Noisier2Inverse: Self-Supervised Learning for Image Reconstruction with Correlated Noise

We propose Noisier2Inverse, a correction-free self-supervised deep learning approach for general inverse prob- lems. The proposed method learns a reconstruction function without the need for ground truth samples and is ap- plicable in cases where measurement noise is statistically correlated. This includes computed tomography, where detector imperfections or photon scattering create correlated noise patterns, as well as microscopy and seismic imaging, where physical interactions during measurement introduce dependencies in the noise structure. Similar to Noisier2Noise, a key step in our approach is the generation of noisier data from which the reconstruction net- work learns. However, unlike Noisier2Noise, the proposed loss function operates in measurement space and is trained to recover an extrapolated image instead of the original noisy one. This eliminates the need for an extrap- olation step during inference, which would otherwise suffer from ill-posedness. We numerically demonstrate that our method clearly outperforms previous self-supervised approaches that account for correlated noise.

Mesh Density Adaptation for Template-based Shape Reconstruction

In 3D shape reconstruction based on template mesh deformation, a regularization, such as smoothness energy, is employed to guide the reconstruction into a desirable direction. In this paper, we highlight an often overlooked property in the regularization: the vertex density in the mesh. Without careful control on the density, the reconstruction may suffer from under-sampling of vertices near shape details. We propose a novel mesh density adaptation method to resolve the under-sampling problem. Our mesh density adaptation energy increases the density of vertices near complex structures via deformation to help reconstruction of shape details. We demonstrate the usability and performance of mesh density adaptation with two tasks, inverse rendering and non-rigid surface registration. Our method produces more accurate reconstruction results compared to the cases without mesh density adaptation.