Face video restoration (FVR) is a challenging but important problem where one seeks to recover a perceptually realistic face videos from a low-quality input. While diffusion probabilistic models (DPMs) have been shown to achieve remarkable performance for face image restoration, they often fail to preserve temporally coherent, high-quality videos, compromising the fidelity of reconstructed faces. We present a new conditional diffusion framework called FLAIR for FVR. FLAIR ensures improved temporal alignments across frames in a computationally efficient fashion by converting a traditional image DPM into a video DPM. The proposed conversion uses a recurrent video refinement layer and a temporal self-attention at different scales. FLAIR also uses a conditional iterative refinement process to balance the perceptual and distortion quality during inference. This process consists of two key components: a data-consistency module that analytically ensures that the generated video precisely matches its degraded observation and a coarse-to-fine image enhancement module specifically for facial regions. Our extensive experiments show superiority of FLAIR over the current state-of-the-art (SOTA) for video super-resolution, deblurring, JPEG restoration, and space-time frame interpolation on two high-quality face video datasets.

Posterior sampling has been shown to be a powerful Bayesian approach for solving imaging inverse problems. The recent plug-and-play unadjusted Langevin algorithm (PnP-ULA) has emerged as a promising method for Monte Carlo sampling and minimum mean squared error (MMSE) estimation by combining physical measurement models with deep-learning priors specified using image denoisers. However, the intricate relationship between the sampling distribution of PnP-ULA and the mismatched data-fidelity and denoiser has not been theoretically analyzed. We address this gap by proposing a posterior-$L_2$ pseudometric and using it to quantify an explicit error bound for PnP-ULA under mismatched posterior distribution. We numerically validate our theory on several inverse problems such as sampling from Gaussian mixture models and image deblurring. Our results suggest that the sensitivity of the sampling distribution of PnP-ULA to a mismatch in the measurement model and the denoiser can be precisely characterized.

Plug-and-Play (PnP) priors is a widely-used family of methods for solving imaging inverse problems by integrating physical measurement models with image priors specified using image denoisers. PnP methods have been shown to achieve state-of-the-art performance when the prior is obtained using powerful deep denoisers. Despite extensive work on PnP, the topic of distribution mismatch between the training and testing data has often been overlooked in the PnP literature. This paper presents a set of new theoretical and numerical results on the topic of prior distribution mismatch and domain adaptation for the alternating direction method of multipliers (ADMM) variant of PnP. Our theoretical result provides an explicit error bound for PnP-ADMM due to the mismatch between the desired denoiser and the one used for inference. Our analysis contributes to the work in the area by considering the mismatch under nonconvex data-fidelity terms and expansive denoisers. Our first set of numerical results quantifies the impact of the prior distribution mismatch on the performance of PnP-ADMM on the problem of image super-resolution. Our second set of numerical results considers a simple and effective domain adaption strategy that closes the performance gap due to the use of mismatched denoisers. Our results suggest the relative robustness of PnP-ADMM to prior distribution mismatch, while also showing that the performance gap can be significantly reduced with only a few training samples from the desired distribution.

Deep model-based architectures (DMBAs) are widely used in imaging inverse problems to integrate physical measurement models and learned image priors. Plug-and-play priors (PnP) and deep equilibrium models (DEQ) are two DMBA frameworks that have received significant attention. The key difference between the two is that the image prior in DEQ is trained by using a specific measurement model, while that in PnP is trained as a general image denoiser. This difference is behind a common assumption that PnP is more robust to changes in the measurement models compared to DEQ. This paper investigates the robustness of DEQ priors to changes in the measurement models. Our results on two imaging inverse problems suggest that DEQ priors trained under mismatched measurement models outperform image denoisers.

Three-dimensional fluorescence microscopy often suffers from anisotropy, where the resolution along the axial direction is lower than that within the lateral imaging plane. We address this issue by presenting Dual-Cycle, a new framework for joint deconvolution and fusion of dual-view fluorescence images. Inspired by the recent Neuroclear method, Dual-Cycle is designed as a cycle-consistent generative network trained in a self-supervised fashion by combining a dual-view generator and prior-guided degradation model. We validate Dual-Cycle on both synthetic and real data showing its state-of-the-art performance without any external training data.

