PET reconstruction via nonlocal means induced prior

The traditional Bayesian priors for maximum a posteriori (MAP) reconstruction methods usually incorporate local neighborhood interactions that penalize large deviations in parameter estimates for adjacent pixels; therefore, only local pixel differences are utilized. This limits their abilities of penalizing the image roughness.

To achieve high-quality PET image reconstruction, this study investigates a MAP reconstruction strategy by incorporating a nonlocal means induced (NLMi) prior (NLMi-MAP) which enables utilizing global similarity information of image.

The present NLMi prior approximates the derivative of Gibbs energy function by an NLM filtering process. Specially, the NLMi prior is obtained by subtracting the current image estimation from its NLM filtered version and feeding the residual error back to the reconstruction filter to yield the new image estimation.

We tested the present NLMi-MAP method with simulated and real PET datasets. Comparison studies with conventional filtered backprojection (FBP) and a few iterative reconstruction methods clearly demonstrate that the present NLMi-MAP method performs better in lowering noise, preserving image edge and in higher signal to noise ratio (SNR).

Extensive experimental results show that the NLMi-MAP method outperforms the existing methods in terms of cross profile, noise reduction, SNR, root mean square error (RMSE) and correlation coefficient (CORR).