FISTA-Net: Learning a Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging

Area of Science:

• Medical Imaging
• Computational Imaging
• Applied Mathematics

Background:

• Inverse problems are crucial for reconstructing images in various imaging modalities.
• Existing model-based methods like FISTA offer interpretability but can be limited in performance.
• Data-driven deep learning methods provide strong regularization but often lack interpretability and require extensive tuning.

Purpose of the Study:

• To propose FISTA-Net, a novel model-based deep learning network for inverse problems.
• To combine the interpretability of model-based algorithms with the performance of deep learning.
• To develop a tuning-free network that learns optimal parameters from data.

Main Methods:

• Unfolding the Fast Iterative Shrinkage/Thresholding Algorithm (FISTA) into a deep neural network architecture.
• Incorporating gradient descent, proximal mapping, and momentum modules.
• Developing a learnable proximal operator network for nonlinear thresholding and enabling end-to-end training.
• Imposing positive and monotonous constraints on learned parameters for stable convergence.

Main Results:

• FISTA-Net demonstrated superior performance in both visual and quantitative evaluations for Electromagnetic Tomography (EMT) and X-ray Computational Tomography (X-ray CT).
• The network achieved state-of-the-art results, outperforming both traditional model-based and deep learning approaches.
• FISTA-Net exhibited robust generalization capabilities across different noise levels and imaging tasks.

Conclusions:

• FISTA-Net offers an effective approach to solving inverse problems in imaging by integrating model-based interpretability with deep learning.
• The proposed network achieves high accuracy and generalization without manual parameter tuning.
• FISTA-Net represents a significant advancement in model-based deep learning for medical and computational imaging applications.