Convergent ADMM Plug and Play PET Image Reconstruction

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.

Deep Unfolding of the DBFB Algorithm with Application to ROI CT Imaging with Limited Angular Density

This paper addresses the problem of image reconstruction for region-of-interest (ROI) computed tomography (CT). While model-based iterative methods can be used for such a problem, their practicability is often limited due to tedious parameterization and slow convergence. In addition, inadequate solutions can be obtained when the retained priors do not perfectly fit the solution space. Deep learning methods offer an alternative approach that is fast, leverages information from large data sets, and thus can reach high reconstruction quality. However, these methods usually rely on black boxes not accounting for the physics of the imaging system, and their lack of interpretability is often deplored. At the crossroads of both methods, unfolded deep learning techniques have been recently proposed. They incorporate the physics of the model and iterative optimization algorithms into a neural network design, leading to superior performance in various applications. This paper introduces a novel, unfolded deep learning approach called U-RDBFB designed for ROI CT reconstruction from limited data. Few-view truncated data are efficiently handled thanks to a robust non-convex data fidelity function combined with sparsity-inducing regularization functions. Iterations of a block dual forward-backward (DBFB) algorithm, embedded in an iterative reweighted scheme, are then unrolled over a neural network architecture, allowing the learning of various parameters in a supervised manner. Our experiments show an improvement over various state-of-the-art methods, including model-based iterative schemes, deep learning architectures, and deep unfolding methods.