  Iterative neural networks (INN) are rapidly gaining attention for solving
inverse problems in imaging, image processing, and computer vision. INNs
combine regression NNs and an iterative model-based image reconstruction (MBIR)
algorithm, often leading to both good generalization capability and
outperforming reconstruction quality over existing MBIR optimization models.
This paper proposes the first fast and convergent INN architecture,
Momentum-Net, by generalizing a block-wise MBIR algorithm that uses momentum
and majorizers with regression NNs. For fast MBIR, Momentum-Net uses momentum
terms in extrapolation modules, and noniterative MBIR modules at each iteration
by using majorizers, where each iteration of Momentum-Net consists of three
core modules: image refining, extrapolation, and MBIR. Momentum-Net guarantees
convergence to a fixed-point for general differentiable (non)convex MBIR
functions (or data-fit terms) and convex feasible sets, under two asymptomatic
conditions. To consider data-fit variations across training and testing
samples, we also propose a regularization parameter selection scheme based on
the "spectral spread" of majorization matrices. Numerical experiments for
light-field photography using a focal stack and sparse-view computational
tomography demonstrate that, given identical regression NN architectures,
Momentum-Net significantly improves MBIR speed and accuracy over several
existing INNs; it significantly improves reconstruction quality compared to a
state-of-the-art MBIR method in each application.
