On a Hidden Property in Computational Imaging

TL;DR

This paper reveals a shared hidden property in the latent spaces of different computational imaging inverse problems, showing that they follow the same underlying equations despite different physical modalities.

Contribution

It uncovers a universal latent space property across FWI, CT, and EM inversion, linking their solutions through common mathematical structures.

Findings

Latent spaces of FWI, CT, and EM inversion share a one-way wave equation structure.

Different modalities have linearly correlated initial conditions in the latent space.

The shared property is consistent across multiple computational imaging problems.

Abstract

Computational imaging plays a vital role in various scientific and medical applications, such as Full Waveform Inversion (FWI), Computed Tomography (CT), and Electromagnetic (EM) inversion. These methods address inverse problems by reconstructing physical properties (e.g., the acoustic velocity map in FWI) from measurement data (e.g., seismic waveform data in FWI), where both modalities are governed by complex mathematical equations. In this paper, we empirically demonstrate that despite their differing governing equations, three inverse problems (FWI, CT, and EM inversion) share a hidden property within their latent spaces. Specifically, using FWI as an example, we show that both modalities (the velocity map and seismic waveform data) follow the same set of one-way wave equations in the latent space, yet have distinct initial conditions that are linearly correlated. This suggests that after projection into the latent embedding space, the two modalities correspond to different solutions of the same equation, connected through their initial conditions. Our experiments confirm that this hidden property is consistent across all three imaging problems, providing a novel perspective for understanding these computational imaging tasks.