Random mesh projectors for inverse problems
This addresses instability in imaging for domains like geophysics and remote sensing where data is scarce, offering an incremental improvement over existing learning-based approaches.
The paper tackles ill-posed inverse problems in imaging with rare ground truth data and few measurements, proposing a method that learns projections into random subspaces and combines them for reconstruction, resulting in improved robustness to noise and unseen corruptions compared to direct learning.
We propose a new learning-based approach to solve ill-posed inverse problems in imaging. We address the case where ground truth training samples are rare and the problem is severely ill-posed - both because of the underlying physics and because we can only get few measurements. This setting is common in geophysical imaging and remote sensing. We show that in this case the common approach to directly learn the mapping from the measured data to the reconstruction becomes unstable. Instead, we propose to first learn an ensemble of simpler mappings from the data to projections of the unknown image into random piecewise-constant subspaces. We then combine the projections to form a final reconstruction by solving a deconvolution-like problem. We show experimentally that the proposed method is more robust to measurement noise and corruptions not seen during training than a directly learned inverse.