# Deep Preconditioners and their application to seismic wavefield processing

arXiv: https://arxiv.org/abs/2207.09938 · HTML: https://mlsanity.com/paper/2207.09938/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 81 references that are in the map.
- First posted on arXiv 20 Jul 2022.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Self-supervised Learning: Generative or Contrastive](https://mlsanity.com/paper/2006.08218/) (2020)
- [Improving Unsupervised Defect Segmentation by Applying Structural Similarity to Autoencoders](https://mlsanity.com/paper/1807.02011/) (2018)
- [Super-Convergence: Very Fast Training of Neural Networks Using Large Learning Rates](https://mlsanity.com/paper/1708.07120/) (2017)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [NETT: Solving Inverse Problems with Deep Neural Networks](https://mlsanity.com/paper/1803.00092/) (2018)
- [Deep-learning inversion: a next generation seismic velocity-model building method](https://mlsanity.com/paper/1902.06267/) (2019)
- [Stochastic seismic waveform inversion using generative adversarial networks as a geological prior](https://mlsanity.com/paper/1806.03720/) (2018)
- [MLReal: Bridging the gap between training on synthetic data and real data applications in machine learning](https://mlsanity.com/paper/2109.05294/) (2021)
- [Interpolation and Denoising of Seismic Data using Convolutional Neural Networks](https://mlsanity.com/paper/1901.07927/) (2019)
- [Semi-supervised Learning for Acoustic Impedance Inversion](https://mlsanity.com/paper/1905.13412/) (2019)
- [A hybrid approach to seismic deblending: when physics meets self-supervision](https://mlsanity.com/paper/2205.15395/) (2022)
- [Seismic data denoising and deblending using deep learning](https://mlsanity.com/paper/1907.01497/) (2019)
- [Sparse aNETT for Solving Inverse Problems with Deep Learning](https://mlsanity.com/paper/2004.09565/) (2020)
- [Anti-Aliasing Add-On for Deep Prior Seismic Data Interpolation](https://mlsanity.com/paper/2101.11361/) (2021)

## Abstract (arXiv)

Seismic data processing heavily relies on the solution of physics-driven inverse problems. In the presence of unfavourable data acquisition conditions (e.g., regular or irregular coarse sampling of sources and/or receivers), the underlying inverse problem becomes very ill-posed and prior information is required to obtain a satisfactory solution. Sparsity-promoting inversion, coupled with fixed-basis sparsifying transforms, represent the go-to approach for many processing tasks due to its simplicity of implementation and proven successful application in a variety of acquisition scenarios. Leveraging the ability of deep neural networks to find compact representations of complex, multi-dimensional vector spaces, we propose to train an AutoEncoder network to learn a direct mapping between the input seismic data and a representative latent manifold. The trained decoder is subsequently used as a nonlinear preconditioner for the physics-driven inverse problem at hand. Synthetic and field data are presented for a variety of seismic processing tasks and the proposed nonlinear, learned transformations are shown to outperform fixed-basis transforms and convergence faster to the sought solution.