Unrolled networks have become prevalent in various computer vision and imaging tasks. Although they have demonstrated remarkable efficacy in solving specific computer vision and computational imaging tasks, their adaptation to other applications presents considerable challenges. This is primarily due to the multitude of design decisions that practitioners working on new applications must navigate, each potentially affecting the network's overall performance. These decisions include selecting the optimization algorithm, defining the loss function, and determining the number of convolutional layers, among others. Compounding the issue, evaluating each design choice requires time-consuming simulations to train, fine-tune the neural network, and optimize for its performance. As a result, the process of exploring multiple options and identifying the optimal configuration becomes time-consuming and computationally demanding. The main objectives of this paper are (1) to unify some ideas and methodologies used in unrolled networks to reduce the number of design choices a user has to make, and (2) to report a comprehensive ablation study to discuss the impact of each of the choices involved in designing unrolled networks and present practical recommendations based on our findings. We anticipate that this study will help scientists and engineers design unrolled networks for their applications and diagnose problems within their networks efficiently.

More recently, deep learning has garnered considerable attention in medical imaging and has demonstrated superior Deep learning methods are highly effective for many image performance in a variety of image reconstruction tasks including reconstruction tasks. However, the performance of supervised X-ray computed tomography [7], positron emission learned models can degrade when applied to distinct tomography [8], and MRI [9]. An important recent trend experimental settings at test time or in the presence of distribution in supervised deep learning for MRI is the development of shifts. In this study, we demonstrate that pruning unrolled networks. While common deep learning architectures deep image reconstruction networks at training time can improve such as U-Nets [10] and transformers [11] have been their robustness to distribution shifts. In particular, we highly successful in MR image reconstruction, they do not consider unrolled reconstruction architectures for accelerated directly incorporate knowledge of the forward model of the magnetic resonance imaging and introduce a method for pruning imaging system (i.e. the underlying physics) into the reconstruction unrolled networks (PUN) at initialization.

Deep unrolling, or unfolding, is an emerging learning-to-optimize method that unrolls a truncated iterative algorithm in the layers of a trainable neural network. However, the convergence guarantees and generalizability of the unrolled networks are still open theoretical problems. To tackle these problems, we provide deep unrolled architectures with a stochastic descent nature by imposing descending constraints during training. The descending constraints are forced layer by layer to ensure that each unrolled layer takes, on average, a descent step toward the optimum during training. We theoretically prove that the sequence constructed by the outputs of the unrolled layers is then guaranteed to converge for unseen problems, assuming no distribution shift between training and test problems. We also show that standard unrolling is brittle to perturbations, and our imposed constraints provide the unrolled networks with robustness to additive noise and perturbations. We numerically assess unrolled architectures trained under the proposed constraints in two different applications, including the sparse coding using learnable iterative shrinkage and thresholding algorithm (LISTA) and image inpainting using proximal generative flow (GLOW-Prox), and demonstrate the performance and robustness benefits of the proposed method.

Neural networks allow solving many ill-posed inverse problems with unprecedented performance. Physics informed approaches already progressively replace carefully hand-crafted reconstruction algorithms in real applications. However, these networks suffer from a major defect: when trained on a given forward operator, they do not generalize well to a different one. The aim of this paper is twofold. First, we show through various applications that training the network with a family of forward operators allows solving the adaptivity problem without compromising the reconstruction quality significantly.Second, we illustrate that this training procedure allows tackling challenging blind inverse problems.Our experiments include partial Fourier sampling problems arising in magnetic resonance imaging (MRI) with sensitivity estimation and off-resonance effects, computerized tomography (CT) with a tilted geometry and image deblurring with Fresnel diffraction kernels.

