Convergent ADMM Plug and Play PET Image Reconstruction

TL;DR

This paper introduces a hybrid PET image reconstruction method combining model-based variational techniques with a learned neural network within an ADMM framework, ensuring convergence through specific parameter constraints.

Contribution

It proposes a novel ADMM-based algorithm with a convergence guarantee by constraining neural network parameters during training.

Findings

The scheme converges to a meaningful fixed point in synthetic brain PET data.

Without the parameter constraint, the algorithm does not converge.

Experimental results demonstrate the effectiveness of the proposed method.

Abstract

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.