Mitigating Topological Noise in 3D Images of Porous Media

Porous media flow is essential to many natural and industrial processes, including environmental cleanup, oil recovery, and CO2 storage. Understanding and optimizing these processes requires characterizing the complex internal structure of these materials. Techniques from Topological Data Analysis, especially persistent homology, are very helpful for this task. However, when working with real-world data—specifically 3D images of porous media—we face significant computational challenges because of the complexity of the datasets and the presence of experimental noise, which can hide key topological features and increase computational costs. We propose a denoising method using Gaussian convolution to smooth the data and reduce noise. We show how well our method works with simulated image datasets, where we add noise to imitate real experimental data, then apply our smoothing technique to denoise. To assess the effectiveness of our method, we use several topological measures to compare the original and denoised datasets. Finally, we discuss the optimal denoising approach that makes these measures closest to the original, noise-free data.