Adrian Celaya

Accurate medical imaging segmentation is crucial for effective medical interventions, but convolutional neural networks (CNNs) still struggle with fine-scale features and image scale variations, particularly in complex tasks like the BraTS brain tumor segmentation challenge. To address these challenges, we propose two architectures, FMG-Net and W-Net, that incorporate geometric multigrid principles into CNNs. Our experiments on the BraTS 2020 dataset show that FMG-Net and W-Net outperform the commonly used U-Net in tumor subcomponent segmentation accuracy and training efficiency. The figure above shows sketches of the U-Net, FMG-Net, and W-Net architectures for different network detphs. More details and results are available here.

The Weighted Normalized Boundary Loss (WNBL) is a boundary-based loss for minimizing the Hausdorff distance for deep learning-based medical imaging segmentation. This novel loss function has more desirable numerical properties than current methods and weighting terms for class imbalance. The WNBL outperforms other losses when tested on the BraTS dataset using a standard 3D U-Net and the state-of-the-art nnUNet architecture.

The WNBL is given below: \begin{align*} \mathcal{L}_{wnbl} = 1 - \frac{\sum_{k = 1}^{C} w_k \sum_{i = 1}^{N} \left(D_{i}^{k}\left((1 - T_{i}^{k})^2 - P_{i}^{k}\right)\right)^2}{\sum_{k = 1}^{C} w_k \sum_{i = 1}^{N} \left(D_{i}^{k}\left((1 - T_{i}^{k})^2 - T_{i}^{k}\right)\right)^2}, \end{align*} where $N$ denotes the total number of pixels (or voxels in the 3D case), $C$ denotes the number of segmentation classes, $P_i^k \in [0, 1]$ is the $i$-th voxel in the $k$-th class of the predicted mask, $T_i^k \in \{0, 1\}$ is the $i$-th voxel in the $k$-th class for the ground truth, and $D_i^k \in \mathbb{R}$ is the $i$-th voxel for the $k$-th class in the ground truth distance transform map. More details and results are available here.

CO$_2$ geological storage is a carbon capture and storage technology that captures CO$_2$ emissions from fixed sources like power plants and stores it in underground saline formations, making it a practical and near-term solution. However, long-term monitoring is necessary to ensure volume storage integrity. 4D gravity monitoring is an effective low-cost and environmentally friendly technique for monitoring geological storage sites. To predict subsurface CO$_2$ plumes, a deep learning approach was developed that outperforms traditional inversion methods, producing high-resolution 3D subsurface reconstructions in near real-time. The figure above highlights the results of two of our proposed approaches. More details and results can be found here.