Acceleration of the direct reconstruction of linear parametric images using nested algorithms

Abstract

Parametric imaging using dynamic positron emission tomography (PET) provides important information for biological research and clinical diagnosis. Indirect and direct methods have been developed for reconstructing linear parametric images from dynamic PET data. Indirect methods are relatively simple and easy to implement because the image reconstruction and kinetic modeling are performed in two separate steps. Direct methods estimate parametric images directly from raw PET data and are statistically more efficient. However, the convergence rate of direct algorithms can be slow due to the coupling between the reconstruction and kinetic modeling. Here we present two fast gradient-type algorithms for direct reconstruction of linear parametric images. The new algorithms decouple the reconstruction and linear parametric modeling at each iteration by employing the principle of optimization transfer. Convergence speed is accelerated by running more sub-iterations of linear parametric estimation because the computation cost of the linear parametric modeling is much less than that of the image reconstruction. Computer simulation studies demonstrated that the new algorithms converge much faster than the traditional expectation maximization (EM) and the preconditioned conjugate gradient algorithms for dynamic PET.

Resolution modeling in PET imaging: Theory, practice, benefits, and pitfalls

“…(1) are very different, decoupling them may result in faster convergence. 58,59 One approach to decoupling the matrices without affecting the image quality is to use the nested EM algorithm. 58 Although the approach was proposed for direct reconstruction of linear parametric images from dynamic PET data, the method is applicable to PET image reconstruction with a factored system matrix.…”

“…58,59 One approach to decoupling the matrices without affecting the image quality is to use the nested EM algorithm. 58 Although the approach was proposed for direct reconstruction of linear parametric images from dynamic PET data, the method is applicable to PET image reconstruction with a factored system matrix. With this method, each image update using the GR model can be implemented by one iteration of EM reconstruction using G followed by multiple iterations of image deconvolution using R. 59 The advantages of this method would be that it gives the same solution as using the GR model directly and it does not require the matrices to be invertible.…”

Advanced kinetic modelling strategies: towards adoption in clinical PET imaging

“…Using the same optimisation transfer approach, Wang and Qi [137] also developed a minorisation-maximisation algorithm to include a simplified reference tissue model within a 4D framework. Finally, along similar lines to the work of Wang and Qi [129,130] and Matthews et al [132], Rahmim et al [138] also used a decoupling technique and a surrogate function with a single compartment model to directly estimate myocardial perfusion in 82 Rb imaging. Achieving a decoupling between the tomographic and the image-based kinetic modelling problems has facilitated the use of existing image reconstruction and kinetic modelling algorithms in a manner similar to the post-reconstruction modelling approach but monotonically converging to the direct parameter estimates of the 4D maximum likelihood problem.…”

“…To tackle these issues, Wang and Qi [129] proposed an algorithm to decouple these two components using this optimisation transfer principle and paraboloidal surrogate functions. In an extension of this work, they used linear Patlak and spectral analysis models as well as nonlinear models within a nested EM algorithm [130,131]. Matthews et al [132] performed similar work in which, after separation of the image and projection space problems, the maximum likelihood image-based problem is transformed into a least squares problem for which many existing methods can be used.…”

Evaluation of a direct 4D reconstruction method using generalised linear least squares for estimating nonlinear micro-parametric maps

“…Some of them have focused on the estimation of linear kinetic parameters based either on a spectral analysis model [14][15][16], or on graphical analysis methods, such as the Patlak [17][18][19] and the Logan plots [20]. These approaches have been successfully applied on clinical data, leading to fast and efficient calculation of parametric maps.…”