Deep neural networks trained as image denoisers are widely used as priors for solving imaging inverse problems. We introduce Stochastic deep Restoration Priors (ShaRP), a novel framework that stochastically leverages an ensemble of deep restoration models beyond denoisers to regularize inverse problems. By using generalized restoration models trained on a broad range of degradations beyond simple Gaussian noise, ShaRP effectively addresses structured artifacts and enables self-supervised training without fully sampled data. We prove that ShaRP minimizes an objective function involving a regularizer derived from the score functions of minimum mean square error (MMSE) restoration operators. We also provide theoretical guarantees for learning restoration operators from incomplete measurements. ShaRP achieves state-of-the-art performance on tasks such as magnetic resonance imaging reconstruction and single-image super-resolution, surpassing both denoiser- and diffusion-model-based methods without requiring retraining.

Deformable image registration (DIR) is an active research topic in biomedical imaging. There is a growing interest in developing DIR methods based on deep learning (DL). A traditional DL approach to DIR is based on training a convolutional neural network (CNN) to estimate the registration field between two input images. While conceptually simple, this approach comes with a limitation that it exclusively relies on a pre-trained CNN without explicitly enforcing fidelity between the registered image and the reference. We present plug-and-play image registration network (PIRATE) as a new DIR method that addresses this issue by integrating an explicit data-fidelity penalty and a CNN prior. PIRATE pre-trains a CNN denoiser on the registration field and "plugs" it into an iterative method as a regularizer. We additionally present PIRATE+ that fine-tunes the CNN prior in PIRATE using deep equilibrium models (DEQ). PIRATE+ interprets the fixed-point iteration of PIRATE as a network with effectively infinite layers and then trains the resulting network end-to-end, enabling it to learn more task-specific information and boosting its performance. Our numerical results on OASIS and CANDI datasets show that our methods achieve state-of-the-art performance on DIR.

Implicit neural representations (INR) have been recently proposed as deep learning (DL) based solutions for image compression. An image can be compressed by training an INR model with fewer weights than the number of image pixels to map the coordinates of the image to corresponding pixel values. While traditional training approaches for INRs are based on enforcing pixel-wise image consistency, we propose to further improve image quality by using a new structural regularizer. We present structural regularization for INR compression (SINCO) as a novel INR method for image compression. SINCO imposes structural consistency of the compressed images to the groundtruth by using a segmentation network to penalize the discrepancy of segmentation masks predicted from compressed images. We validate SINCO on brain MRI images by showing that it can achieve better performance than some recent INR methods.

Plug-and-play (PnP) prior is a well-known class of methods for solving imaging inverse problems by computing fixed-points of operators combining physical measurement models and learned image denoisers. While PnP methods have been extensively used for image recovery with known measurement operators, there is little work on PnP for solving blind inverse problems. We address this gap by presenting a new block-coordinate PnP (BC-PnP) method that efficiently solves this joint estimation problem by introducing learned denoisers as priors on both the unknown image and the unknown measurement operator. We present a new convergence theory for BC-PnP compatible with blind inverse problems by considering nonconvex data-fidelity terms and expansive denoisers. Our theory analyzes the convergence of BC-PnP to a stationary point of an implicit function associated with an approximate minimum mean-squared error (MMSE) denoiser. We numerically validate our method on two blind inverse problems: automatic coil sensitivity estimation in magnetic resonance imaging (MRI) and blind image deblurring. Our results show that BC-PnP provides an efficient and principled framework for using denoisers as PnP priors for jointly estimating measurement operators and images.

Plug-and-Play Priors (PnP) and Regularization by Denoising (RED) are widely-used frameworks for solving imaging inverse problems by computing fixed-points of operators combining physical measurement models and learned image priors. While traditional PnP/RED formulations have focused on priors specified using image denoisers, there is a growing interest in learning PnP/RED priors that are end-to-end optimal. The recent Deep Equilibrium Models (DEQ) framework has enabled memory-efficient end-to-end learning of PnP/RED priors by implicitly differentiating through the fixed-point equations without storing intermediate activation values. However, the dependence of the computational/memory complexity of the measurement models in PnP/RED on the total number of measurements leaves DEQ impractical for many imaging applications. We propose ODER as a new strategy for improving the efficiency of DEQ through stochastic approximations of the measurement models. We theoretically analyze ODER giving insights into its convergence and ability to approximate the traditional DEQ approach. Our numerical results suggest the potential improvements in training/testing complexity due to ODER on three distinct imaging applications.

Deep neural networks for medical image reconstruction are traditionally trained using high-quality ground-truth images as training targets. Recent work on Noise2Noise (N2N) has shown the potential of using multiple noisy measurements of the same object as an alternative to having a ground-truth. However, existing N2N-based methods are not suitable for learning from the measurements of an object undergoing nonrigid deformation. This paper addresses this issue by proposing the deformation-compensated learning (DeCoLearn) method for training deep reconstruction networks by compensating for object deformations. A key component of DeCoLearn is a deep registration module, which is jointly trained with the deep reconstruction network without any ground-truth supervision. We validate DeCoLearn on both simulated and experimentally collected magnetic resonance imaging (MRI) data and show that it significantly improves imaging quality.

Deep unfolding networks are rapidly gaining attention for solving imaging inverse problems. However, the computational and memory complexity of existing deep unfolding networks scales with the size of the full measurement set, limiting their applicability to certain large-scale imaging inverse problems. We propose SCRED-Net as a novel methodology that introduces a stochastic approximation to the unfolded regularization by denoising (RED) algorithm. Our method uses only a subset of measurements within each cascade block, making it scalable to a large number of measurements for efficient end-to-end training. We present numerical results showing the effectiveness of SCRED-Net on intensity diffraction tomography (IDT) and sparse-view computed tomography (CT). Our results show that SCRED-Net matches the performance of a batch deep unfolding network at a fraction of training and operational complexity.