Inverse Problems in the field of Seismic Imaging have at least two distinctive features: their size, both in terms of data and model space, and their strongly ill posed nature (and hence uncertainty in the resulting parameter estimates).
In the light of these considerations, it is possible to notice how many geophysical applications could benefit from the joint use of signal processing and machine learning paradigms. Indeed, the availability of huge datasets enables the use of data-driven approaches and not only model-based analysis, which helps the scientists relaxing strong assumptions on the physical phenomena under evaluation.
Moreover, training of Convolutional Neural Networks (CNNs) is typically carried out through iterative cost-function minimization. This means we are experiencing an increasing availability of frameworks optimised for minimizing complex cost functions, which can be exploited in a signal processing fashion.
As a matter of fact, we can use CNNs to solve minimization problems turning their overfitting downside into an asset. This means, rather than using the amount of available data for generalizing the application scenarios, specialize a specific architecture to the analysis of a single image.
With the right cost function, the architecture becomes an operator for any specific task (e.g. deblurring, migration, interpolation) and the training step can be interpreted as an estimation of parameters for a huge filtering operation (i.e., which is the best filter that fits a specific data observation).
This thesis aims at evaluating machine learning paradigms in those signal processing and imaging applications where the underlying physics is of crucial importance, such as geophysical exploration.
In particular, it will improve over state of the art by focusing on: the agnosticism of the learning paradigm, in order to generalize from the training data; preprocessing that has been proven to be crucial for fitting the network computation capabilities; and finally how to embed physical constraints into the loss functions and the architecture design choices.
The proposed approaches will be proven also on real-world data for ensuring a strong practical impact of the project outcome.