Variational volume reconstruction with the Deep Ritz Method

TL;DR

This paper introduces a neural network-based variational method for reconstructing 3D volumes from sparse, noisy slice data, eliminating the need for segmentation and reducing computational costs, with applications in biomedical imaging.

Contribution

The paper proposes a novel neural network approach using the Deep Ritz method for efficient, segmentation-free volume reconstruction from limited noisy slices, addressing key challenges in biomedical imaging.

Findings

Produces high-quality reconstructions from sparse, noisy data

Operates efficiently in seconds, even with limited slices

Avoids segmentation, simplifying preprocessing

Abstract

We present a novel approach to variational volume reconstruction from sparse, noisy slice data using the Deep Ritz method. Motivated by biomedical imaging applications such as MRI-based slice-to-volume reconstruction (SVR), our approach addresses three key challenges: (i) the reliance on image segmentation to extract boundaries from noisy grayscale slice images, (ii) the need to reconstruct volumes from a limited number of slice planes, and (iii) the computational expense of traditional mesh-based methods. We formulate a variational objective that combines a regression loss designed to avoid image segmentation by operating on noisy slice data directly with a modified Cahn-Hilliard energy incorporating anisotropic diffusion to regularize the reconstructed geometry. We discretize the phase field with a neural network, approximate the objective at each optimization step with Monte Carlo integration, and use ADAM to find the minimum of the approximated variational objective. While the stochastic integration may not yield the true solution to the variational problem, we demonstrate that our method reliably produces high-quality reconstructed volumes in a matter of seconds, even when the slice data is sparse and noisy.