Convergent ADMM Plug and Play PET Image Reconstruction
This work addresses convergence issues in PET image reconstruction for medical imaging, but it is incremental as it builds on existing ADMM Plug and Play methods by adding a constraint for stability.
The authors tackled the problem of ensuring convergence in hybrid PET image reconstruction algorithms that combine model-based variational reconstruction with a deep neural network (DNN) in an ADMM Plug and Play framework, and they showed that enforcing a constraint on network parameters during learning leads to experimental convergence to a meaningful fixed point in a synthetic brain exam, whereas without this constraint, the algorithm did not converge.
In this work, we investigate hybrid PET reconstruction algorithms based on coupling a model-based variational reconstruction and the application of a separately learnt Deep Neural Network operator (DNN) in an ADMM Plug and Play framework. Following recent results in optimization, fixed point convergence of the scheme can be achieved by enforcing an additional constraint on network parameters during learning. We propose such an ADMM algorithm and show in a realistic [18F]-FDG synthetic brain exam that the proposed scheme indeed lead experimentally to convergence to a meaningful fixed point. When the proposed constraint is not enforced during learning of the DNN, the proposed ADMM algorithm was observed experimentally not to converge.