Acceleration of maximum likelihood reconstruction, using frequency amplification and attenuation compensation

Algorithms that calculate maximum likelihood (ML) and maximum a posteriori solutions using expectation-maximization have been successfully applied to SPECT and PET. These algorithms are appealing because of their solid theoretical basis and their guaranteed convergence. A major drawback is the slow convergence, which results in-long processing times. The authors present 2 new heuristic acceleration methods for maximum likelihood reconstruction of ECT images. The first method incorporates a frequency-dependent amplification in the calculations, to compensate for the low pass filtering of the backprojection operation. In the second method, an amplification factor is incorporated that suppresses the effect of attenuation on the updating factors. Both methods are compared to the 1-dimensional line search method proposed by Lewitt. All 3 methods accelerate the ML algorithm. On the authors' test images, Lewitt's method produced the strongest acceleration of the three individual methods. However, the combination of the frequency amplification with the line search method results in a new algorithm with still better performance. Under certain conditions, an effective frequency amplification can be already achieved by skipping some of the calculations required for ML.