PET system to provide the mixed electronic signal and outputting the mixed electronic signal from the detectors, the mixed electronic signal representing a mixture of images; receiving the mixed electronic signal from the detectors by an image processing system of the PET system; determining candidate signal components from the mixed electronic signal; directly minimizing mutual information (MI) criteria between each candidate signal component without relying on model probability density functions by setting initial parameters and starting minimization near a global minimum and subsequently testing for convergence at the global minimum; and optimizing candidate signal components using polar coordinates to produce optimized signal components; extracting a component of the mixed electronic signal from the mixed electronic signal with the optimized signal components; and displaying an image from the extracted component on a display, wherein the displayed image is an extracted image from the mixture of images.