Random mesh projectors for inverse problems
arXiv:1805.11718
Abstract
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.
arXiv commentS. Gupta and K. Kothari contributed equally
References in corpus (16)
- Adam: A Method for Stochastic Optimization
- Deep Convolutional Neural Network for Inverse Problems in Imaging
- Image reconstruction by domain transform manifold learning
- LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop
- Deep Image Prior
- Deep Residual Learning for Compressed Sensing CT Reconstruction via Persistent Homology Analysis
- Amortised MAP Inference for Image Super-resolution
- Maximal Sparsity with Deep Networks?
- Local Analysis of Inverse Problems: Hölder Stability and Iterative Reconstruction
- Image Prediction for Limited-angle Tomography via Deep Learning with Convolutional Neural Network
- Adversarial Regularizers in Inverse Problems
- One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Models
- Sketchy Decisions: Convex Low-Rank Matrix Optimization with Optimal Storage
- Deep Learning-Guided Image Reconstruction from Incomplete Data
- Iterative Hessian sketch: Fast and accurate solution approximation for constrained least-squares
- Travel time tomography with adaptive dictionaries