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NeRF Solves Undersampled MRI Reconstruction

Tae Jun Jang, Chang Min Hyun

TL;DR

A novel undersampled magnetic resonance imaging (MRI) technique that leverages the concept of Neural Radiance Field (NeRF) and serves two benefits: (i) It can be used potentially for diagnostic MR imaging, where data acquisition is relatively rare or limited against diversity of clinical images while undersampled reconstruction is highly demanded.

Abstract

This article presents a novel undersampled magnetic resonance imaging (MRI) technique that leverages the concept of Neural Radiance Field (NeRF). With radial undersampling, the corresponding imaging problem can be reformulated into an image modeling task from sparse-view rendered data; therefore, a high dimensional MR image is obtainable from undersampled k-space data by taking advantage of implicit neural representation. A multi-layer perceptron, which is designed to output an image intensity from a spatial coordinate, learns the MR physics-driven rendering relation between given measurement data and desired image. Effective undersampling strategies for high-quality neural representation are investigated. The proposed method serves two benefits: (i) The learning is based fully on single undersampled k-space data, not a bunch of measured data and target image sets. It can be used potentially for diagnostic MR imaging, such as fetal MRI, where data acquisition is relatively rare or limited against diversity of clinical images while undersampled reconstruction is highly demanded. (ii) A reconstructed MR image is a scan-specific representation highly adaptive to the given k-space measurement. Numerous experiments validate the feasibility and capability of the proposed approach.

NeRF Solves Undersampled MRI Reconstruction

TL;DR

A novel undersampled magnetic resonance imaging (MRI) technique that leverages the concept of Neural Radiance Field (NeRF) and serves two benefits: (i) It can be used potentially for diagnostic MR imaging, where data acquisition is relatively rare or limited against diversity of clinical images while undersampled reconstruction is highly demanded.

Abstract

This article presents a novel undersampled magnetic resonance imaging (MRI) technique that leverages the concept of Neural Radiance Field (NeRF). With radial undersampling, the corresponding imaging problem can be reformulated into an image modeling task from sparse-view rendered data; therefore, a high dimensional MR image is obtainable from undersampled k-space data by taking advantage of implicit neural representation. A multi-layer perceptron, which is designed to output an image intensity from a spatial coordinate, learns the MR physics-driven rendering relation between given measurement data and desired image. Effective undersampling strategies for high-quality neural representation are investigated. The proposed method serves two benefits: (i) The learning is based fully on single undersampled k-space data, not a bunch of measured data and target image sets. It can be used potentially for diagnostic MR imaging, such as fetal MRI, where data acquisition is relatively rare or limited against diversity of clinical images while undersampled reconstruction is highly demanded. (ii) A reconstructed MR image is a scan-specific representation highly adaptive to the given k-space measurement. Numerous experiments validate the feasibility and capability of the proposed approach.
Paper Structure (13 sections, 46 equations, 6 figures, 2 tables)

This paper contains 13 sections, 46 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Method
  3. Inverse problem for undersampled MRI reconstruction
  4. Reformulation into an image modeling task from sparse-view rendered data
  5. Implicit neural representation for undersampled MRI reconstruction
  6. Sampling strategy
  7. Generalization to 3D MR imaging
  8. Result
  9. Experimental set-up
  10. Comparison study
  11. Acceleration factor analysis
  12. Sampling study
  13. Conclusion and Discussion

Figures (6)

  • Figure 1: Implicit neural representation for undersampled MRI reconstruction with radial sampling.
  • Figure 2: Comparison study: Reconstruction results in four different scans by using IFFT, CS, SL, INK, and our method.
  • Figure 3: Qualitative and quantitative results for acceleration factor analysis. The top figure shows reconstruction results for IFFT and the proposed method when $R=4,8,12$. Three graphs below present SSIM, PSNR, and training time results.
  • Figure 4: Qualitative results for sampling study. The top figures in (b)-(f) present radial undersampled $k$-space data for sampling methods. The middle figures show the corresponding reconstruction results by the proposed method. The bottom figures are zoomed images.
  • Figure 5: Results for a case of involved anomalies and high acceleration factor of $R=12$ (41 spokes).
  • ...and 1 more figures