[Paper Review] Robust Compressed Sensing MRI with Deep Generative Priors

Ajil Jalal, Marius Arvinte+4 more|arXiv (Cornell University)|Aug 3, 2021

Sparse and Compressive Sensing TechniquesEngineering79 references46 citations

TL;DR

The paper applies a score-based generative prior within the CSGM framework to multi-coil MRI, using Langevin posterior sampling for robust, distribution-shift-tolerant reconstruction and uncertainty quantification.

ABSTRACT

The CSGM framework (Bora-Jalal-Price-Dimakis'17) has shown that deep generative priors can be powerful tools for solving inverse problems. However, to date this framework has been empirically successful only on certain datasets (for example, human faces and MNIST digits), and it is known to perform poorly on out-of-distribution samples. In this paper, we present the first successful application of the CSGM framework on clinical MRI data. We train a generative prior on brain scans from the fastMRI dataset, and show that posterior sampling via Langevin dynamics achieves high quality reconstructions. Furthermore, our experiments and theory show that posterior sampling is robust to changes in the ground-truth distribution and measurement process. Our code and models are available at: \url{https://github.com/utcsilab/csgm-mri-langevin}.

Motivation & Objective

• Demonstrate successful application of CSGM with a score-based generator for complex-valued MR images without assuming a fixed measurement scheme.
• Show that posterior sampling with Langevin dynamics yields high-quality MRI reconstructions under diverse sampling patterns and anatomies.
• Assess robustness of the method to distribution shifts and its ability to provide uncertainty quantification through multiple posterior samples.

Proposed method

• Train a score-based generative model (NCSNv2) on brain MRI slices to capture complex-valued MR image statistics.
• Use posterior sampling with Langevin dynamics to draw reconstructions from the posterior mu(x|y) under a general forward model A and measurements y.
• Incorporate an annealed Langevin scheme with a score estimate and a data-fidelity term that accounts for the measurement noise.
• Employ a forward model for multi-coil MRI with coil sensitivities and k-space sampling to define A, without assuming a specific sampling scheme during training.

Experimental results

Research questions

• RQ1 Can a score-based generative prior trained on brain MRI reconstruct other anatomies (e.g., knee, abdomen) under various sampling patterns?
• RQ2 Is posterior sampling with the learned prior robust to distribution shifts in anatomy and measurement processes, compared to end-to-end supervised methods?
• RQ3 Does posterior sampling provide reliable uncertainty quantification for reconstructed MR images?
• RQ4 How does the proposed method perform relative to traditional sparsity-based and end-to-end methods under realistic accelerated MRI conditions?

Key findings

• Posterior sampling with a score-based generator yields competitive reconstructions in-distribution and shows robustness to out-of-distribution sampling patterns and anatomies.
• The approach enables multiple reconstructions from the posterior, enabling voxel-wise uncertainty estimates.
• The method demonstrates robustness to test-time distribution shifts and can handle changes in sampling patterns and anatomy better than some end-to-end baselines in certain scenarios.
• It provides qualitative improvements with fewer artifacts when faced with unseen anatomies (e.g., abdomen, knee) and varying coil configurations.