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.

SMUG: Towards robust MRI reconstruction by smoothed unrolling

Although deep learning (DL) has gained much popularity for accelerated magnetic resonance imaging (MRI), recent studies have shown that DL-based MRI reconstruction models could be oversensitive to tiny input perturbations (that are called 'adversarial perturbations'), which cause unstable, low-quality reconstructed images. This raises the question of how to design robust DL methods for MRI reconstruction. 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 operation. RS, which improves the tolerance of a model against input noises, has been widely used in the design of adversarial defense for image classification. Yet, we find that the conventional design that applies RS to the entire DL process is ineffective for MRI reconstruction. We show that SMUG addresses the above issue by customizing the RS operation based on the unrolling architecture of the DL-based MRI reconstruction model. Compared to the vanilla RS approach and several variants of SMUG, we show that SMUG improves the robustness of MRI reconstruction with respect to a diverse set of perturbation sources, including perturbations to the input measurements, different measurement sampling rates, and different unrolling steps. Code for SMUG will be available at https://github.com/LGM70/SMUG.

REPNP: Plug-and-Play with Deep Reinforcement Learning Prior for Robust Image Restoration

Image restoration schemes based on the pre-trained deep models have received great attention due to their unique flexibility for solving various inverse problems. In particular, the Plug-and-Play (PnP) framework is a popular and powerful tool that can integrate an off-the-shelf deep denoiser for different image restoration tasks with known observation models. However, obtaining the observation model that exactly matches the actual one can be challenging in practice. Thus, the PnP schemes with conventional deep denoisers may fail to generate satisfying results in some real-world image restoration tasks. We argue that the robustness of the PnP framework is largely limited by using the off-the-shelf deep denoisers that are trained by deterministic optimization. To this end, we propose a novel deep reinforcement learning (DRL) based PnP framework, dubbed RePNP, by leveraging a light-weight DRL-based denoiser for robust image restoration tasks. Experimental results demonstrate that the proposed RePNP is robust to the observation model used in the PnP scheme deviating from the actual one. Thus, RePNP can generate more reliable restoration results for image deblurring and super resolution tasks. Compared with several state-of-the-art deep image restoration baselines, RePNP achieves better results subjective to model deviation with fewer model parameters.

Learning Sparsity-Promoting Regularizers using Bilevel Optimization

We present a method for supervised learning of sparsity-promoting regularizers for denoising signals and images. Sparsity-promoting regularization is a key ingredient in solving modern signal reconstruction problems; however, the operators underlying these regularizers are usually either designed by hand or learned from data in an unsupervised way. The recent success of supervised learning (mainly convolutional neural networks) in solving image reconstruction problems suggests that it could be a fruitful approach to designing regularizers. Towards this end, we propose to denoise signals using a variational formulation with a parametric, sparsity-promoting regularizer, where the parameters of the regularizer are learned to minimize the mean squared error of reconstructions on a training set of ground truth image and measurement pairs. Training involves solving a challenging bilievel optimization problem; we derive an expression for the gradient of the training loss using the closed-form solution of the denoising problem and provide an accompanying gradient descent algorithm to minimize it. Our experiments with structured 1D signals and natural images show that the proposed method can learn an operator that outperforms well-known regularizers (total variation, DCT-sparsity, and unsupervised dictionary learning) and collaborative filtering for denoising. While the approach we present is specific to denoising, we believe that it could be adapted to the larger class of inverse problems with linear measurement models, giving it applicability in a wide range of signal reconstruction settings.

Adaptive Local Neighborhood-based Neural Networks for MR Image Reconstruction from Undersampled Data

Recent medical image reconstruction techniques focus on generating high-quality medical images suitable for clinical use at the lowest possible cost and with the fewest possible adverse effects on patients. Recent works have shown significant promise for reconstructing MR images from sparsely sampled k-space data using deep learning. In this work, we propose a technique that rapidly estimates deep neural networks directly at reconstruction time by fitting them on small adaptively estimated neighborhoods of a training set. In brief, our algorithm alternates between searching for neighbors in a data set that are similar to the test reconstruction, and training a local network on these neighbors followed by updating the test reconstruction. Because our reconstruction model is learned on a dataset that is structurally similar to the image being reconstructed rather than being fit on a large, diverse training set, it is more adaptive to new scans. It can also handle changes in training sets and flexible scan settings, while being relatively fast. Our approach, dubbed LONDN-MRI, was validated on the FastMRI multi-coil knee data set using deep unrolled reconstruction networks. Reconstructions were performed at four fold and eight fold undersampling of k-space with 1D variable-density random phase-encode undersampling masks. Our results demonstrate that our proposed locally-trained method produces higher-quality reconstructions compared to models trained globally on larger datasets.