Evaluation of a cross-validation stopping rule in MLE SPECT reconstruction

One of the problems in the routine use of the maximum-likelihood estimator method-expectation maximization (MLE-EM) algorithm is to decide when the iterative process should be stopped. We studied a cross-validation stopping rule to assess its usefulness in SPECT. We tested this stopping rule criterion in the MLE-EM algorithm without acceleration as well as in two accelerating algorithms, the successive substitutions algorithm (SSA) and the additive algorithm (AA). Different values of an acceleration factor were tested in SSA and AA. Our results from numerical and physical phantoms show that the stopping rule based on the cross-validation ratio (CVR) takes into account the similarity of the reconstructed image to the ideal image, noise and the contrast of the image. CVR yields reconstructed images with balanced values of the figures of merit (FOM) employed to assess the image quality. The CVR criterion can be used in the original MLE-EM algorithm as well as in SSA and AA. The reconstructed images obtained with SSA and AA showed FOM values that were very similar. These results were justified by considering AA to be an approximate form of SSA. The range of validity for the acceleration factor in SSA and AA was found to be [1, 2]. In this range, an inverse function connects the acceleration factor to the number of iterations needed to attain prefixed values of FOMs.