Matthew King-Roskamp (McGill University)

Title: Incorporating data into the maximum entropy to the mean framework for Image processing

Abstract: Ill-posed linear inverse problems are of fundamental interest in a wide array of mathematical, physical, and machine learning applications. For many image recovery applications one can enforce solution regularity via prior, problem specific, knowledge. One such method is via the principle of maximum entropy to the mean, which solves a high-level distribution valued problem to denoise and deblur images. This framework has seen recent success in the realm of blind barcode deblurring and other structured image classes.

While the current literature of maximum entropy has both rich theoretical justification and recovery guarantees, there has not yet been any work to incorporate data-driven priors into this regime, in the flavor of classical machine learning approaches. By constructing priors from data, one can boost the performance of this method, while maintaining error bounds. This is a key requirement for applications in fields such as medical imaging, where failure cases must be well understood.

References:

• The maximum entropy on the mean for image deblurring. Rioux, Choksi, Hoheisel et. al. ( https://arxiv.org/abs/2002.10434 )
• Maximum entropy on the mean and the Cramer rate function in statistical estimation and inverse problems. Vaisbord et el. ( https://arxiv.org/abs/2211.05205 )