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.

Combining Deep Learning and Adaptive Sparse Modeling for Low-dose CT Reconstruction

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 measurement undersampling 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, and 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 sparse representations-based (unsupervised) learned or analytical priors. Our results demonstrate the promising performance of the proposed framework compared to recent reconstruction methods.

Multi-layer Clustering-based Residual Sparsifying Transform for Low-dose CT Image Reconstruction

The recently proposed sparsifying transform models incur low computational cost and have been applied to medical imaging. Meanwhile, deep models with nested network structure reveal great potential for learning features in different layers. In this study, we propose a network-structured sparsifying transform learning approach for X-ray computed tomography (CT), which we refer to as multi-layer clustering-based residual sparsifying transform (MCST) learning. The proposed MCST scheme learns multiple different unitary transforms in each layer by dividing each layer's input into several classes. We apply the MCST model to low-dose CT (LDCT) reconstruction by deploying the learned MCST model into the regularizer in penalized weighted least squares (PWLS) reconstruction. We conducted LDCT reconstruction experiments on XCAT phantom data and Mayo Clinic data and trained the MCST model with 2 (or 3) layers and with 5 clusters in each layer. The learned transforms in the same layer showed rich features while additional information is extracted from representation residuals. Our simulation results demonstrate that PWLS-MCST achieves better image reconstruction quality than the conventional FBP method and PWLS with edge-preserving (EP) regularizer. It also outperformed recent advanced methods like PWLS with a learned multi-layer residual sparsifying transform prior (MARS) and PWLS with a union of learned transforms (ULTRA), especially for displaying clear edges and preserving subtle details.

Learning Nonlocal Sparse and Low-Rank Models for Image Compressive Sensing

The compressive sensing (CS) scheme exploits much fewer measurements than suggested by the Nyquist-Shannon sampling theorem to accurately reconstruct images, which has attracted considerable attention in the computational imaging community. While classic image CS schemes employed sparsity using analytical transforms or bases, the learning-based approaches have become increasingly popular in recent years. Such methods can effectively model the structures of image patches by optimizing their sparse representations or learning deep neural networks, while preserving the known or modeled sensing process. Beyond exploiting local image properties, advanced CS schemes adopt nonlocal image modeling, by extracting similar or highly correlated patches at different locations of an image to form a group to process jointly. More recent learning-based CS schemes apply nonlocal structured sparsity prior using group sparse representation (GSR) and/or low-rank (LR) modeling, which have demonstrated promising performance in various computational imaging and image processing applications. This article reviews some recent works in image CS tasks with a focus on the advanced GSR and LR based methods. Furthermore, we present a unified framework for incorporating various GSR and LR models and discuss the relationship between GSR and LR models. Finally, we discuss the open problems and future directions in the field.

Sparse-view Cone Beam CT Reconstruction using Data-consistent Supervised and Adversarial Learning from Scarce Training Data

Reconstruction of CT images from a limited set of projections through an object is important in several applications ranging from medical imaging to industrial settings. As the number of available projections decreases, traditional reconstruction techniques such as the FDK algorithm and model-based iterative reconstruction methods perform poorly. Recently, data-driven methods such as deep learning-based reconstruction have garnered a lot of attention in applications because they yield better performance when enough training data is available. However, even these methods have their limitations when there is a scarcity of available training data. This work focuses on image reconstruction in such settings, i.e., when both the number of available CT projections and the training data is extremely limited. We adopt a sequential reconstruction approach over several stages using an adversarially trained shallow network for 'destreaking' followed by a data-consistency update in each stage. To deal with the challenge of limited data, we use image subvolumes to train our method, and patch aggregation during testing. To deal with the computational challenge of learning on 3D datasets for 3D reconstruction, we use a hybrid 3D-to-2D mapping network for the 'destreaking' part. Comparisons to other methods over several test examples indicate that the proposed method has much potential, when both the number of projections and available training data are highly limited.