An investigation of temporal regularization techniques for dynamic PET reconstructions using temporal splines

The use of a temporal B‐spline basis for the reconstruction of dynamic positron emission tomography data was investigated. Maximum likelihood (ML) reconstructions using an expectation maximization framework and maximum A‐posteriori (MAP) reconstructions using the generalized expectation maximization framework were evaluated. Different parameters of the B‐spline basis of such as order, number of basis functions and knot placing were investigated in a reconstruction task using simulated dynamic list‐mode data. We found that a higher order basis reduced both the bias and variance. Using a higher number of basis functions in the modeling of the time activity curves (TACs) allowed the algorithm to model faster changes of the TACs, however, the TACs became noisier. We have compared ML, Gaussian postsmoothed ML and MAP reconstructions. The noise level in the ML reconstructions was controlled by varying the number of basis functions. The MAP algorithm penalized the integrated squared curvature of the reconstructed TAC. The postsmoothed ML was always outperformed in terms of bias and variance properties by the MAP and ML reconstructions. A simple adaptive knot placing strategy was also developed and evaluated. It is based on an arc length redistribution scheme during the reconstruction. The free knot reconstruction allowed a more accurate reconstruction while reducing the noise level especially for fast changing TACs such as blood input functions. Limiting the number of temporal basis functions combined with the adaptive knot placing strategy is in this case advantageous for regularization purposes when compared to the other regularization techniques.