Momentum-Net: Fast and Convergent Iterative Neural Network for Inverse Problems

Area of Science:

• Computer Vision
• Image Processing
• Machine Learning

Background:

• Iterative neural networks (INNs) are emerging for inverse problems, combining neural networks with model-based image reconstruction (MBIR).
• Existing INNs offer good generalization and reconstruction quality but can lack speed and convergence guarantees.

Purpose of the Study:

• To introduce the first fast and convergent iterative neural network (INN) architecture, Momentum-Net.
• To generalize block-wise MBIR algorithms using momentum and majorizers with regression neural networks for improved performance.

Main Methods:

• Momentum-Net integrates regression neural networks with a generalized block-wise MBIR algorithm incorporating momentum and majorizers.
• Each iteration comprises image refining, extrapolation (using momentum), and non-iterative MBIR (using majorizers).
• A regularization parameter selection scheme based on the spectral spread of majorization matrices is proposed to handle data-fit variations.

Main Results:

• Momentum-Net demonstrates guaranteed convergence for general differentiable MBIR functions and convex feasible sets.
• Numerical experiments in light-field photography and sparse-view CT show significant improvements in MBIR speed and accuracy over existing INNs.
• Reconstruction quality is notably enhanced compared to state-of-the-art MBIR methods.

Conclusions:

• Momentum-Net represents a significant advancement in INN architectures for inverse problems.
• The proposed architecture offers a faster, more accurate, and convergent solution for model-based image reconstruction.
• This work paves the way for more efficient and effective image reconstruction techniques in various scientific domains.