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.

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.

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.

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.