Solving Inverse Problems in Medical Imaging with Score-Based Generative Models (2111.08005v2)

Abstract: Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Existing solutions based on machine learning typically train a model to directly map measurements to medical images, leveraging a training dataset of paired images and measurements. These measurements are typically synthesized from images using a fixed physical model of the measurement process, which hinders the generalization capability of models to unknown measurement processes. To address this issue, we propose a fully unsupervised technique for inverse problem solving, leveraging the recently introduced score-based generative models. Specifically, we first train a score-based generative model on medical images to capture their prior distribution. Given measurements and a physical model of the measurement process at test time, we introduce a sampling method to reconstruct an image consistent with both the prior and the observed measurements. Our method does not assume a fixed measurement process during training, and can thus be flexibly adapted to different measurement processes at test time. Empirically, we observe comparable or better performance to supervised learning techniques in several medical imaging tasks in CT and MRI, while demonstrating significantly better generalization to unknown measurement processes.

• The paper introduces an unsupervised approach leveraging score-based generative models to reconstruct CT and MRI images from incomplete data.
• The method formulates the reconstruction as a linear inverse problem and uses a proximal optimization technique integrated with iterative sampling.
• Empirical results show competitive performance in tasks like sparse-view CT, metal artifact removal, and undersampled MRI, outperforming traditional supervised methods.

Insights on Solving Inverse Problems in Medical Imaging with Score-Based Generative Models

The paper presents a method for addressing inverse problems in medical imaging, specifically targeting applications in computed tomography (CT) and magnetic resonance imaging (MRI). It introduces a novel unsupervised approach by using score-based generative models to reconstruct medical images from partial measurements.

Overview of Approach

Inverse problems in the context of medical imaging involve reconstructing an image from incomplete data, which is often acquired through projections in CT or spatial frequencies in MRI. Existing solutions largely rely on supervised learning models that are trained on paired datasets of images and measurements, potentially limiting their generalizability to new or changing measurement processes. This paper addresses this limitation by leveraging score-based generative models to capture the prior distribution of medical images without requiring a fixed measurement process.

The authors utilize score-based generative models, which have demonstrated effectiveness in probabilistic image generation tasks. Once a generative model is trained on a representative dataset of medical images, it can be employed to reconstruct images from varying measurement processes due to its unsupervised nature. This is particularly beneficial for medical imaging applications characterized by partial and sparse data acquisition, such as low-dose CT or undersampled MRI.

Methodology

The salient feature of the proposed method is the unsupervised training of a score-based generative model using the prior distribution of medical images. During inference, the model generates samples from the posterior distribution consistent with both the measurements and the learned data prior—a formulation that accommodates unknown measurement processes at test time. The paper proposes a convenient form for the linear measurement process and an efficient sampling approach to harmonize with existing iterative sampling schemes of score-based generative models.

In technical terms, the model formulates the image reconstruction as a linear inverse problem, where the unknown image signal is estimated from noisy observations. Utilizing properties of the linear operator associated with the measurement process, the authors propose a proximal optimization method to approximate solutions aligned with the derived observations.

Empirical Validation

The proposed method is put to empirical test across several tasks, including sparse-view CT reconstruction, metal artifact removal (MAR) for CT, and undersampled MRI reconstruction. In comparison to state-of-the-art supervised methods, the score-based approach shows competitive or enhanced performance metrics, such as peak signal-to-noise ratio (PSNR) and structural similarity (SSIM), even when evaluated on the same measurement processes used during training of the supervised counterparts.

Moreover, the paper demonstrates the flexibility and adaptability of this method to generalize across different numbers of measurements at test time—something that traditional supervised models struggle with. A notable result is the model's capacity to handle diverse CT tasks, including sparse-view reconstruction and MAR, simultaneously using a unified score model.

Theoretical and Practical Implications

The unsupervised framework posed in this paper has significant implications for the future of AI in medical imaging. On a theoretical level, it aligns with the growing trend towards leveraging generative models for solving complex inverse problems, illustrating how prior distributions can be effectively captured and utilized without direct supervision. Practically, this approach presents a robust alternative to supervised methods, offering greater adaptability to variable data acquisition strategies that are common in clinical environments. It shows potential for wide applicability in handling diverse imaging scenarios, circumventing the necessity for retraining models with each variation in measurement processes.

Given these promising results, further research could explore the integration of this approach with other forms of conditional generative models and its scalability to three-dimensional or even four-dimensional space considering temporal data, thereby extending its applicability in more dynamic clinical settings. The approach outlined in the paper serves as a keystone in the ongoing evolution of machine learning applications within medical imaging, presenting new opportunities for enhancing diagnostic accuracy and efficiency through advanced inverse problem-solving techniques.