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, 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 momentums and majorizers with regression NNs. For fast MBIR, Momentum-Net uses momentum terms in extrapolation modules, and noniterative MBIR modules at each layer by using majorizers, where each layer 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 radius 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.
Image reconstruction in low-count PET is particularly challenging because gammas from natural radioactivity in Lu-based crystals cause high random fractions that lower the measurement signal-to-noise-ratio (SNR). In model-based image reconstruction (MBIR), using more iterations of an unregularized method may increase the noise, so incorporating regularization into the image reconstruction is desirable to control the noise. New regularization methods based on learned convolutional operators are emerging in MBIR. We modify the architecture of a variational neural network, BCD-Net, for PET MBIR, and demonstrate the efficacy of the trained BCD-Net using XCAT phantom data that simulates the low true coincidence count-rates with high random fractions typical for Y-90 PET patient imaging after Y-90 microsphere radioembolization. Numerical results show that the proposed BCD-Net significantly improves PET reconstruction performance compared to MBIR methods using non-trained regularizers, total variation (TV) and non-local means (NLM), and a non-MBIR method using a single forward pass deep neural network, U-Net. BCD-Net improved activity recovery for a hot sphere significantly and reduced noise, whereas non-trained regularizers had a trade-off between noise and quantification. BCD-Net improved CNR and RMSE by 43.4% (85.7%) and 12.9% (29.1%) compared to TV (NLM) regularized MBIR. Moreover, whereas the image reconstruction results show that the non-MBIR U-Net over-fits the training data, BCD-Net successfully generalizes to data that differs from training data. Improvements were also demonstrated for the clinically relevant phantom measurement data where we used training and testing datasets having very different activity distribution and count-level.