Limited-Angle Computed Tomography (LACT) is a nondestructive 3D imaging technique used in a variety of applications ranging from security to medicine. The limited angle coverage in LACT is often a dominant source of severe artifacts in the reconstructed images, making it a challenging imaging inverse problem. Diffusion models are a recent class of deep generative models for synthesizing realistic images using image denoisers. In this work, we present DOLCE as the first framework for integrating conditionally-trained diffusion models and explicit physical measurement models for solving imaging inverse problems. DOLCE achieves the SOTA performance in highly ill-posed LACT by alternating between the data-fidelity and sampling updates of a diffusion model conditioned on the transformed sinogram. We show through extensive experimentation that unlike existing methods, DOLCE can synthesize high-quality and structurally coherent 3D volumes by using only 2D conditionally pre-trained diffusion models. We further show on several challenging real LACT datasets that the same pretrained DOLCE model achieves the SOTA performance on drastically different types of images.

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.

Regularization by denoising (RED) is a widely-used framework for solving inverse problems by leveraging image de-noisers as image priors. Recent work has reported the state-of-the-art performance of RED in a number of imaging applications using pre-trained deep neural nets as denoisers. Despite the recent progress, the stable convergence of RED algorithms remains an open problem. The existing RED theory only guarantees stability for convex data-fidelity terms and nonexpansive denoisers. This work addresses this issue by developing a new monotone RED (MRED) algorithm, whose convergence does not require nonexpansiveness of the deep denoising prior. Simulations on image deblurring and compressive sensing recovery from random matrices show the stability of MRED even when the traditional RED diverges.

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.

The plug-and-play priors (PnP) and regularization by denoising (RED) methods have become widely used for solving inverse problems by leveraging pre-trained deep denoisers as image priors. While the empirical imaging performance and the theoretical convergence properties of these algorithms have been widely investigated, their recovery properties have not previously been theoretically analyzed. We address this gap by showing how to establish theoretical recovery guarantees for PnP/RED by assuming that the solution of these methods lies near the fixed-points of a deep neural network. We also present numerical results comparing the recovery performance of PnP/RED in compressive sensing against that of recent compressive sensing algorithms based on generative models. Our numerical results suggest that PnP with a pre-trained artifact removal network provides significantly better results compared to the existing state-of-the-art methods.

Recent work has shown the effectiveness of the plug-and-play priors (PnP) framework for regularized image reconstruction. However, the performance of PnP depends on the quality of the denoisers used as priors. In this letter, we design a novel PnP denoising prior, called multiple self-similarity net (MSSN), based on the recurrent neural network (RNN) with self-similarity matching using multi-head attention mechanism. Unlike traditional neural net denoisers, MSSN exploits different types of relationships among non-local and repeating features to remove the noise in the input image. We numerically evaluate the performance of MSSN as a module within PnP for solving magnetic resonance (MR) image reconstruction. Experimental results show the stable convergence and excellent performance of MSSN for reconstructing images from highly compressive Fourier measurements.

Plug-and-play priors (PnP) is a methodology for regularized image reconstruction that specifies the prior through an image denoiser. While PnP algorithms are well understood for denoisers performing maximum a posteriori probability (MAP) estimation, they have not been analyzed for the minimum mean squared error (MMSE) denoisers. This letter addresses this gap by establishing the first theoretical convergence result for the iterative shrinkage/thresholding algorithm (ISTA) variant of PnP for MMSE denoisers. We show that the iterates produced by PnP-ISTA with an MMSE denoiser converge to a stationary point of some global cost function. We validate our analysis on sparse signal recovery in compressive sensing by comparing two types of denoisers, namely the exact MMSE denoiser and the approximate MMSE denoiser obtained by training a deep neural net.

In the past decade, sparsity-driven regularization has led to significant improvements in image reconstruction. Traditional regularizers, such as total variation (TV), rely on analytical models of sparsity. However, increasingly the field is moving towards trainable models, inspired from deep learning. Deep image prior (DIP) is a recent regularization framework that uses a convolutional neural network (CNN) architecture without data-driven training. This paper extends the DIP framework by combining it with the traditional TV regularization. We show that the inclusion of TV leads to considerable performance gains when tested on several traditional restoration tasks such as image denoising and deblurring.

We consider the problem of estimating a vector from its noisy measurements using a prior specified only through a denoising function. Recent work on plug-and-play priors (PnP) and regularization-by-denoising (RED) has shown the state-of-the-art performance of estimators under such priors in a range of imaging tasks. In this work, we develop a new block coordinate RED algorithm that decomposes a large-scale estimation problem into a sequence of updates over a small subset of the unknown variables. We theoretically analyze the convergence of the algorithm and discuss its relationship to the traditional proximal optimization. Our analysis complements and extends recent theoretical results for RED-based estimation methods. We numerically validate our method using several denoiser priors, including those based on convolutional neural network (CNN) denoisers.