Momentum-Net: Fast and convergent iterative neural network for inverse problems
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
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NSF-PAR ID:
10309167
Journal Name:
IEEE Transactions on Pattern Analysis and Machine Intelligence
ISSN:
0162-8828
5. Deconvolution can be used to obtain sharp images or volumes from blurry or encoded measurements in imaging systems. Given knowledge of the system’s point spread function (PSF) over the field of view, a reconstruction algorithm can be used to recover a clear image or volume. Most deconvolution algorithms assume shift-invariance; however, in realistic systems, the PSF varies laterally and axially across the field of view due to aberrations or design. Shift-varying models can be used, but are often slow and computationally intensive. In this work, we propose a deep-learning-based approach that leverages knowledge about the system’s spatially varying PSFs for fast 2D and 3D reconstructions. Our approach, termed MultiWienerNet, uses multiple differentiable Wiener filters paired with a convolutional neural network to incorporate spatial variance. Trained using simulated data and tested on experimental data, our approach offers a$625−<#comment/>1600×<#comment/>$increase in speed compared to iterative methods with a spatially varying model, and outperforms existing deep-learning-based methods that assume shift invariance.