uDiG-DIP: Unrolled Diffusion-Guided Deep Image Prior For Medical Image Reconstruction

Deep learning (DL) methods have been extensively applied to various image recovery problems, including magnetic resonance imaging (MRI) and computed tomography (CT) reconstruction. Beyond supervised models, other approaches have been recently explored including two key recent schemes: Deep Image Prior (DIP) that is an unsupervised scan-adaptive method that leverages the network architecture as implicit regularization but can suffer from noise overfitting, and diffusion models (DMs), where the sampling procedure of a pre-trained generative model is modified to allow sampling from the measurement-conditioned distribution through approximations. In this paper, we propose combining DIP and DMs for MRI and CT reconstruction, motivated by (i) the impact of the DIP network input and (ii) the use of DMs as diffusion purifiers (DPs). Specifically, we propose an unrolled procedure that iteratively optimizes the DIP network with a DM-refined adaptive input using a loss with data consistency and autoencoding terms. We term the approach unrolled Diffusion-Guided DIP (uDiG-DIP). Our experimental results demonstrate that uDiG-DIP achieves superior reconstruction results compared to leading DM-based baselines and the original DIP for MRI and CT tasks.

SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems

Diffusion models (DMs) are a class of generative models that allow sampling from a distribution learned over a training set. When applied to solving inverse imaging problems (IPs), the reverse sampling steps of DMs are typically modified to approximately sample from a measurement-conditioned distribution in the image space. However, these modifications may be unsuitable for certain settings (such as in the presence of measurement noise) and non-linear tasks, as they often struggle to correct errors from earlier sampling steps and generally require a large number of optimization and/or sampling steps. To address these challenges, we state three conditions for achieving measurement-consistent diffusion trajectories. Building on these conditions, we propose a new optimization-based sampling method that not only enforces the standard data manifold measurement consistency and forward diffusion consistency, as seen in previous studies, but also incorporates backward diffusion consistency that maintains a diffusion trajectory by optimizing over the input of the pre-trained model at every sampling step. By enforcing these conditions, either implicitly or explicitly, our sampler requires significantly fewer reverse steps. Therefore, we refer to our accelerated method as Step-wise Triple-Consistent Sampling (SITCOM). Compared to existing state-of-the-art baseline methods, under different levels of measurement noise, our extensive experiments across five linear and three non-linear image restoration tasks demonstrate that SITCOM achieves competitive or superior results in terms of standard image similarity metrics while requiring a significantly reduced run-time across all considered tasks.

Learning Robust Features for Scatter Removal and Reconstruction in Dynamic ICF X-Ray Tomography

Density reconstruction from X-ray projections is an important problem in radiography with key applications in scientific and industrial X-ray computed tomography (CT). Often, such projections are corrupted by unknown sources of noise and scatter, which when not properly accounted for, can lead to significant errors in density reconstruction. In the setting of this problem, recent deep learning-based methods have shown promise in improving the accuracy of density reconstruction. In this article, we propose a deep learning-based encoder-decoder framework wherein the encoder extracts robust features from noisy/corrupted X-ray projections and the decoder reconstructs the density field from the features extracted by the encoder. We explore three options for the latent-space representation of features: physics-inspired supervision, self-supervision, and no supervision. We find that variants based on self-supervised and physicsinspired supervised features perform better over a range of unknown scatter and noise. In extreme noise settings, the variant with self-supervised features performs best. After investigating further details of the proposed deep-learning methods, we conclude by demonstrating that the newly proposed methods are able to achieve higher accuracy in density reconstruction when compared to a traditional iterative technique.

Optimal Eye Surgeon: Finding Image Priors through Sparse Generators at Initialization

We introduce Optimal Eye Surgeon (OES), a framework for pruning and training deep image generator networks. Typically, untrained deep convolutional networks, which include image sampling operations, serve as effective image priors (Ulyanov et al., 2018). However, they tend to overfit to noise in image restoration tasks due to being overparameterized. OES addresses this by adaptively pruning networks at random initialization to a level of underparameterization. This process effectively captures low-frequency image components even without training, by just masking. When trained to fit noisy images, these pruned subnetworks, which we term Sparse-DIP, resist overfitting to noise. This benefit arises from underparameterization and the regularization effect of masking, constraining them in the manifold of image priors. We demonstrate that subnetworks pruned through OES surpass other leading pruning methods, such as the Lottery Ticket Hypothesis, which is known to be suboptimal for image recovery tasks (Wu et al., 2023). Our extensive experiments demonstrate the transferability of OES-masks and the characteristics of sparse-subnetworks for image generation. Code is available at https://github.com/Avra98/Optimal-Eye-Surgeon.git.

Analysis of Deep Image Prior and Exploiting Self-Guidance for Image Reconstruction

The ability of deep image prior (DIP) to recover high-quality images from incomplete or corrupted measurements has made it popular in inverse problems in image restoration and medical imaging including magnetic resonance imaging (MRI). However, conventional DIP suffers from severe overfitting and spectral bias effects. In this work, we first provide an analysis of how DIP recovers information from undersampled imaging measurements by analyzing the training dynamics of the underlying networks in the kernel regime for different architectures. This study sheds light on important underlying properties for DIP-based recovery. Current research suggests that incorporating a reference image as network input can enhance DIP's performance in image reconstruction compared to using random inputs. However, obtaining suitable reference images requires supervision, and raises practical difficulties. In an attempt to overcome this obstacle, we further introduce a self-driven reconstruction process that concurrently optimizes both the network weights and the input while eliminating the need for training data. Our method incorporates a novel denoiser regularization term which enables robust and stable joint estimation of both the network input and reconstructed image. We demonstrate that our self-guided method surpasses both the original DIP and modern supervised methods in terms of MR image reconstruction performance and outperforms previous DIP-based schemes for image inpainting.

