Learning-Assisted Fast Determination of Regularization Parameter in Constrained Image Reconstruction

Objective:
To leverage machine learning (ML) for fast selection of optimal regularization parameter in constrained image reconstruction.
Methods:
Constrained image reconstruction is often formulated as a regularization problem and selecting a good regularization parameter value is an essential step. We solved this problem using an ML-based approach by leveraging the finding that for a specific constrained reconstruction problem defined for a fixed class of image functions, the optimal regularization parameter value is weakly subject-dependent and the dependence can be captured using few experimental data. The proposed method has four key steps: a) solution of a given constrained reconstruction problem for a few (say, 3) pre-selected regularization parameter values, b) extraction of multiple approximated quality metrics from the initial reconstructions, c) predicting the true quality metrics values from the approximated values using pre-trained neural networks, and d) determination of the optimal regularization parameter by fusing the predicted quality metrics.
Results:
The effectiveness of the proposed method was demonstrated in two constrained reconstruction problems. Compared with L-curve-based method, the proposed method determined the regularization parameters much faster and produced substantially improved reconstructions. Our method also outperformed state-of-the-art learning-based methods when trained with limited experimental data.
Conclusion:
This paper demonstrates the feasibility and improved reconstruction quality by using machine learning to determine the regularization parameter in constrained reconstruction.
Significance:
The proposed method substantially reduces the computational burden of the traditional methods (e.g., L-curve) or relaxes the requirement of large training data by modern learning-based methods, thus enhancing the practical utility of constrained reconstruction.