Survey of Deep Learning Methods for Inverse Problems

TL;DR

This survey compares deep learning strategies for inverse problems, analyzing their robustness across different problem types and identifying the most effective approach for each scenario.

Contribution

It classifies deep learning solutions into three categories, evaluates their robustness through extensive experiments, and recommends the most robust method per inverse problem class.

Findings

Robustness varies with problem type and presence of measurement outliers.

Deep Regularizer methods are most effective for image denoising.

Data Consistency Optimizer performs best in inverse rendering.

Abstract

In this paper we investigate a variety of deep learning strategies for solving inverse problems. We classify existing deep learning solutions for inverse problems into three categories of Direct Mapping, Data Consistency Optimizer, and Deep Regularizer. We choose a sample of each inverse problem type, so as to compare the robustness of the three categories, and report a statistical analysis of their differences. We perform extensive experiments on the classic problem of linear regression and three well-known inverse problems in computer vision, namely image denoising, 3D human face inverse rendering, and object tracking, selected as representative prototypes for each class of inverse problems. The overall results and the statistical analyses show that the solution categories have a robustness behaviour dependent on the type of inverse problem domain, and specifically dependent on whether or not the problem includes measurement outliers. Based on our experimental results, we conclude by proposing the most robust solution category for each inverse problem class.