Learned imaging with constraints and uncertainty quantification
This work addresses imaging challenges in domains like geophysics or medical imaging by combining deep learning with traditional constraints, though it appears incremental as it builds on existing frameworks.
The paper tackles the problem of wave-based least-squares imaging by integrating deep convolutional neural networks with handcrafted constraints to leverage their ability to generate natural images, resulting in a method based on expectation-maximization that estimates network parameters through maximum-likelihood estimation.
We outline new approaches to incorporate ideas from deep learning into wave-based least-squares imaging. The aim, and main contribution of this work, is the combination of handcrafted constraints with deep convolutional neural networks, as a way to harness their remarkable ease of generating natural images. The mathematical basis underlying our method is the expectation-maximization framework, where data are divided in batches and coupled to additional "latent" unknowns. These unknowns are pairs of elements from the original unknown space (but now coupled to a specific data batch) and network inputs. In this setting, the neural network controls the similarity between these additional parameters, acting as a "center" variable. The resulting problem amounts to a maximum-likelihood estimation of the network parameters when the augmented data model is marginalized over the latent variables.