Talk by Patrick Putzky

You are all cordially invited to the AMLab colloquium coming Tuesday May 3 at 16:00 in C3.163, where Patrick Putzky will give a talk titled “Neural Networks for estimation in inverse problems”. Afterwards there are drinks and snacks!

Abstract: Many statistical problems arising in the natural sciences can be treated as an inverse problem: Measurements are transformed, subsampled or noisy observations of a quantity of interest. The main task is to infer the quantity of interest from the measurements.

Inverse problems are challenging because they are typically ill-posed. For example, if the number of variables in the quantity of interest exceeds the number observed variables, there is no unique solution to the inverse problem. To constrain the solution space the inverse problem is often phrased in terms of Bayes’ theorem. This allows to inject prior knowledge about the quantity of interest into the inference procedure. In practice, however, priors are often chosen to be overly simple (1) with respect to the complexity of the data, and (2) due to limitations in the inference procedure.

To overcome these limitations we propose an inference method which prevents the explicit notion of a prior. Instead, we suggest a neural network architecture which learns an inverse model for a given inference task. This approach has been frequently adressed before to solve problems such as image denoising, image deconvolution or image superresolution. However, the notion of the forward model has been mostly ignored in these approaches.

Our approach builds on previous neural network approaches for learning inverse models while explicitly making use of the forward model. The result is an iterative model which draws inspiration from gradient based inference methods. Our approach enables for learning a task specific inference model that has – compared to the traditional approach – the potential to (1) model complex data more reliably and (2) perform more efficiently in time critical tasks.

In the talk I will use the deconvolution problem in radio astronomy as a running example of an inverse problem, and on simulated data I will demonstrate how our approach compares to more traditional approaches. As a second example I will show some results for image superresolution.