Variational Inference for Computational Imaging Inverse Problems

2019/04/12 by Francesco Tonolini, Jack Radford, Tonolini, Francesco +7
Computer Science · Engineering · Physics and Astronomy · #Advanced X-ray Imaging Techniques #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques

paper · doi:10.48550/arxiv.1904.06264

openalex publication_date 2019/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be trained, which in imaging applications implicates prohibitively expensive collections with specific imaging instruments. This paper introduces a novel framework to train variational inference for inverse problems exploiting in combination few experimentally collected data, domain expertise and existing image data sets. In such a way, Bayesian machine learning models can solve imaging inverse problems with minimal data collection efforts. Extensive simulated experiments show the advantages of the proposed framework. The approach is then applied to two real experimental optics settings: holographic image reconstruction and imaging through highly scattering media. In both settings, state of the art reconstructions are achieved with little collection of training data.

Citations

• Auto-Encoding Variational Bayes
• Phase Retrieval with Application to Optical Imaging: A contemporary overview
• A Framework for Validation of Computer Models
• Improved total variation-based CT image reconstruction applied to clinical data
• Stable signal recovery from incomplete and inaccurate measurements
• Generative Adversarial Text to Image Synthesis
• Conditional Image Synthesis With Auxiliary Classifier GANs
• Compressed Sensing using Generative Models
• Deep Generative Adversarial Networks for Compressed Sensing Automates MRI
• Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization
• Probabilistic Residual Learning for Aleatoric Uncertainty in Image\n Restoration
• Learning Multiple Layers of Features from Tiny Images

Related

• Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview
• On the Quantification of Image Reconstruction Uncertainty without Training Data
• Quantifying Model Uncertainty in Inverse Problems via Bayesian Deep Gradient Descent
• Learning from small data sets: Patch-based regularizers in inverse problems for image reconstruction
• Learning from small data sets: Patch-based regularizers in inverse problems for image reconstruction