Improving Efficiency of Diffusion Models via Multi-Stage Framework and Tailored Multi-Decoder Architectures

Diffusion models, emerging as powerful deep generative tools, excel in various applications. They operate through a two-steps process: introducing noise into training samples and then employing a model to convert random noise into new samples (e.g., images). However, their remarkable generative performance is hindered by slow training and sampling. This is due to the necessity of tracking extensive forward and reverse diffusion trajectories, and employing a large model with numerous parameters across multiple timesteps (i.e., noise levels). To tackle these challenges, we present a multi-stage framework inspired by our empirical findings. These observations indicate the advantages of employing distinct parameters tailored to each timestep while retaining universal parameters shared across all time steps. Our approach involves segmenting the time interval into multiple stages where we employ custom multi-decoder U-net architecture that blends time-dependent models with a universally shared encoder. Our framework enables the efficient distribution of computational resources and mitigates inter-stage interference, which substantially improves training efficiency. Extensive numerical experiments affirm the effectiveness of our framework, showcasing significant training and sampling efficiency enhancements on three state-of-the-art diffusion models, including large-scale latent diffusion models. Furthermore, our ablation studies illustrate the impact of two important components in our framework: (i) a novel timestep clustering algorithm for stage division, and (ii) an innovative multi-decoder U-net architecture, seamlessly integrating universal and customized hyperparameters.

Patient-Adaptive and Learned MRI Data Undersampling Using Neighborhood Clustering

There has been much recent interest in adapting undersampled trajectories in MRI based on training data. In this work, we propose a novel patient-adaptive MRI sampling algorithm based on grouping scans within a training set. Scan-adaptive sampling patterns are optimized together with an image reconstruction network for the training scans. The training optimization alternates between determining the best sampling pattern for each scan (based on a greedy search or iterative coordinate descent (ICD)) and training a reconstructor across the dataset. The eventual scan-adaptive sampling patterns on the training set are used as labels to predict sampling design using nearest neighbor search at test time. The proposed algorithm is applied to the fastMRI knee multicoil dataset and demonstrates improved performance over several baselines.

Robust MRI Reconstruction by Smoothed Unrolling (SMUG)

As the popularity of deep learning (DL) in the field of magnetic resonance imaging (MRI) continues to rise, recent research has indicated that DL-based MRI reconstruction models might be excessively sensitive to minor input disturbances, including worst-case additive perturbations. This sensitivity often leads to unstable, aliased images. This raises the question of how to devise DL techniques for MRI reconstruction that can be robust to train-test variations. To address this problem, we propose a novel image reconstruction framework, termed Smoothed Unrolling (SMUG), which advances a deep unrolling-based MRI reconstruction model using a randomized smoothing (RS)-based robust learning approach. RS, which improves the tolerance of a model against input noises, has been widely used in the design of adversarial defense approaches for image classification tasks. Yet, we find that the conventional design that applies RS to the entire DL-based MRI model is ineffective. In this paper, we show that SMUG and its variants address the above issue by customizing the RS process based on the unrolling architecture of a DL-based MRI reconstruction model. Compared to the vanilla RS approach, we show that SMUG improves the robustness of MRI reconstruction with respect to a diverse set of instability sources, including worst-case and random noise perturbations to input measurements, varying measurement sampling rates, and different numbers of unrolling steps. Furthermore, we theoretically analyze the robustness of our method in the presence of perturbations.

Enhancing Low-dose CT Image Reconstruction by Integrating Supervised and Unsupervised Learning

Traditional model-based image reconstruction (MBIR) methods combine forward and noise models with simple object priors. Recent application of deep learning methods for image reconstruction provides a successful data-driven approach to addressing the challenges when reconstructing images with undersampled measurements or various types of noise. In this work, we propose a hybrid supervised-unsupervised learning framework for X-ray computed tomography (CT) image reconstruction. The proposed learning formulation leverages both sparsity or unsupervised learning-based priors and neural network reconstructors to simulate a fixed-point iteration process. Each proposed trained block consists of a deterministic MBIR solver and a neural network. The information flows in parallel through these two reconstructors and is then optimally combined. Multiple such blocks are cascaded to form a reconstruction pipeline. We demonstrate the efficacy of this learned hybrid model for low-dose CT image reconstruction with limited training data, where we use the NIH AAPM Mayo Clinic Low Dose CT Grand Challenge dataset for training and testing. In our experiments, we study combinations of supervised deep network reconstructors and MBIR solver with learned sparse representation-based priors or analytical priors. Our results demonstrate the promising performance of the proposed framework compared to recent low-dose CT reconstruction methods.

Diffusion-based Adversarial Purification for Robust Deep MRI Reconstruction

Deep learning (DL) methods have been extensively employed in magnetic resonance imaging (MRI) reconstruction, demonstrating remarkable performance improvements compared to traditional non-DL methods. However, recent studies have uncovered the susceptibility of these models to carefully engineered adversarial perturbations. In this paper, we tackle this issue by leveraging diffusion models. Specifically, we introduce a defense strategy that enhances the robustness of DL-based MRI reconstruction methods through the utilization of pre-trained diffusion models as adversarial purifiers. Unlike conventional state-of-the-art adversarial defense methods (e.g., adversarial training), our proposed approach eliminates the need to solve a minimax optimization problem to train the image reconstruction model from scratch, and only requires fine-tuning on purified adversarial examples. Our experimental findings underscore the effectiveness of our proposed technique when benchmarked against leading defense methodologies for MRI reconstruction such as adversarial training and randomized smoothing.