# Auto-Linear Phenomenon in Subsurface Imaging

arXiv: https://arxiv.org/abs/2305.13314 · HTML: https://mlsanity.com/paper/2305.13314/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 27 Apr 2023.

## Builds on (most cited first, 9 of 9)

- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Sim-to-Real via Sim-to-Sim: Data-efficient Robotic Grasping via Randomized-to-Canonical Adaptation Networks](https://mlsanity.com/paper/1812.07252/) (2018)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [InversionNet: A Real-Time and Accurate Full Waveform Inversion with CNNs and continuous CRFs](https://mlsanity.com/paper/1811.07875/) (2018)
- [OpenFWI: Large-Scale Multi-Structural Benchmark Datasets for Seismic Full Waveform Inversion](https://mlsanity.com/paper/2111.02926/) (2021)
- [Unsupervised Learning of Full-Waveform Inversion: Connecting CNN and Partial Differential Equation in a Loop](https://mlsanity.com/paper/2110.07584/) (2021)
- [An Intriguing Property of Geophysics Inversion](https://mlsanity.com/paper/2204.13731/) (2022)

## Built on by (most cited first, 6 of 6)

- [A Unified Framework for Forward and Inverse Problems in Subsurface Imaging using Latent Space Translations](https://mlsanity.com/paper/2410.11247/) (2024)
- [Edge-InversionNet: Enabling Efficient Inference of InversionNet on Edge Devices](https://mlsanity.com/paper/2310.09667/) (2023)
- [Survey of Deep Learning and Physics-Based Approaches in Computational Wave Imaging](https://mlsanity.com/paper/2410.08329/) (2024)
- [On a Hidden Property in Computational Imaging](https://mlsanity.com/paper/2410.08498/) (2024)
- [Improving Full Waveform Inversion in Large Model Era](https://mlsanity.com/paper/2603.00377/) (2026)
- [IQ-JEPA: A Joint-Embedding Predictive Architecture with a Hermitian Vision Transformer for Sound Speed and Attenuation Estimation from Ultrasound IQ Data](https://mlsanity.com/paper/2607.22351/) (2026)

## Abstract (arXiv)

Subsurface imaging involves solving full waveform inversion (FWI) to predict geophysical properties from measurements. This problem can be reframed as an image-to-image translation, with the usual approach being to train an encoder-decoder network using paired data from two domains: geophysical property and measurement. A recent seminal work (InvLINT) demonstrates there is only a linear mapping between the latent spaces of the two domains, and the decoder requires paired data for training. This paper extends this direction by demonstrating that only linear mapping necessitates paired data, while both the encoder and decoder can be learned from their respective domains through self-supervised learning. This unveils an intriguing phenomenon (named Auto-Linear) where the self-learned features of two separate domains are automatically linearly correlated. Compared with existing methods, our Auto-Linear has four advantages: (a) solving both forward and inverse modeling simultaneously, (b) applicable to different subsurface imaging tasks and achieving markedly better results than previous methods, (c)enhanced performance, especially in scenarios with limited paired data and in the presence of noisy data, and (d) strong generalization ability of the trained encoder and decoder.