Visual Intelligence Online Seminar #68: Solving geophysical inverse problems with measurement-guided diffusion models
Presented by Matteo Ravasi, Senior Research Advisor at Shearwater GeoServices
Geophysicists have long recognized the importance of quantifying the uncertainty associated with geophysical inverse problems, whether they are used for processing, imaging, or parameter estimation purposes. The inability to create representative prior and proposal distributions, and therefore realistic posterior samples, has hindered the widespread adoption of acceptance-rejection algorithms, such as those from the family of Monte-Carlo Markov Chain methods.
In this talk, Matteo Ravasi will present a solution that promises to solve such a hurdle by leveraging the power of the latest (and greatest) generative models, namely diffusion models. More specifically, Ravasi considers two sampling algorithms recently proposed under the name of Diffusion Posterior Sampling (DPS) and Pseudo-inverse Guided Diffusion Model (PGDM).
When: 30th January, 1:00 PM - 2:00 PM CET
Where: Online (sign-up link)
Geophysicists have long recognized the importance of quantifying the uncertainty associated with geophysical inverse problems, whether they are used for processing, imaging, or parameter estimation purposes. The inability to create representative prior and proposal distributions (and therefore realistic posterior samples) has, however, hindered the widespread adoption of acceptance-rejection algorithms, such as those from the family of Monte-Carlo Markov Chain methods. In this talk, I present a solution that promises to solve such a hurdle by leveraging the power of the latest (and greatest) generative models, namely diffusion models. More specifically, I consider two sampling algorithms recently proposed under the name of Diffusion Posterior Sampling (DPS) and Pseudo-inverse Guided Diffusion Model (PGDM), respectively. In DSP, the guidance term used at each step of the reverse diffusion process is obtained by applying the adjoint of the modeling operator to the residual obtained from a one-step denoising estimate of the solution. On the other hand, PGDM utilizes a pseudo-inverse operator that originates from the fact that the one-step denoised solution is not assumed to be deterministic, rather modeled as a Gaussian distribution. Through an extensive set of numerical examples on two very different geophysical inverse problems (namely, seismic interpolation and seismic inversion), I show that two key aspects for the success of any measurement-guided diffusion process are: i) our ability to re-parametrize the inverse problem such that the sought after model is bounded between -1 and 1 (a pre-requisite for any diffusion model); ii) the choice of the training dataset used to learn the implicit prior that guides the reverse diffusion process. Numerical examples on synthetic and field datasets also reveal that PGDM outperforms DPS in both scenarios at limited additional cost
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