The classical sparse coding (SC) model represents visual stimuli as a linear combination of a handful of learned basis functions that are Gabor-like when trained on natural image data. However, the Gabor-like filters learned by classical sparse coding far overpredict well-tuned simple cell receptive field profiles observed empirically. While neurons fire sparsely, neuronal populations are also organized in physical space by their sensitivity to certain features. In V1, this organization is a smooth progression of orientations along the cortical sheet. A number of subsequent models have either discarded the sparse dictionary learning framework entirely or whose updates have yet to take advantage of the surge in unrolled, neural dictionary learning architectures. A key missing theme of these updates is a stronger notion of \emph{structured sparsity}. We propose an autoencoder architecture (WLSC) whose latent representations are implicitly, locally organized for spectral clustering through a Laplacian quadratic form of a bipartite graph, which generates a diverse set of artificial receptive fields that match primate data in V1 as faithfully as recent contrastive frameworks like Local Low Dimensionality, or LLD \citep{lld} that discard sparse dictionary learning. By unifying sparse and smooth coding in models of the early visual cortex through our autoencoder, we also show that our regularization can be interpreted as early-stage specialization of receptive fields to certain classes of stimuli; that is, we induce a weak clustering bias for later stages of cortex where functional and spatial segregation (i.e. topography) are known to occur. The results show an imperative for \emph{spatial regularization} of both the receptive fields and firing rates to begin to describe feature disentanglement in V1 and beyond.

Physics-driven deep learning methods have emerged as a powerful tool for computational magnetic resonance imaging (MRI) problems, pushing reconstruction performance to new limits. This article provides an overview of the recent developments in incorporating physics information into learningbased MRI reconstruction. We consider inverse problems with both linear and non-linear forward models for computational MRI, and review the classical approaches for solving these. We then focus on physics-driven deep learning approaches, covering physics-driven loss functions, plug-and-play methods, generative models, and unrolled networks. We highlight domain-specific challenges such as real-and complex-valued building blocks of neural networks, and translational applications in MRI with linear and non-linear forward models. Finally, we discuss common issues and open challenges, and draw connections to the importance of physics-driven learning when combined with other downstream tasks in the medical imaging pipeline. K. Hammernik and D. Rueckert are with the Institute of AI and Informatics in Medicine, Technical University of Munich and the Department of Computing, Imperial College London. T. Küstner is with the Department of Diagnostic and Interventional Radiology, University Hospital of Tuebingen. B. Yaman and M. Akçakaya are with the Department of Electrical and Computer Engineering, and Center for Magnetic Resonance Research, University of Minnesota, USA. Z. Huang is with the Center for Biomedical Imaging, Department of Radiology, New York University. F. Knoll is with the Department Artificial Intelligence in Biomedical Engineering, Friedrich-Alexander University Erlangen. Magnetic resonance imaging (MRI) is a non-invasive radiation-free imaging modality with a plethora of clinical applications and extensively-studied physics underpinnings. The relationship between the acquired MRI data and the underlying magnetization is characterized by Bloch equations, and depends on a number of parameters, including the magnetic fields (e.g. the static B These intricate dependencies are encoded in the so-called k-space, corresponding to the spatial Fourier transform of the object's magnetization. It depends on the imaging sequence and reflects physiological, functional or hardware characteristics. For many applications, an analytical expression can be derived (e.g. via hard pulse approximation from the Bloch equations) for which a few examples are summarized in Table I (linear and non-linear models).

Unrolled neural networks emerged recently as an effective model for learning inverse maps appearing in image restoration tasks. However, their generalization risk (i.e., test mean-squared-error) and its link to network design and train sample size remains mysterious. Leveraging the Stein's Unbiased Risk Estimator (SURE), this paper analyzes the generalization risk with its bias and variance components for recurrent unrolled networks. We particularly investigate the degrees-of-freedom (DOF) component of SURE, trace of the end-to-end network Jacobian, to quantify the prediction variance. We prove that DOF is well-approximated by the weighted \textit{path sparsity} of the network under incoherence conditions on the trained weights. Empirically, we examine the SURE components as a function of train sample size for both recurrent and non-recurrent (with many more parameters) unrolled networks. Our key observations indicate that: 1) DOF increases with train sample size and converges to the generalization risk for both recurrent and non-recurrent schemes; 2) recurrent network converges significantly faster (with less train samples) compared with non-recurrent scheme, hence recurrence serves as a regularization for low sample size regimes.

A while back, I discussed Recurrent Neural Networks (RNNs), a type of artificial neural network in which some of the connections between neurons point "backwards". When a sequence of inputs is fed into such a network, the backward arrows feed information about earlier input values back into the system at later steps. One thing that I didn't describe in that post was how to train such a network. So in this post, I want to present one way of thinking about training an RNN, called unrolling. Recall that a neural network is defined by a directed graph, i.e. a graph in which each edge has an arrow pointing from one endpoint to the other.