Multi-scale Convolutional Neural Networks for Inverse Problems

TL;DR

This paper introduces a novel multi-scale convolutional neural network architecture that efficiently solves various inverse image problems across domains, enabling statistical solutions through big data rather than explicit mathematical inversion.

Contribution

The paper presents a new neural network design that converges quickly and generalizes across inverse problems, shifting focus from reconstruction methods to what can be reconstructed.

Findings

Effective at phase prediction from intensity data

Successful in imaging objects from diffused reflections

Denoising of electron microscopy images

Abstract

Inverse problems exist in many domains such as phase imaging, image processing, and computer vision. These problems are often solved with application-specific algorithms, even though their nature remains the same: mapping input image(s) to output image(s). Deep convolutional neural networks have shown great potential for highly variable tasks across many image-based domains, but are usually difficult to train due to their inner high non-linearities. We propose a novel neural network architecture highlighting fast convergence as a generic solution addressing image(s)-to-image(s) inverse problems of different domains. Here we show that this approach is effective at predicting phases from direct intensity measurements, imaging objects from diffused reflections and denoising scanning transmission electron microscopy images, with just different training datasets. This opens a way to solve problems statistically through big data, in contrast to implementing explicit inversion algorithms from their mathematical formulas. Previous works have targeted much more on \textit{how} can we reconstruct rather than \textit{what} can be reconstructed. Our strategy offers a paradigm shift.